Expressions: Difference between revisions

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It is possible to define properties using mathematical expressions. From the GUI, spin boxes or input fields that are bound to properties contain a blue icon [[Image:Sketcher_Expressions.png|32px]]. Clicking on the icon or typing the equal sign {{KEY|&#61;}} brings up the expression editor for that particular property.
It is possible to define properties using mathematical expressions. In the GUI, spin boxes or input fields that are bound to properties contain a blue icon [[Image:Bound-expression.svg|24px]]. Clicking on the icon or typing the equal sign {{KEY|&#61;}} brings up the expression editor for that particular property.


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A FreeCAD expression is a mathematical expression following notation for the standard mathematical operators and functions as described below. In addition, the expression may reference other properties, and also use conditionals. Numbers in an expression may have an optional unit attached to them.
A FreeCAD expression is a mathematical expression using the standard mathematical [[#Supported_operators|operators]], [[#Supported_functions|functions]] and [[#Supported_constants|predefined constants]] as described below. In addition, the expression may reference object properties, and also use [[#Conditional_expressions|conditionals]]. Numbers in an expression may have an optional [[#Units|unit]] attached to them.


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Numbers may use either a comma ',' or a decimal point '.' separating whole digits from decimals.
Numbers may use either a comma {{incode|,}} or a decimal point {{incode|.}} to separate whole digits from decimals. When the decimal marker is used, it ''must'' be followed by at least one digit. Thus, the expressions {{incode|1. + 2.}} and {{incode|1, + 2,}} are invalid, but {{incode|1.0 + 2.0}} and {{incode|1,0 + 2,0}} are valid.
When the decimal marker is used, it ''must'' be followed by at least one digit.
Thus, the expressions '''1.+2.''' and '''1,+2,''' are invalid, but '''1.0 + 2.0''' and '''1,0 + 2,0''' are valid.


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Operators and functions are unit-aware, and require valid combinations of units, if supplied. For example, '''2mm + 4mm''' is a valid expression, while '''2mm + 4''' is not (the reason for this is that an expression like '''1in + 4''' will most likely be interpreted as '''1in + 4in''' by humans, but all units are converted to the SI system internally, and the system is not able to guess this). These [[#Units|units]] are currently recognized.
Operators and functions are unit-aware, and require valid combinations of units, if supplied. For example, {{incode|2mm + 4mm}} is a valid expression, while {{incode|2mm + 4}} is not. This also applies to references to object properties that have units, such as Length properties. Thus {{incode|Pad001.Length + 1}} is invalid since it adds a pure number to a property with length units, it requires {{incode|Pad001.Length + 1mm}}.


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Some unit related errors can seem unintuitive, with expressions either being rejected or producing results that do not match the units of the property being set. Here are some examples:
You can use [[#Supported Constants|predefined constants]] and [[#Supported Functions|functions]].

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{{incode|1/2mm}} is not interpreted as half a millimeter but as {{incode|1/(2mm)}}, resulting in: {{incode|0.5 mm^-1}}.

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{{incode|sqrt(2)mm}} is not valid because the function call is not a number. This has to be entered as {{incode|sqrt(2) * 1mm}}.

===Function arguments=== <!--T:97-->

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Multiple arguments to a function may be separated by either a semicolon {{incode|;}} or a comma <em>followed by a space</em> {{incode|, }}. In the latter case, the comma is converted to a semicolon after entry. When a semicolon is used, no trailing space is necessary.

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Arguments may include references to cells in a spreadsheet. A cell reference consists of the cell's uppercase row letter followed by its column number, for example {{incode|A1}}. A cell may also be referenced by using the cell's alias instead, for example {{incode|Spreadsheet.MyPartWidth}}.


===Referencing objects=== <!--T:69-->
===Referencing objects=== <!--T:69-->


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You can reference to an object by its {{incode|Name}} or by its {{incode|Label}}. In the case of a {{incode|Label}}, it must be enclosed in double {{incode|<<}} and {{incode|>>}} symbols, such as {{incode|<<Label>>}}.
As already shown above, you can reference an object by its {{PropertyData|Name}}. But you can also use its {{PropertyData|Label}}. In the case of a {{PropertyData|Label}}, it must be enclosed in double {{incode|<<}} and {{incode|>>}} symbols, such as {{incode|<<Label>>}}.


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You can reference any numerical property of this object. For example, to refer to a Cylinder's height, you may use {{incode|Cylinder.Height}} or {{incode|<<Long_name_of_cylinder>>.Height}}.
You can reference any property of an object. For example, to reference a Cylinder's height, you may use {{incode|Cylinder.Height}} or {{incode|<<Label_of_cylinder>>.Height}}.

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To reference list objects, the syntax is {{incode|<<object_label>>.list[list_index]}} or {{incode|object_name.list[list_index]}}. If you want for example reference a constraint in a sketch, do it this way '''<<MySketch>>.Constraints[16]'''. If you are in the same sketch you can omit its name and just use '''Constraints[16]'''.<br/>
'''Note:''' The index starts with 0, therefore constraint 17 has the index 16.


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For more info about referencing objects, see [[#Reference To CAD-Data|this section]].
For more information about referencing objects, see [[#Reference_to_CAD_data|Reference to CAD data]].


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== Supported constants == <!--T:58-->

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The following constants are supported:

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{| class="wikitable"
!style="width: 33%;"|Constant
!style="width: 66%;"|Description
|-
| style="text-align:center;" | '''e'''
| [https://en.wikipedia.org/wiki/E_(mathematical_constant) Euler's number]
|-
| style="text-align:center;" | '''pi'''
| [https://en.wikipedia.org/wiki/Pi Pi]
|}

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== Supported operators == <!--T:96-->

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The following operators are supported:
The following operators are supported:

{| class="wikitable float-right mw-collapsible mw-uncollapsed"
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{| class="wikitable"
!style="width: 33%;"|Operator
!style="width: 33%;"|Operator
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 63: Line 95:
|}
|}


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==Supported Constants== <!--T:58-->


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== Supported functions == <!--T:5-->
The following constants are supported:
{| class="wikitable float-right mw-collapsible mw-uncollapsed"
!style="width: 33%;"|Constant
!style="width: 66%;"|Description
|-
| style="text-align:center;" | '''e'''
| [https://en.wikipedia.org/wiki/E_(mathematical_constant) Euler's number]
|-
| style="text-align:center;" | '''pi'''
| [https://en.wikipedia.org/wiki/Pi Pi]
|}


== Supported Functions == <!--T:5-->
=== General mathematical functions === <!--T:55-->


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=== General Mathematical Functions === <!--T:55-->
The following mathematical functions are supported:


==== Trigonometric functions ==== <!--T:160-->
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The mathematical functions listed below are available.


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[https://en.wikipedia.org/wiki/Trigonometric_functions Trigonometric functions] use degree as their default unit. For radians add {{incode|rad}} following the <em>first</em> value in an expression. So e.g. {{incode|cos(45)}} is the same as {{incode|cos(pi rad / 4)}}. Expressions in degrees can use either {{incode|deg}} or {{incode|°}}, e.g. {{incode|360deg - atan2(3; 4)}} or {{incode|360&deg; - atan2(3; 4)}}. If an expression is without units and needs to be converted to degrees or radians for compatibility, multiply by {{incode|1deg}}, {{incode|1°}} or {{incode|1rad}} as appropriate, e.g. {{incode|(360 - X) * 1deg}}; {{incode|(360 - X) * 1°}}; {{incode|(0.5 + pi / 2) * 1rad}}.
Multiple arguments to a function may be separated by either a semicolon ';' or a comma <em>followed by a space</em> ', '. In the latter case, the comma is converted to a semicolon after entry. When a semicolon is used, no trailing space is necessary.


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{| class="wikitable"
[https://en.wikipedia.org/wiki/Trigonometric_functions Trigonometric functions] use degree as their default unit. For radian measure, add '''rad''' following the <em>first</em> value in an expression. So e.g. '''cos(45)''' is the same as '''cos(pi rad / 4)'''. Expressions in degrees can use either '''deg''' or '''°''', e.g. '''360deg - atan2(3; 4)''' or '''360&deg; - atan2(3; 4)'''. If an expression is without units and needs to be converted to degrees or radians for compatibility, multiply by '''1&nbsp;deg''', '''1&nbsp;°''' or '''1&nbsp;rad''' as appropriate, e.g. '''(360 - X) * 1deg'''; '''(360 - X) * 1°'''; '''(0.5 + pi / 2) * 1rad'''. <br/>
!style="width: 15%;"|Function
These trigonometric functions are supported:
!style="width: 55%;"|Description
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Function
!style="width: 30%;"|Input range
!style="width: 33%;"|Description
!style="width: 33%;"|Value range
|-
|-
| acos(x)
| {{incode|acos(x)}}
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc cosine]
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc cosine]
| -1 <= x <= 1
| -1 <= x <= 1
|-
|-
| asin(x)
| {{incode|asin(x)}}
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc sine]
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc sine]
| -1 <= x <= 1
| -1 <= x <= 1
|-
|-
| atan(x)
| {{incode|atan(x)}}
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc tangent]
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc tangent], return value in the range -90° < value < 90°
| all
| all
|-
|-
| atan2(x, y)
| {{incode|atan2(y; x)}}
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc tangent] of ''x/y''
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc tangent] of ''y/x'' accounting for quadrant, return value in the range -180° < value <= 180°
| all, except y = 0
| all, the invalid input x = y = 0 returns 0
|-
|-
| cos(x)
| {{incode|cos(x)}}
| [https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions Cosine]
| [https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions Cosine]
| all
| all
|-
|-
| cosh(x)
| {{incode|cosh(x)}}
| [https://en.wikipedia.org/wiki/Hyperbolic_function#Trigonometric_definitions Hyperbolic cosine]
| [https://en.wikipedia.org/wiki/Hyperbolic_function#Trigonometric_definitions Hyperbolic cosine]
| all
| all
|-
|-
| sin(x)
| {{incode|sin(x)}}
| [https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions Sine]
| [https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions Sine]
| all
| all
|-
|-
| sinh(x)
| {{incode|sinh(x)}}
| [https://en.wikipedia.org/wiki/Hyperbolic_function#Trigonometric_definitions Hyperbolic sine]
| [https://en.wikipedia.org/wiki/Hyperbolic_function#Trigonometric_definitions Hyperbolic sine]
| all
| all
|-
|-
| tan(x)
| {{incode|tan(x)}}
| [https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions Tangent]
| [https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions Tangent]
| all, except of x = n·90 with n = integer
| all, except x = n*90 with n = odd integer
|-
|-
| tanh(x)
| {{incode|tanh(x)}}
| [https://en.wikipedia.org/wiki/Hyperbolic_function#Trigonometric_definitions Hyperbolic tangent]
| [https://en.wikipedia.org/wiki/Hyperbolic_function#Trigonometric_definitions Hyperbolic tangent]
| all
| all
|-
| {{incode|hypot(x; y)}}
| [https://en.wikipedia.org/wiki/Pythagorean_addition Pythagorean addition] ('''hypot'''enuse), e.g. hypot(4; 3) = 5
| x and y >= 0
|-
| {{incode|cath(x; y)}}
| Given hypotenuse, and one side, returns other side of triangle, e.g. cath(5; 3) = 4
| x >= y >= 0
|}
|}

==== Exponential and logarithmic functions ==== <!--T:162-->


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{| class="wikitable"
These functions for exponentiation and logarithmization are supported:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Function
!style="width: 33%;"|Function
!style="width: 33%;"|Description
!style="width: 33%;"|Description
!style="width: 33%;"|Value range
!style="width: 33%;"|Input range
|-
|-
| exp(x)
| {{incode|exp(x)}}
| [https://en.wikipedia.org/wiki/Exponential_function#Formal_definition Exponential function]
| [https://en.wikipedia.org/wiki/Exponential_function#Formal_definition Exponential function]
| all
| all
|-
|-
| log(x)
| {{incode|log(x)}}
| [https://en.wikipedia.org/wiki/Natural_logarithm Natural logarithm]
| [https://en.wikipedia.org/wiki/Natural_logarithm Natural logarithm]
| x > 0
| x > 0
|-
|-
| log10(x)
| {{incode|log10(x)}}
| [https://en.wikipedia.org/wiki/Common_logarithm Common logarithm]
| [https://en.wikipedia.org/wiki/Common_logarithm Common logarithm]
| x > 0
| x > 0
|-
|-
| pow(x, y)
| {{incode|pow(x; y)}}
| [https://en.wikipedia.org/wiki/Exponentiation Exponentiation]
| [https://en.wikipedia.org/wiki/Exponentiation Exponentiation]
| all
| all
|-
|-
| sqrt(x)
| {{incode|sqrt(x)}}
| [https://en.wikipedia.org/wiki/Square_root Square root]
| [https://en.wikipedia.org/wiki/Square_root Square root]
| x >= 0
| x >= 0
|-
| {{incode|cbrt(x)}} {{Version|0.21}}
| [https://en.wikipedia.org/wiki/Cube_root Cubic root]
| all
|}
|}

==== Rounding, truncation and remainder functions ==== <!--T:163-->


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{| class="wikitable"
These functions for rounding, truncation and remainder are supported:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 20%;"|Function
!style="width: 20%;"|Function
!style="width: 55%;"|Description
!style="width: 55%;"|Description
!style="width: 25%;"|Value range
!style="width: 25%;"|Input range
|-
|-
| abs(x)
| {{incode|abs(x)}}
| [https://en.wikipedia.org/wiki/Absolute_value Absolute value]
| [https://en.wikipedia.org/wiki/Absolute_value Absolute value]
| all
| all
|-
|-
| ceil(x)
| {{incode|ceil(x)}}
| [https://en.wikipedia.org/wiki/Floor_and_ceiling_functions Ceiling function] smallest integer value greater than or equal to x
| [https://en.wikipedia.org/wiki/Floor_and_ceiling_functions Ceiling function], smallest integer value greater than or equal to x
| all
| all
|-
|-
| floor(x)
| {{incode|floor(x)}}
| [https://en.wikipedia.org/wiki/Floor_and_ceiling_functions Floor function], largest integer value less than or equal to x
| [https://en.wikipedia.org/wiki/Floor_and_ceiling_functions Floor function], largest integer value less than or equal to x
| all
| all
|-
|-
| mod(x, y)
| {{incode|mod(x; y)}}
| [https://en.wikipedia.org/wiki/Remainder Remainder] after dividing ''x'' by ''y''
| [https://en.wikipedia.org/wiki/Remainder Remainder] after dividing ''x'' by ''y'', sign of result is that of the dividend.
| all, except y = 0
| all, except y = 0
|-
|-
| round(x)
| {{incode|round(x)}}
| [https://en.wikipedia.org/wiki/Rounding Rounding] to the nearest integer
| [https://en.wikipedia.org/wiki/Rounding Rounding] to the nearest integer
| all
| all
|-
|-
| trunc(x)
| {{incode|trunc(x)}}
| [https://en.wikipedia.org/wiki/Truncation Truncation] to the nearest integer
| [https://en.wikipedia.org/wiki/Truncation Truncation] to the nearest integer in the direction of zero
| all
| all
|}
|}


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=== Statistical / Aggregate Functions === <!--T:8-->

[https://en.wikipedia.org/wiki/Aggregate_function Aggregate functions] take one or more arguments, separated by a semicolon ';' or a comma ''and'' a space ', '.<br/>
=== Statistical / aggregate functions === <!--T:99-->
Arguments may include references to cells in a spreadsheet. Cell references consist of the (CAPITAL) row letter followed by the column number.<br/>

Arguments may include ranges of cells (two cell references separated by a colon), for example '''average(B1:B8)'''.
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[https://en.wikipedia.org/wiki/Aggregate_function Aggregate functions] take one or more arguments.<br>

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Individual arguments to aggregate functions may consist of ranges of cells. A range of cells is expressed as two cell references separated by a colon {{Incode|:}}, for example {{Incode|average(B1:B8)}} or {{Incode|sum(A1:A4; B1:B4)}}.
The cell references may also use cell aliases, for example {{Incode|average(StartTemp:EndTemp)}}.

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The following aggregate functions are supported:


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{| class="wikitable"
These aggregate functions are supported:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 20%;"|Function
!style="width: 20%;"|Function
!style="width: 55%;"|Description
!style="width: 55%;"|Description
!style="width: 25%;"|Value range
!style="width: 25%;"|Input range
|-
|-
| average(x:y)
| {{incode|average(a; b; c; ...)}}
| [https://en.wikipedia.org/wiki/Arithmetic_mean Arithmetic mean] of values in cells x through y; sum(x:y) / count(x:y)
| [https://en.wikipedia.org/wiki/Arithmetic_mean Average] value of the arguments, same as sum(a; b; c; ...) / count(a; b; c; ...)
| all
| all
|-
|-
| count(x:y)
| {{incode|count(a; b; c; ...)}}
| [https://en.wikipedia.org/wiki/Counting Counting] of cells from x through y
| [https://en.wikipedia.org/wiki/Counting Count] of the arguments, typically used for cell ranges
| all
| all
|-
|-
| max(x:y)
| {{incode|max(a; b; c; ...)}}
| [https://en.wikipedia.org/wiki/Maxima_and_minima Maximum] value in cells x through y
| [https://en.wikipedia.org/wiki/Maxima_and_minima Maximum] value of the arguments
| all
| all
|-
|-
| min(x:y)
| {{incode|min(a; b; c; ...)}}
| [https://en.wikipedia.org/wiki/Maxima_and_minima Minimum] value in cells x through y
| [https://en.wikipedia.org/wiki/Maxima_and_minima Minimum] value of the arguments
| all
| all
|-
|-
| stddev(x:y)
| {{incode|stddev(a; b; c; ...)}}
| [https://en.wikipedia.org/wiki/Standard_deviation Standard deviation] of values in cells x through y
| [https://en.wikipedia.org/wiki/standard_deviation Standard deviation] of the values of the arguments
| all
| all
|-
|-
| sum(x: y)
| {{incode|sum(a; b; c; ...)}}
| [https://en.wikipedia.org/wiki/Summation Sum] of values in cells x through y
| [https://en.wikipedia.org/wiki/Summation Sum] of the values of the arguments, typically used for cell ranges
| all
| all
|}
|}


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== Conditional Expressions == <!--T:32-->

=== String manipulation === <!--T:101-->

==== String identification ==== <!--T:102-->

<!--T:103-->
Strings are identified in expressions by surrounding them with opening/closing double chevrons (as are labels).

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In following example, "TEXT" is recognized as a string : {{incode|<<TEXT>>}}

==== String concatenation ==== <!--T:105-->

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Strings can be concatenated using the '+' sign.

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Following example {{incode|<<MY>> + <<TEXT>>}} will be concatenated to "MYTEXT".

==== String conversion ==== <!--T:180-->

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Numerical values can be converted to strings with the {{incode|str}} function:

</translate>
{{incode|str(Box.Length.Value)}}
<translate>

==== String formatting ==== <!--T:108-->

<!--T:109-->
String formatting is supported using the (old) %-style Python way.

<!--T:110-->
All %-specifiers as defined in [https://docs.python.org/3/library/stdtypes.html#printf-style-string-formatting Python documentation].

<!--T:111-->
As an example, supposing you have a default 10mm-side cube named 'Box' (default FreeCAD naming), the following expression {{incode|<<Cube length : %s>> % Box.Length}} will expand to "Cube length : 10.0 mm"

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For more than one %-specifier use the following syntax: {{incode|<<Cube length is %s and width is %s>> % tuple(Box.Length; Box.Width)}}. Or use concatenation: {{incode|<<Cube length is %s>> % Box.Length + << and width is %s>> % Box.Width}}. Both will expand to "Cube length is 10.0 mm and width is 10.0 mm".

<!--T:113-->
A FreeCAD sample file using string formatting is available [https://forum.freecadweb.org/viewtopic.php?f=8&t=58657 in the forum]

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=== Object creation functions === <!--T:116-->

<!--T:117-->
The following objects may be created in expressions using the following functions:

<!--T:193-->
{| class="wikitable"
! Type
! Function
! Description
|-
| {{incode|Tuple}}
| {{incode|tuple(a; b; ...)}}
| Example: {{incode|tuple(2; 1; 2)}}
|-
| {{incode|List}}
| {{incode|list(a; b; ...)}}
| Example: {{incode|list(2; 1; 2)}}
|-
| rowspan="2" | [[Vector API|{{incode|Vector}}]]
| {{incode|vector(x; y; z)}}
| rowspan="2" | Create a vector using three unit-less or {{incode|Length}} unit values.
Example: {{incode|vector(2; 1; 3)}}
|-
| {{incode|create(<<vector>>; x; y; z)}}
|-
| rowspan="2" | [[Matrix API|{{incode|Matrix}}]]
|
matrix(
a<sub>11</sub>; a<sub>12</sub>; a<sub>13</sub>; a<sub>14</sub>;
a<sub>21</sub>; a<sub>22</sub>; a<sub>23</sub>; a<sub>24</sub>;
a<sub>31</sub>; a<sub>32</sub>; a<sub>33</sub>; a<sub>34</sub>;
a<sub>41</sub>; a<sub>42</sub>; a<sub>43</sub>; a<sub>44</sub>
)
| rowspan="2" | Create a 4x4 matrix in [https://en.wikipedia.org/wiki/Row-_and_column-major_order row-major order]:
<math>
\begin{bmatrix}
a_{11} & a_{12} & a_{13} & a_{14} \\
a_{21} & a_{22} & a_{23} & a_{24} \\
a_{31} & a_{32} & a_{33} & a_{34} \\
a_{41} & a_{42} & a_{43} & a_{44} \\
\end{bmatrix}
</math>

<!--T:194-->
A minimum of 1 argument can be supplied such as {{incode|matrix(1)}} which creates an identity matrix.

<!--T:195-->
Example: {{incode|matrix(1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16)}}
|-
| {{incode|create(<<matrix>>; a<sub>11</sub>; a<sub>12</sub>; ...; a<sub>44</sub>)}}
|-
| rowspan="4" | {{incode|Rotation}}
| {{incode|rotation(axis; angle)}}
| rowspan="4" | Create a {{incode|Rotation}} by specifying its {{incode|axis}} ({{incode|Vector}}) and {{incode|angle}} ({{incode|Angle}} unit or unit-less), or three Euler angles {{incode|α}}, {{incode|β}}, {{incode|γ}}.
Examples:
* {{incode|rotation(vector(0; 1; 0); 45)}}
* {{incode|create(<<rotation>>; 30; 30; 30)}}
|-
| {{incode|rotation(α; β; γ)}}
|-
| {{incode|create(<<rotation>>; axis; angle)}}
|-
| {{incode|create(<<rotation>>; α; β; γ)}}
|-
| rowspan="5" | [[Placement_API|{{incode|Placement}}]]
| {{incode|placement(base; rotation)}}
| rowspan="5" | Create a {{incode|Placement}} with various parameters, including:
* {{incode|base}}: base location ({{incode|Vector}})
* {{incode|center}}: center location ({{incode|Vector}})
* {{incode|rotation}}: {{incode|Rotation}}
* {{incode|axis}}: Rotation axis ({{incode|Vector}})
* {{incode|angle}}: Rotation angle (unit-less or {{incode|Angle}} unit value)
* {{incode|matrix}}: {{incode|Matrix}}

<!--T:196-->
Examples:
* {{incode|placement(vector(2; 1; 3); rotation(vector(0; 0; 1); 45))}}
* {{incode|create(<<placement>>; create(<<vector>>; 2; 1; 2); create(<<rotation>>; create(<<vector>>; 0; 1; 0); 45))}}
|-
| {{incode|placement(base; rotation; center)}}
|-
| {{incode|placement(base; axis; angle)}}
|-
| {{incode|placement(matrix)}}
|-
| {{incode|create(<<placement>>; ...)}}
|}

</translate>{{Top}}<translate>

=== Vector functions === <!--T:202-->

<!--T:204-->
Functions: {{Version|0.22}}.

<!--T:203-->
{| class="wikitable"
! Function / Operator
! Description
|-
| {{incode|v1 + v2}}
| Add two vectors.
|-
| {{incode|v1 - v2}}
| Subtract two vectors.
|-
| {{incode|v * s}}
| Uniformly scale a vector by {{incode|s}}.
|-
| {{incode|vangle(v1; v2)}}
| Angle between two vectors in degrees.
|-
| {{incode|vcross(v1; v2)}}
| Cross product of two vectors <math>v_1 \times v_2</math>.
|-
| {{incode|v1 * v2}}
| rowspan="2" | Dot product of two vectors <math>v_1 \cdot v_2</math>.
|-
| {{incode|vdot(v1; v2)}}
|-
| {{incode|vlinedist(v1; v2; v3)}}
| Distance between vector {{incode|v1}} and a line through {{incode|v2}} in direction {{incode|v3}}.
|-
| {{incode|vlinesegdist(v1; v2; v3)}}
| Distance between vector {{incode|v1}} and the closest point on a line segment from {{incode|v2}} to {{incode|v3}}.
|-
| {{incode|vlineproj(v1; v2; v3)}}
| Project vector {{incode|v1}} on a line through {{incode|v2}} in direction {{incode|v3}}.
|-
| {{incode|vnormalize(v)}}
| Normalize a vector to a unit vector.
|-
| {{incode|vplanedist(v1)}}
| Distance between vector {{incode|v1}} and a plane defined by a point {{incode|v2}} and a normal {{incode|v3}}.
|-
| {{incode|vplaneproj(v1)}}
| Project vector {{incode|v1}} on a plane defined by a point {{incode|v2}} and a normal {{incode|v3}}.
|-
| {{incode|vscale(v; sx; sy; sz)}}
| rowspan="4" | Non-uniformly scale a vector by {{incode|sx}} in the X direction, {{incode|sy}} in the Y direction, and {{incode|sz}} in the Z direction.
|-
| {{incode|vscalex(v; sx)}}
|-
| {{incode|vscaley(v; sy)}}
|-
| {{incode|vscalez(v; sz)}}
|}

</translate>{{Top}}<translate>

=== Matrix functions === <!--T:143-->

<!--T:197-->
{{incode|Rotation}} and {{incode|Placement}} can each be represented by a {{incode|Matrix}}. The following functions all take in a {{incode|Matrix}}, {{incode|Rotation}}, or {{incode|Placement}} as their first parameter denoted in the table below by {{incode|m}}. The type of the returned object is the same as the object supplied in the first argument except when using {{incode|mtranslate}} on a {{incode|Rotation}}, in which case a {{incode|Placement}} will be returned.

<!--T:198-->
{| class="wikitable"
! Function
! Description
|-
| {{incode|minvert(m)}}
| Calculate the [https://en.wikipedia.org/wiki/Invertible_matrix Inverse matrix].
|-
| {{incode|mrotate(m; rotation)}}
| rowspan="3" | [https://en.wikipedia.org/wiki/Transformation_matrix#Rotation_2 Rotate] by either:
* a {{incode|Rotation}}
* an axis ({{incode|Vector}}) and an angle ({{incode|Angle}} unit or unit-less)
* three Euler angles {{incode|α}}, {{incode|β}}, {{incode|γ}}
|-
| {{incode|mrotate(m; axis; angle)}}
|-
| {{incode|mrotate(m; α; β; γ)}}
|-
| {{incode|mrotatex(m; angle)}}
| [https://en.wikipedia.org/wiki/Transformation_matrix#Rotation_2 Rotate] around the X axis.
|-
| {{incode|mrotatey(m; angle)}}
| [https://en.wikipedia.org/wiki/Transformation_matrix#Rotation_2 Rotate] around the Y axis.
|-
| {{incode|mrotatez(m; angle)}}
| [https://en.wikipedia.org/wiki/Transformation_matrix#Rotation_2 Rotate] around the Z axis.
|-
| {{incode|mtranslate(m; vector)}}
| rowspan="2" | [https://en.wikipedia.org/wiki/Translation_(geometry)#Matrix_representation Translate] by a {{incode|vector}} ({{incode|Vector}}) or X, Y, Z values. If a {{incode|Rotation}} is translated, the returned object is a {{incode|Placement}}.
|-
| {{incode|mtranslate(m; x; y; z)}}
|-
| {{incode|mscale(m; vector)}}
| rowspan="2" | [https://en.wikipedia.org/wiki/Scaling_(geometry)#Matrix_representation Scale] by a {{incode|vector}} ({{incode|Vector}}) or X, Y, Z values.
|-
| {{incode|mscale(m; x; y; z)}}
|}

</translate>{{Top}}<translate>

== Conditional expressions == <!--T:32-->


<!--T:10-->
<!--T:10-->
Conditional expressions are of the form '''condition ? resultTrue : resultFalse'''. The condition is defined as an expression that evaluates to either '0' (false) or non-zero (true).
Conditional expressions are of the form {{incode|condition ? resultTrue : resultFalse}}. The condition is defined as an expression that evaluates to either {{incode|0}} (false) or non-zero (true).
Note that enclosing the conditional expression in parentheses is currently considered an error. {{VersionMinus|0.19}}


<!--T:33-->
<!--T:33-->
The following [https://en.wikipedia.org/wiki/Relational_operator#Standard_relational_operators relational operators] are defined:
The following [https://en.wikipedia.org/wiki/Relational_operator#Standard_relational_operators relational operators] are defined:
{| class="wikitable float-right mw-collapsible mw-uncollapsed"
{| class="wikitable"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 264: Line 548:
| less than or equal to
| less than or equal to
|}
|}

</translate>{{Top}}<translate>


== Units == <!--T:34-->
== Units == <!--T:34-->


<!--T:35-->
<!--T:35-->
Units can directly be used in expressions. The parser connects them to the previous value. So ''''2mm'''' or ''''2 mm'''' is valid while '''' mm'''' is invalid because there is no preceding value.
Units can be used directly in expressions. The parser connects them to the previous value. So {{incode|2mm}} or {{incode|2 mm}} is valid while {{incode|mm}} is invalid because there is no preceding value.


<!--T:56-->
<!--T:56-->
All values must have a unit. Therefore you must in general use a unit for values in spreadsheets.<br/>
All values must have a unit. Therefore you must in general use a unit for values in spreadsheets.<br/>
In some cases it works even without a unit, for example if you have e.g. in spreadsheet cell B1 just the number ''1.5'' and refer to it for a pad height. This only works because the pad height predefines the unit ''mm'' that is used if no unit is given. It will nevertheless fail if you use for the pad height e.g. '''Sketch1.Constraints.Width - Spreadsheet.B1''' because ''Sketch1.Constraints.Width'' has a unit and ''Spreadsheet.B1'' has not.
In some cases it works even without a unit, for example if you have e.g. in spreadsheet cell B1 just the number {{incode|1.5}} and refer to it for a pad height. This only works because the pad height predefines the unit {{incode|mm}} that is used if no unit is given. It will nevertheless fail if you use for the pad height e.g. {{incode|Sketch1.Constraints.Width - Spreadsheet.B1}} because {{incode|Sketch1.Constraints.Width}} has a unit and {{incode|Spreadsheet.B1}} has not.


<!--T:57-->
<!--T:57-->
Units with exponents can directly be entered. So e.g. '''mm^3''' will be recognized as mm³ and '''m^3''' will be recognized as m³.
Units with exponents can directly be entered. So e.g. {{incode|mm^3}} will be recognized as mm³ and {{incode|m^3}} will be recognized as m³.


<!--T:36-->
<!--T:36-->
If you have a variable with a name of a unit you must put the variable into '''<< >>''' to prevent that it will be recognized as unit. For example if you have the dimension ''''Sketch.Constraints.A'''' it would be recognized as unit ampere. Therefore you must write it in the expression as ''''Sketch.Constraints.<<A>>''''.
If you have a variable whose name is that of a unit you must put the variable between {{incode|<< >>}} to prevent it from being recognized as a unit. For example if you have the dimension {{incode|Sketch.Constraints.A}} it would be recognized as the unit ampere. Therefore you must write it in the expression as {{incode|Sketch.Constraints.<<A>>}}.


<!--T:37-->
<!--T:37-->
The following units are recognized by the expression parser:
The following units are recognized by the expression parser:

=== Amount of substance === <!--T:165-->


<!--T:38-->
<!--T:38-->
{| class="wikitable mw-collapsible mw-collapsed"
Amount of substance:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 295: Line 582:
| [https://en.wikipedia.org/wiki/Mole_(unit) Mole]
| [https://en.wikipedia.org/wiki/Mole_(unit) Mole]
|}
|}

=== Angle === <!--T:166-->


<!--T:39-->
<!--T:39-->
{| class="wikitable mw-collapsible mw-collapsed"
Angle:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| °
| °
| [https://en.wikipedia.org/wiki/Degree_(angle) Degree]; alternative to the unit ''deg''
| [https://en.wikipedia.org/wiki/Degree_(angle) Degree]; alternative to the unit deg
|-
|-
| deg
| deg
| [https://en.wikipedia.org/wiki/Degree_(angle) Degree]; alternative to the unit ''°''
| [https://en.wikipedia.org/wiki/Degree_(angle) Degree]; alternative to the unit °
|-
|-
| rad
| rad
Line 315: Line 603:
|-
|-
| S
| S
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Second of arc]
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Second of arc]; alternative to the unit ″
|-
|-
| ″
| ″
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Second of arc]; alternative to the unit ''S''
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Second of arc]; alternative to the unit S
|-
|-
| M
| M
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Minute of arc]
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Minute of arc]; alternative to the unit ′
|-
|-
| ′
| ′
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Minute of arc]; alternative to the unit ''M''
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Minute of arc]; alternative to the unit M
|}
|}

=== Current === <!--T:167-->


<!--T:40-->
<!--T:40-->
{| class="wikitable mw-collapsible mw-collapsed"
Current:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 345: Line 634:
| Mega[https://en.wikipedia.org/wiki/Ampere ampere]
| Mega[https://en.wikipedia.org/wiki/Ampere ampere]
|}
|}

=== Electric capacitance === <!--T:183-->


<!--T:75-->
<!--T:75-->
{| class="wikitable mw-collapsible mw-collapsed"
Electrical Capacitance:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| pF
| pF
| Pico[https://en.wikipedia.org/wiki/Farad farad], {{Version|0.19}}
| Pico[https://en.wikipedia.org/wiki/Farad farad]
|-
|-
| nF
| nF
| Nano[https://en.wikipedia.org/wiki/Farad farad], {{Version|0.19}}
| Nano[https://en.wikipedia.org/wiki/Farad farad]
|-
|-
| uF
| uF
| Micro[https://en.wikipedia.org/wiki/Farad farad]; alternative to the unit ''µF'', {{Version|0.19}}
| Micro[https://en.wikipedia.org/wiki/Farad farad]; alternative to the unit µF
|-
|-
| µF
| µF
| Micro[https://en.wikipedia.org/wiki/Farad farad]; alternative to the unit ''uF'', {{Version|0.19}}
| Micro[https://en.wikipedia.org/wiki/Farad farad]; alternative to the unit uF
|-
|-
| mF
| mF
| Milli[https://en.wikipedia.org/wiki/Farad farad], {{Version|0.19}}
| Milli[https://en.wikipedia.org/wiki/Farad farad]
|-
|-
| F
| F
| [https://en.wikipedia.org/wiki/Farad Farad]; 1 F = 1 s^4·A^2/m^2/kg, {{Version|0.19}}
| [https://en.wikipedia.org/wiki/Farad Farad]; 1 F = 1 s^4·A^2/m^2/kg
|}
|}


<!--T:79-->
=== Electric charge === <!--T:184-->

Electrical Conductance:
<!--T:73-->
{| class="wikitable float-right mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
|-
| C
| [https://en.wikipedia.org/wiki/Coulomb Coulomb]; 1 C = 1 A*s
|}

=== Electric conductivity === <!--T:185-->

<!--T:186-->
{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| uS
| uS
| Micro[https://en.wikipedia.org/wiki/Siemens_(unit) siemens]; alternative to the unit ''µS'', {{Version|0.19}}
| Micro[https://en.wikipedia.org/wiki/Siemens_(unit) siemens]; alternative to the unit µS
|-
|-
| µS
| µS
| Micro[https://en.wikipedia.org/wiki/Siemens_(unit) siemens]; alternative to the unit ''uS'', {{Version|0.19}}
| Micro[https://en.wikipedia.org/wiki/Siemens_(unit) siemens]; alternative to the unit uS
|-
|-
| mS
| mS
| Milli[https://en.wikipedia.org/wiki/Siemens_(unit) siemens], {{Version|0.19}}
| Milli[https://en.wikipedia.org/wiki/Siemens_(unit) siemens]
|-
|-
| S
| S
| [https://en.wikipedia.org/wiki/Siemens_(unit) Siemens]; 1 S = 1 s^3·A^2/kg/m^2, {{Version|0.19}}
| [https://en.wikipedia.org/wiki/Siemens_(unit) Siemens]; 1 S = 1 s^3·A^2/kg/m^2
|-
| kS
| Kilo[https://en.wikipedia.org/wiki/Siemens_(unit) Siemens]
|-
| MS
| Mega[https://en.wikipedia.org/wiki/Siemens_(unit) Siemens]
|}
|}

=== Electric inductance === <!--T:187-->


<!--T:76-->
<!--T:76-->
{| class="wikitable mw-collapsible mw-collapsed"
Electrical Inductance:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| nH
| nH
| Nano[https://en.wikipedia.org/wiki/Henry_(unit) henry], {{Version|0.19}}
| Nano[https://en.wikipedia.org/wiki/Henry_(unit) henry]
|-
|-
| uH
| uH
| Micro[https://en.wikipedia.org/wiki/Henry_(unit) henry]; alternative to the unit ''µH'', {{Version|0.19}}
| Micro[https://en.wikipedia.org/wiki/Henry_(unit) henry]; alternative to the unit µH
|-
|-
| µH
| µH
| Micro[https://en.wikipedia.org/wiki/Henry_(unit) henry]; alternative to the unit ''uH'', {{Version|0.19}}
| Micro[https://en.wikipedia.org/wiki/Henry_(unit) henry]; alternative to the unit uH
|-
|-
| mH
| mH
| Milli[https://en.wikipedia.org/wiki/Henry_(unit) henry], {{Version|0.19}}
| Milli[https://en.wikipedia.org/wiki/Henry_(unit) henry]
|-
|-
| H
| H
| [https://en.wikipedia.org/wiki/Henry_(unit) Henry]; 1 H = 1 kg·m^2/s^2/A^2, {{Version|0.19}}
| [https://en.wikipedia.org/wiki/Henry_(unit) Henry]; 1 H = 1 kg·m^2/s^2/A^2
|}
|}


<!--T:80-->
=== Electric potential === <!--T:188-->
Electrical Resistance:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
|-
| Ohm
| [https://en.wikipedia.org/wiki/Ohm Ohm]; 1 Ohm = 1 kg·m^2/s^3/A^2, {{Version|0.19}}
|-
| kOhm
| Kilo[https://en.wikipedia.org/wiki/Ohm ohm], {{Version|0.19}}
|-
| MOhm
| Mega[https://en.wikipedia.org/wiki/Ohm ohm], {{Version|0.19}}
|}

<!--T:73-->
Electric Charge:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
|-
| C
| [https://en.wikipedia.org/wiki/Coulomb Coulomb]; 1 C = 1 A·s, {{Version|0.19}}
|}


<!--T:74-->
<!--T:74-->
{| class="wikitable mw-collapsible mw-collapsed"
Electric Potential:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 453: Line 737:
| Kilo[https://en.wikipedia.org/wiki/Volt volt]
| Kilo[https://en.wikipedia.org/wiki/Volt volt]
|}
|}

=== Electric resistance === <!--T:189-->

<!--T:80-->
{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
|-
| Ohm
| [https://en.wikipedia.org/wiki/Ohm Ohm]; 1 Ohm = 1 kg·m^2/s^3/A^2
|-
| kOhm
| Kilo[https://en.wikipedia.org/wiki/Ohm ohm]
|-
| MOhm
| Mega[https://en.wikipedia.org/wiki/Ohm ohm]
|}

=== Energy/work === <!--T:168-->


<!--T:41-->
<!--T:41-->
Energy / Work:
{| class="wikitable float-right mw-collapsible mw-collapsed"
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
Line 467: Line 769:
|-
|-
| kJ
| kJ
| Kilo[https://en.wikipedia.org/wiki/Joule joule], {{Version|0.19}}
| Kilo[https://en.wikipedia.org/wiki/Joule joule]
|-
|-
| eV
| eV
| [https://en.wikipedia.org/wiki/Electronvolt Electronvolt]; 1 ev = 1.602176634e-19 J, {{Version|0.19}}
| [https://en.wikipedia.org/wiki/Electronvolt Electronvolt]; 1 eV = 1.602176634e-19 J
|-
|-
| keV
| keV
| Kilo[https://en.wikipedia.org/wiki/Electronvolt electronvolt], {{Version|0.19}}
| Kilo[https://en.wikipedia.org/wiki/Electronvolt electronvolt]
|-
|-
| MeV
| MeV
| Mega[https://en.wikipedia.org/wiki/Electronvolt electronvolt], {{Version|0.19}}
| Mega[https://en.wikipedia.org/wiki/Electronvolt electronvolt]
|-
|-
| kWh
| kWh
| [https://en.wikipedia.org/wiki/Kilowatt_hour Kilowatt hour]; 1 kWh = 3.6e6 J, {{Version|0.19}}
| [https://en.wikipedia.org/wiki/Kilowatt_hour Kilowatt hour]; 1 kWh = 3.6e6 J
|-
|-
| Ws
| Ws
| [https://en.wikipedia.org/wiki/Joule#Watt_second Watt second]; alternative to the unit ''Joule''
| [https://en.wikipedia.org/wiki/Joule#Watt_second Watt second]; alternative to the unit Joule
|-
|-
| VAs
| VAs
| [https://en.wikipedia.org/wiki/Joule Volt-ampere-second]; alternative to the unit ''Joule''
| [https://en.wikipedia.org/wiki/Joule Volt-ampere-second]; alternative to the unit Joule
|-
|-
| CV
| CV
| [https://en.wikipedia.org/wiki/Joule Coulomb-volt]; alternative to the unit ''Joule''
| [https://en.wikipedia.org/wiki/Joule Coulomb-volt]; alternative to the unit Joule
|-
|-
| cal
| cal
| [https://en.wikipedia.org/wiki/Calorie Calorie]; 1 cal = 4.184 J, {{Version|0.19}}
| [https://en.wikipedia.org/wiki/Calorie Calorie]; 1 cal = 4.184 J
|-
|-
| kcal
| kcal
| Kilo[https://en.wikipedia.org/wiki/Calorie calorie], {{Version|0.19}}
| Kilo[https://en.wikipedia.org/wiki/Calorie calorie]
|}
|}

=== Force === <!--T:169-->


<!--T:42-->
<!--T:42-->
{| class="wikitable mw-collapsible mw-collapsed"
Force:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 518: Line 821:
| [https://en.wikipedia.org/wiki/Pound_(force) Pound of force]
| [https://en.wikipedia.org/wiki/Pound_(force) Pound of force]
|}
|}

=== Length === <!--T:170-->


<!--T:43-->
<!--T:43-->
{| class="wikitable mw-collapsible mw-collapsed"
Length:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 529: Line 833:
|-
|-
| um
| um
| Micro[https://en.wikipedia.org/wiki/Metre meter]; alternative to the unit ''µm''
| Micro[https://en.wikipedia.org/wiki/Metre meter]; alternative to the unit µm
|-
|-
| µm
| µm
| Micro[https://en.wikipedia.org/wiki/Metre meter]; alternative to the unit ''mu''
| Micro[https://en.wikipedia.org/wiki/Metre meter]; alternative to the unit um
|-
|-
| mm
| mm
Line 539: Line 843:
| cm
| cm
| Centi[https://en.wikipedia.org/wiki/Metre meter]
| Centi[https://en.wikipedia.org/wiki/Metre meter]
|-
| mm
| Milli[https://en.wikipedia.org/wiki/Metre meter]
|-
|-
| dm
| dm
Line 553: Line 854:
|-
|-
| mil
| mil
| [https://en.wikipedia.org/wiki/Thousandth_of_an_inch Thousandth of an inch]; alternative to the unit ''thou''
| [https://en.wikipedia.org/wiki/Thousandth_of_an_inch Thousandth of an inch]; alternative to the unit thou
|-
|-
| thou
| thou
| [https://en.wikipedia.org/wiki/Thousandth_of_an_inch Thousandth of an inch]; alternative to the unit ''mil''
| [https://en.wikipedia.org/wiki/Thousandth_of_an_inch Thousandth of an inch]; alternative to the unit mil
|-
|-
| in
| in
| [https://en.wikipedia.org/wiki/Inch Inch]
| [https://en.wikipedia.org/wiki/Inch Inch]; alternative to the unit "
|-
| "
| [https://en.wikipedia.org/wiki/Inch Inch]; alternative to the unit in
|-
|-
| ft
| ft
Line 565: Line 869:
|-
|-
| '
| '
| [https://en.wikipedia.org/wiki/Foot_(unit) Foot]; alternative to the unit ''ft''
| [https://en.wikipedia.org/wiki/Foot_(unit) Foot]; alternative to the unit ft
|-
|-
| yd
| yd
Line 573: Line 877:
| [https://en.wikipedia.org/wiki/Mile Mile]
| [https://en.wikipedia.org/wiki/Mile Mile]
|}
|}

=== Luminous intensity === <!--T:171-->


<!--T:44-->
<!--T:44-->
{| class="wikitable mw-collapsible mw-collapsed"
Luminous Intensity:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 584: Line 889:
|}
|}


<!--T:81-->
=== Magnetic flux === <!--T:190-->
Magnetic Field Strength:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
|-
| Oe
| [https://en.wikipedia.org/wiki/Oersted Oersted]; 1 Oe = 79.57747 A/m, {{Version|0.19}}
|}


<!--T:82-->
<!--T:82-->
{| class="wikitable mw-collapsible mw-collapsed"
Magnetic Flux:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| Wb
| Wb
| [https://en.wikipedia.org/wiki/Weber_(unit) Weber]; 1 Wb = 1 kg*m^2/s^2/A, {{Version|0.19}}
| [https://en.wikipedia.org/wiki/Weber_(unit) Weber]; 1 Wb = 1 kg*m^2/s^2/A
|}
|}

=== Magnetic flux density === <!--T:191-->


<!--T:77-->
<!--T:77-->
{| class="wikitable mw-collapsible mw-collapsed"
Magnetic Flux Density:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| G
| G
| [https://en.wikipedia.org/wiki/Gauss_(unit) Gauss]; 1 G = 1 e-4 T, {{Version|0.19}}
| [https://en.wikipedia.org/wiki/Gauss_(unit) Gauss]; 1 G = 1 e-4 T
|-
|-
| T
| T
| [https://en.wikipedia.org/wiki/Tesla_(unit) Tesla]; 1 T = 1 kg/s^2/A, {{Version|0.19}}
| [https://en.wikipedia.org/wiki/Tesla_(unit) Tesla]; 1 T = 1 kg/s^2/A
|}
|}

=== Mass === <!--T:172-->


<!--T:45-->
<!--T:45-->
{| class="wikitable mw-collapsible mw-collapsed"
Mass:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| ug
| ug
| Micro[https://en.wikipedia.org/wiki/Gram gram]; alternative to the unit ''µg''
| Micro[https://en.wikipedia.org/wiki/Gram gram]; alternative to the unit µg
|-
|-
| µg
| µg
| Micro[https://en.wikipedia.org/wiki/Gram gram]; alternative to the unit ''ug''
| Micro[https://en.wikipedia.org/wiki/Gram gram]; alternative to the unit ug
|-
|-
| mg
| mg
Line 645: Line 943:
|-
|-
| lb
| lb
| [https://en.wikipedia.org/wiki/Pound_(mass) Pound]; alternative to the unit ''lbm''
| [https://en.wikipedia.org/wiki/Pound_(mass) Pound]; alternative to the unit lbm
|-
|-
| lbm
| lbm
| [https://en.wikipedia.org/wiki/Pound_(mass) Pound]; alternative to the unit ''lb''
| [https://en.wikipedia.org/wiki/Pound_(mass) Pound]; alternative to the unit lb
|-
|-
| st
| st
Line 656: Line 954:
| [https://en.wikipedia.org/wiki/Hundredweight Hundredweight]
| [https://en.wikipedia.org/wiki/Hundredweight Hundredweight]
|}
|}

=== Power === <!--T:173-->


<!--T:61-->
<!--T:61-->
{| class="wikitable mw-collapsible mw-collapsed"
Power:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 667: Line 966:
|-
|-
| kW
| kW
| Kilo[https://en.wikipedia.org/wiki/Watt watt], {{Version|0.19}}
| Kilo[https://en.wikipedia.org/wiki/Watt watt]
|-
| VA
| [https://en.wikipedia.org/wiki/Volt-ampere Volt-ampere]
|}
|}

=== Pressure === <!--T:174-->


<!--T:46-->
<!--T:46-->
{| class="wikitable mw-collapsible mw-collapsed"
Pressure:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 690: Line 987:
| GPa
| GPa
| Giga[https://en.wikipedia.org/wiki/Pascal_(unit) pascal]
| Giga[https://en.wikipedia.org/wiki/Pascal_(unit) pascal]
|-
| mbar
| Milli[https://en.wikipedia.org/wiki/Bar_(unit) Bar], {{Version|0.19}}
|-
| bar
| [https://en.wikipedia.org/wiki/Bar_(unit) Bar], {{Version|0.19}}
|-
|-
| uTorr
| uTorr
| Micro[https://en.wikipedia.org/wiki/Torr torr]; alternative to the unit ''µTorr''
| Micro[https://en.wikipedia.org/wiki/Torr torr]; alternative to the unit µTorr
|-
|-
| µTorr
| µTorr
| Micro[https://en.wikipedia.org/wiki/Torr torr]; alternative to the unit ''uTorr''
| Micro[https://en.wikipedia.org/wiki/Torr torr]; alternative to the unit uTorr
|-
|-
| mTorr
| mTorr
Line 714: Line 1,005:
| ksi
| ksi
| Kilo[https://en.wikipedia.org/wiki/Pounds_per_square_inch pound-force per square inch]
| Kilo[https://en.wikipedia.org/wiki/Pounds_per_square_inch pound-force per square inch]
|-
| Mpsi
| Mega[https://en.wikipedia.org/wiki/Pounds_per_square_inch pound-force per square inch], {{Version|0.19}}
|}
|}

=== Temperature === <!--T:175-->


<!--T:47-->
<!--T:47-->
{| class="wikitable mw-collapsible mw-collapsed"
Temperature:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| uK
| uK
| Micro[https://en.wikipedia.org/wiki/Kelvin kelvin]; alternative to the unit ''µK''
| Micro[https://en.wikipedia.org/wiki/Kelvin kelvin]; alternative to the unit µK
|-
|-
| µK
| µK
| Micro[https://en.wikipedia.org/wiki/Kelvin kelvin]; alternative to the unit ''uK''
| Micro[https://en.wikipedia.org/wiki/Kelvin kelvin]; alternative to the unit uK
|-
|-
| mK
| mK
Line 737: Line 1,026:
| [https://en.wikipedia.org/wiki/Kelvin Kelvin]
| [https://en.wikipedia.org/wiki/Kelvin Kelvin]
|}
|}

=== Time === <!--T:176-->


<!--T:48-->
<!--T:48-->
{| class="wikitable mw-collapsible mw-collapsed"
Time:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 754: Line 1,044:
|-
|-
| Hz (1/s)
| Hz (1/s)
| [https://en.wikipedia.org/wiki/Hertz Hertz], {{Version|0.19}}
| [https://en.wikipedia.org/wiki/Hertz Hertz]
|-
|-
| kHz
| kHz
| Kilo[https://en.wikipedia.org/wiki/Hertz hertz], {{Version|0.19}}
| Kilo[https://en.wikipedia.org/wiki/Hertz hertz],
|-
|-
| MHz
| MHz
| Mega[https://en.wikipedia.org/wiki/Hertz hertz], {{Version|0.19}}
| Mega[https://en.wikipedia.org/wiki/Hertz hertz]
|-
|-
| GHz
| GHz
| Giga[https://en.wikipedia.org/wiki/Hertz hertz], {{Version|0.19}}
| Giga[https://en.wikipedia.org/wiki/Hertz hertz]
|-
|-
| THz
| THz
| Tera[https://en.wikipedia.org/wiki/Hertz hertz], {{Version|0.19}}
| Tera[https://en.wikipedia.org/wiki/Hertz hertz]
|}
|}


<!--T:49-->
=== Volume === <!--T:177-->
Torque:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
|-
| Nm
| [https://en.wikipedia.org/wiki/Newton_metre Newton metre]
|}


<!--T:50-->
<!--T:50-->
{| class="wikitable mw-collapsible mw-collapsed"
Volume:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| ml
| ml
| Milli[https://en.wikipedia.org/wiki/Litre liter], {{Version|0.19}}
| Milli[https://en.wikipedia.org/wiki/Litre liter]
|-
|-
| l
| l
Line 792: Line 1,073:
|-
|-
| cft
| cft
| Cubic[https://en.wikipedia.org/wiki/Foot_(unit) foot], {{Version|0.19}}
| Cubic[https://en.wikipedia.org/wiki/Foot_(unit) foot]
|}
|}

=== Special imperial units === <!--T:192-->


<!--T:78-->
<!--T:78-->
{| class="wikitable mw-collapsible mw-collapsed"
Special imperial units:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| mph
| mph
| [https://en.wikipedia.org/wiki/Miles_per_hour Miles per hour], {{Version|0.19}}
| [https://en.wikipedia.org/wiki/Miles_per_hour Miles per hour]
|-
|-
| sqft
| sqft
| [https://en.wikipedia.org/wiki/Square_foot Square foot], {{Version|0.19}}
| [https://en.wikipedia.org/wiki/Square_foot Square foot]
|}
|}

=== Unsupported units === <!--T:178-->

<!--T:179-->
The following commonly used units are not yet supported, for some an alternative is provided:


<!--T:51-->
<!--T:51-->
{| class="wikitable mw-collapsible mw-collapsed"
The following commonly used units are not yet supported:
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 25%;"|Unit
!style="width: 25%;"|Unit
!style="width: 50%;"|Description
!style="width: 50%;"|Description
Line 824: Line 1,110:
|-
|-
| u
| u
| [https://en.wikipedia.org/wiki/Unified_atomic_mass_unit Atomic mass unit]; alternative to the unit 'Da'
| [https://en.wikipedia.org/wiki/Unified_atomic_mass_unit Atomic mass unit]; alternative to the unit Da
| 1.66053906660e-27 kg
| 1.66053906660e-27 kg
|-
|-
| Da
| Da
| [https://en.wikipedia.org/wiki/Unified_atomic_mass_unit Dalton]; alternative to the unit 'u'
| [https://en.wikipedia.org/wiki/Unified_atomic_mass_unit Dalton]; alternative to the unit u
| 1.66053906660e-27 kg
| 1.66053906660e-27 kg
|-
|-
Line 848: Line 1,134:
|}
|}


</translate>{{Top}}<translate>
==Invalid Characters and Names==


==Invalid characters and names== <!--T:85-->

<!--T:86-->
The expression feature is very powerful but to achieve this power it has some limitations concerning some characters. To overcome this, FreeCAD offers to use labels and reference them instead of the object names. In labels you can use almost all special characters.
The expression feature is very powerful but to achieve this power it has some limitations concerning some characters. To overcome this, FreeCAD offers to use labels and reference them instead of the object names. In labels you can use almost all special characters.


<!--T:87-->
In cases where you cannot use a label, like for example the name of a sketch constraints, you must be aware what characters are not allowed.
In cases where you cannot use a label, such as the name of a sketch's constraints, you must be aware what characters are not allowed.


===Labels===
===Labels=== <!--T:88-->


<!--T:89-->
For labels there are no invalid characters, only some characters needs to be escaped when they are references:
For [[Object_name#Label|labels]] there are no invalid characters, however some characters need to be escaped:
{| class="wikitable float-right mw-collapsible mw-uncollapsed"
{| class="wikitable"
!style="width: 33%;"|Characters
!style="width: 33%;"|Characters
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| {{incode|'}}, {{incode|\}}, {{incode|"}}
| style="text-align:center;" | ''' ' ''', '''\'''
| They need to be escaped by adding '''\''' in front of them.</br>For example label ''Sketch\002'' must be referenced as ''<Sketch\\002>''
| Need to be escaped by adding {{incode|\}} in front of them.
|}
|}


<!--T:90-->
===Names===
For example, the label {{incode|Sketch\002}} must be referenced as {{incode|<<Sketch\\002>>}}.


===Names=== <!--T:91-->
Names of objects like dimensions, sketches etc. may not have the characters listed below. They may also not be equal to a unit.


<!--T:92-->
For example this is possible: '''<<Sketch>>.Constraints.T2üßµ@'''</br>while this is invalid:
[[Object_name#Name|Names]] of objects like dimensions, sketches, etc. may not have the characters or character sequences listed below, otherwise the name is invalid:
'''<<Sketch>>.Constraints.test\result_2''' or '''<<Sketch>>.Constraints.mol'''


<!--T:93-->
The following characters in names are invalid:
{| class="wikitable float-right mw-collapsible mw-uncollapsed"
{| class="wikitable"
!style="width: 33%;"|Characters
!style="width: 33%;"|Characters / Character sequences
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| style="text-align:center;" | '''+''', '''-''', '''*''', '''/''', '''^''', '''_''', '''°''', '''<''', '''>''', '''(''', ''')''', '''{''', '''}''', '''[''', ''']''', '''.''', ''',''', '''='''
| '''+''', '''-''', '''*''', '''/''', '''^''', '''_''', '''<''', '''>''', '''(''', ''')''', '''{''', '''}''', '''[''', ''']''', '''.''', ''',''', '''='''
| Characters that are math operators or units or part of mathematical constructs
| Characters that are math operators or part of mathematical constructs
|-
| '''A''', '''kA''', '''mA''', '''MA''', '''J''', '''K''', ''' ' ''', ''' ft ''', '''°''', and many more!
| Characters and character sequences that are units (see the [[#Units|Units]] paragraph)
|-
|-
| style="text-align:center;" | '''#''', '''!''', '''?''', '''§''', '''$''', '''%''', '''&''', ''':''', ''';''', '''\''', '''|''', '''~'''
| '''#''', '''!''', '''?''', '''§''', '''$''', '''%''', '''&''', ''':''', ''';''', '''\''', '''<nowiki>|</nowiki>''', '''~''', '''∆''', '''¿''', and many more!
| Characters used as placeholder or to trigger special operations
| Characters used as placeholder or to trigger special operations
|-
|-
| style="text-align:center;" | '''´''', '''`''', ''' ' ''', '''"'''
| '''pi''', '''e'''
| Mathematical constants
|-
| '''´''', '''`''', ''' ' ''', '''"'''
| Characters used for accents
| Characters used for accents
|-
|-
| space
| style="text-align:center;" | space
| A space define the end of a name and can therefore not be used
| A space defines the end of a name and can therefore not be used
|}
|}


== Reference To CAD-Data == <!--T:12-->
<!--T:95-->
For example, the following name is valid: {{incode|<<Sketch>>.Constraints.T2üßµ@}}. While these are invalid names: {{incode|<<Sketch>>.Constraints.test\result_2}} (\r means "carriage return") or {{incode|<<Sketch>>.Constraints.mol}} (mol is a unit).

<!--T:94-->
Since shorter names (especially if they have only one or two characters) can easily result in invalid names, consider using longer names and/or establishing a suitable naming convention.

===Cell aliases=== <!--T:114-->

<!--T:182-->
See [[Spreadsheet_SetAlias#Usage|Spreadsheet SetAlias]].

</translate>{{Top}}<translate>

== Reference to CAD data == <!--T:12-->


<!--T:13-->
<!--T:13-->
It is possible to use data from the model itself in an expression. To reference a property use "object.property". If the property is a compound of fields, the individual fields can be accessed as "object.property.field".
It is possible to use data from the model itself in an expression. To reference a property use {{incode|object_name.property}} or {{incode|<<object_label>>.property}}, labels must be enclosed in {{incode|<<}} and {{incode|>>}}. If you want to use labels they must be unique.

<!--T:205-->
All next examples reference the object by its name, but in all cases the object label can also be used.

<!--T:206-->
If the property is a compound of fields, the individual fields can be accessed as {{incode|object_name.property.field}}.

<!--T:71-->
To reference list objects use {{incode|object_name.list[list_index]}}. If you want to reference a constraint in a sketch, use {{incode|Sketch.Constraints[16]}}. If you are in the same sketch you may omit its name and just use {{incode|Constraints[16]}}. Note that the index starts with 0, therefore Constraint17 has to be referenced as {{incode|Constraints[16]}}.

<!--T:207-->
To reference the object itself use the {{incode|_self}} pseudo property: {{incode|object_name._self}}.


<!--T:14-->
<!--T:14-->
The following table shows some examples:
The following table shows some more examples:
{| class="wikitable"
{|{{Prettytable}}
!CAD-Data
!CAD data
!Call in expression
!Call in expression
!Result
!Result
|-
|-
|Parametric Length of a Part-Workbench Cube
|Length of a [[Part_Box|Part Box]]
|{{incode|Cube.Length}}
|{{incode|Box.Length}}
|{{incode|Length}} with units mm
|Length with units (mm)
|-
|-
|Volume of the Cube
|Volume of the Box
|{{incode|Cube.Shape.Volume}}
|{{incode|Box.Shape.Volume}}
|{{incode|Volume}} in mm&sup3; without units
|Volume in mm&sup3; without units
|-
|-
|Type of the Cube-shape
|Shape type of the Box
|{{incode|Cube.Shape.ShapeType}}
|{{incode|Box.Shape.ShapeType}}
|String: Solid
|String: Solid
|-
|-
|Label of the Cube
|Label of the Box
|{{incode|Cube.Label}}
|{{incode|Box.Label}}
|String: Label
|String: Label
|-
|-
|x-coordinate of center of mass of the Cube
|X-coordinate of center of mass of the Box
|{{incode|Cube.Shape.CenterOfMass.x}}
|{{incode|Box.Shape.CenterOfMass.x}}
|x-coordinate in mm without units
|X-coordinate in mm without units
|-
|X-coordinate of the Box placement
|{{incode|Box.Placement.Base.x}}
|X-coordinate with units (mm)
|-
|X-component of the rotation axis of the Box placement
|{{incode|Box.Placement.Rotation.Axis.x}}
|X-component of the unit vector in mm without units
|-
|Rotation angle of the Box placement
|{{incode|Box.Placement.Rotation.Angle}}
|Rotation angle with units (deg)
|-
|Full Box object
|{{incode|Box._self}}
|Object of type <Part::PartFeature>
|-
|-
|Value of constraint in a sketch
|Value of constraint in a sketch
|{{incode|Constraints.Width}}
|{{incode|Constraints.Width}}
|Numeric value of the named constraint '{{incode|Width}}' in the sketch, if the expression is used in the sketch itself.
|Numeric value of the named constraint {{incode|Width}} in the sketch, if the expression is used in the sketch itself.
|-
|-
|Value of constraint in a sketch
|Value of constraint in a sketch
|{{incode|MySketch.Constraints.Width}}
|{{incode|MySketch.Constraints.Width}}
|Numeric value of the named constraint '{{incode|Width}}' in the sketch, if the expression is used outside of the sketch.
|Numeric value of the named constraint {{incode|Width}} in the sketch, if the expression is used outside of the sketch.
|-
|-
|Value of a spreadsheet alias
|Value of a spreadsheet alias
|{{incode|Spreadsheet.Depth}}
|{{incode|Spreadsheet.Depth}}
|Value of the alias "{{incode|Depth}}" in the spreadsheet "{{incode|Spreadsheet}}"
|Value of the alias {{incode|Depth}} in the spreadsheet {{incode|Spreadsheet}}
|-
|-
|Value of a local property
|Value of a local property
|{{incode|Length}}
|{{incode|Length}}
|Value of the {{incode|Length}} property in e.g a Pad object, if the expression is used in e.g Length2 in the same object.
|Value of the {{PropertyData|Length}} property in e.g a Pad object, if the expression is used in e.g {{PropertyData|Length2}} in the same object.
|}
|}

=== Cyclic dependencies === <!--T:208-->

<!--T:209-->
FreeCAD checks dependencies based on the relationship between document objects, not properties. This means that you cannot provide data to an object and query that same object for results. For example, even though there are no cyclic dependencies when the properties themselves are considered, you may not have an object which gets its dimensions from a spreadsheet and then display the volume of that object in the same spreadsheet. You have to use two spreadsheets, one to drive your model and the other for reporting.

<!--T:210-->
As a workaround it is possible to display a cell range from the second spreadsheet in the first (or vice versa) by creating a [[Spreadsheet_Workbench#Cell_binding|cell binding]] with the {{MenuCommand|Hide dependency of binding}} option.

<!--T:211-->
Another way to workaround cyclic dependencies is to hide the reference by using the {{incode|href}} or {{incode|hiddenref}} function for individual expressions, for example: {{incode|href(Box.Length)}}.

<!--T:212-->
Please note that both mentioned workarounds should be used with caution, and that they do not work if the properties that are reported depend on dimensions that are driven from the same spreadsheet.

</translate>{{Top}}<translate>


== Document-wide global variables == <!--T:15-->
== Document-wide global variables == <!--T:15-->
Line 943: Line 1,298:
<!--T:16-->
<!--T:16-->
There is no concept of global variables in FreeCAD at the moment. Instead, arbitrary variables can be defined as cells in a spreadsheet using the [[Spreadsheet Workbench|Spreadsheet workbench]], and then be given a name using the alias property for the cell (right-click on cell). Then they can be accessed from any expression just as any other object property.
There is no concept of global variables in FreeCAD at the moment. Instead, arbitrary variables can be defined as cells in a spreadsheet using the [[Spreadsheet Workbench|Spreadsheet workbench]], and then be given a name using the alias property for the cell (right-click on cell). Then they can be accessed from any expression just as any other object property.

</translate>{{Top}}<translate>


== Cross-document linking == <!--T:20-->
== Cross-document linking == <!--T:20-->


<!--T:21-->
<!--T:21-->
It is possible (with limitations) to define a Property of an object in your current document (".FCstd" file) by using an Expression to reference a Property of an object contained in a different document (".FCstd" file). For example, a cell in a spreadsheet or the Length of a Part Cube, etc. in one document can be defined by an Expression that references the X Placement value or another Property of an object contained in a different document.
It is possible (with limitations) to define a Property of an object in your current document (".FCstd" file) by using an Expression to reference a Property of an object contained in a different document (".FCstd" file). For example, a cell in a spreadsheet or the {{PropertyData|Length}} of a Part Cube, etc. in one document can be defined by an Expression that references the X Placement value or another Property of an object contained in a different document.


<!--T:22-->
<!--T:22-->
A document's name is used to reference it from other documents. When saving a document the first time, you choose a file name; this is usually different from the initial default "Unnamed1" (or its translated equivalent). To prevent links being lost when the master document is renamed upon saving, it is recommended that you first create the master document, create a spreadsheet inside it, and save it. Subsequently, you can still make changes to the file and its spreadsheet but you should not rename it.
A document's name is used to reference it from other documents. When saving a document the first time, you choose a file name; this is usually different from the initial default "Unnamed1" (or its translated equivalent). To prevent links being lost when the master document is renamed upon saving, it is recommended that you first create the master document, create a spreadsheet inside it, and save it. Subsequently, you can still make changes to the file and its spreadsheet but you should not rename it.


<!--T:23-->
<!--T:23-->
Once the master document with the spreadsheet is created and saved (named), it is safe to create dependent documents. For example, assuming you name the master document "{{incode|master}}", the spreadsheet "{{incode|modelConstants}}", and give a cell an alias-name "{{incode|Length}}", you can then access the value as:
Once the master document with the spreadsheet is created and saved (named), it is safe to create dependent documents. For example, assuming you name the master document {{incode|master}}, the spreadsheet {{incode|modelConstants}}, and give a cell an alias-name {{incode|Length}}, you can then access the value as:


</translate>
<!--T:65-->
master#modelConstants.Length
{{incode|master#modelConstants.Length}}
<translate>


<!--T:66-->
<!--T:66-->
'''Note:''' that the master document must be loaded for the values in the master to be available to the dependent document.
Note that the master document must be loaded for the values in the master to be available to the dependent document.

<!--T:24-->
Unfortunately, the integrated checker sometimes claims that a valid name doesn't exist. Continue typing anyway. When you have completed the full reference, the {{Button|OK}} button will become active.


<!--T:25-->
<!--T:25-->
Of course, it's up to you to load the corresponding documents later when you want to change anything.
Of course, it's up to you to load the corresponding documents later when you want to change anything.

</translate>{{Top}}<translate>


== Known issues / remaining tasks == <!--T:17-->
== Known issues / remaining tasks == <!--T:17-->


<!--T:18-->
<!--T:18-->
* FreeCAD does not yet have a built-in expression manager where all expressions in a document are listed, and can be created, deleted, queried, etc. But an addon is available: [https://github.com/gbroques/fcxref fcxref expression manager].
* The dependency graph is based on the relationship between document objects, not properties. This means that you cannot provide data to an object and query that same object for results. For example, even though there are no cyclic dependencies when the properties themselves are considered, you may not have an object which gets its dimensions from a spreadsheet and then display the volume of that object in the same spreadsheet. As a work-around, use multiple spreadsheets -- one to drive your model, and one for reporting.
* Open bugs/tickets for Expressions can be found on [https://github.com/FreeCAD/FreeCAD/issues?q=is%3Aissue+is%3Aopen+label%3AExpressions GitHub].
* The expression parser does not handle parentheses well, and is unable to properly parse some expressions. For example: "'''= (A1 > A2) ? 1 : 0'''" results in an error, while "'''= A1 > A2 ? 1 : 0'''" is accepted. The expression "'''= 5 + ((A1>A2) ? 1 : 0)'''" cannot be entered in any form.

* As stated above, unfortunately, the integrated checker sometimes claims that a valid name doesn't exist. Continue typing anyway. When you have completed the full reference, the {{Button|OK}} button will become active.
</translate>{{Top}}<translate>
* There is no expression manager implemented where all expressions in a document are listed, and can be created, deleted, queried, etc.

* The names of Sketcher constraints must not contain any blanks when the value is calculated by an expression, see [https://forum.freecadweb.org/viewtopic.php?p=302500#p302381; forum discussion].
* Open bugs/tickets for Expressions can be found in the [https://freecadweb.org/tracker/set_project.php?project_id=4;20 FreeCAD Bugtracker Expressions category]


</translate>
</translate>
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Latest revision as of 04:53, 9 January 2024

Overview

It is possible to define properties using mathematical expressions. In the GUI, spin boxes or input fields that are bound to properties contain a blue icon . Clicking on the icon or typing the equal sign = brings up the expression editor for that particular property.

A FreeCAD expression is a mathematical expression using the standard mathematical operators, functions and predefined constants as described below. In addition, the expression may reference object properties, and also use conditionals. Numbers in an expression may have an optional unit attached to them.

Numbers may use either a comma , or a decimal point . to separate whole digits from decimals. When the decimal marker is used, it must be followed by at least one digit. Thus, the expressions 1. + 2. and 1, + 2, are invalid, but 1.0 + 2.0 and 1,0 + 2,0 are valid.

Operators and functions are unit-aware, and require valid combinations of units, if supplied. For example, 2mm + 4mm is a valid expression, while 2mm + 4 is not. This also applies to references to object properties that have units, such as Length properties. Thus Pad001.Length + 1 is invalid since it adds a pure number to a property with length units, it requires Pad001.Length + 1mm.

Some unit related errors can seem unintuitive, with expressions either being rejected or producing results that do not match the units of the property being set. Here are some examples:

1/2mm is not interpreted as half a millimeter but as 1/(2mm), resulting in: 0.5 mm^-1.

sqrt(2)mm is not valid because the function call is not a number. This has to be entered as sqrt(2) * 1mm.

Function arguments

Multiple arguments to a function may be separated by either a semicolon ; or a comma followed by a space , . In the latter case, the comma is converted to a semicolon after entry. When a semicolon is used, no trailing space is necessary.

Arguments may include references to cells in a spreadsheet. A cell reference consists of the cell's uppercase row letter followed by its column number, for example A1. A cell may also be referenced by using the cell's alias instead, for example Spreadsheet.MyPartWidth.

Referencing objects

As already shown above, you can reference an object by its DataName. But you can also use its DataLabel. In the case of a DataLabel, it must be enclosed in double << and >> symbols, such as <<Label>>.

You can reference any property of an object. For example, to reference a Cylinder's height, you may use Cylinder.Height or <<Label_of_cylinder>>.Height.

For more information about referencing objects, see Reference to CAD data.

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Supported constants

The following constants are supported:

Constant Description
e Euler's number
pi Pi

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Supported operators

The following operators are supported:

Operator Description
+ Addition
- Subtraction
* Multiplication
/ Floating point Division
% Remainder
^ Exponentiation

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Supported functions

General mathematical functions

The following mathematical functions are supported:

Trigonometric functions

Trigonometric functions use degree as their default unit. For radians add rad following the first value in an expression. So e.g. cos(45) is the same as cos(pi rad / 4). Expressions in degrees can use either deg or °, e.g. 360deg - atan2(3; 4) or 360° - atan2(3; 4). If an expression is without units and needs to be converted to degrees or radians for compatibility, multiply by 1deg, or 1rad as appropriate, e.g. (360 - X) * 1deg; (360 - X) * 1°; (0.5 + pi / 2) * 1rad.

Function Description Input range
acos(x) Arc cosine -1 <= x <= 1
asin(x) Arc sine -1 <= x <= 1
atan(x) Arc tangent, return value in the range -90° < value < 90° all
atan2(y; x) Arc tangent of y/x accounting for quadrant, return value in the range -180° < value <= 180° all, the invalid input x = y = 0 returns 0
cos(x) Cosine all
cosh(x) Hyperbolic cosine all
sin(x) Sine all
sinh(x) Hyperbolic sine all
tan(x) Tangent all, except x = n*90 with n = odd integer
tanh(x) Hyperbolic tangent all
hypot(x; y) Pythagorean addition (hypotenuse), e.g. hypot(4; 3) = 5 x and y >= 0
cath(x; y) Given hypotenuse, and one side, returns other side of triangle, e.g. cath(5; 3) = 4 x >= y >= 0

Exponential and logarithmic functions

Function Description Input range
exp(x) Exponential function all
log(x) Natural logarithm x > 0
log10(x) Common logarithm x > 0
pow(x; y) Exponentiation all
sqrt(x) Square root x >= 0
cbrt(x) introduced in version 0.21 Cubic root all

Rounding, truncation and remainder functions

Function Description Input range
abs(x) Absolute value all
ceil(x) Ceiling function, smallest integer value greater than or equal to x all
floor(x) Floor function, largest integer value less than or equal to x all
mod(x; y) Remainder after dividing x by y, sign of result is that of the dividend. all, except y = 0
round(x) Rounding to the nearest integer all
trunc(x) Truncation to the nearest integer in the direction of zero all

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Statistical / aggregate functions

Aggregate functions take one or more arguments.

Individual arguments to aggregate functions may consist of ranges of cells. A range of cells is expressed as two cell references separated by a colon :, for example average(B1:B8) or sum(A1:A4; B1:B4). The cell references may also use cell aliases, for example average(StartTemp:EndTemp).

The following aggregate functions are supported:

Function Description Input range
average(a; b; c; ...) Average value of the arguments, same as sum(a; b; c; ...) / count(a; b; c; ...) all
count(a; b; c; ...) Count of the arguments, typically used for cell ranges all
max(a; b; c; ...) Maximum value of the arguments all
min(a; b; c; ...) Minimum value of the arguments all
stddev(a; b; c; ...) Standard deviation of the values of the arguments all
sum(a; b; c; ...) Sum of the values of the arguments, typically used for cell ranges all

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String manipulation

String identification

Strings are identified in expressions by surrounding them with opening/closing double chevrons (as are labels).

In following example, "TEXT" is recognized as a string : <<TEXT>>

String concatenation

Strings can be concatenated using the '+' sign.

Following example <<MY>> + <<TEXT>> will be concatenated to "MYTEXT".

String conversion

Numerical values can be converted to strings with the str function:

str(Box.Length.Value)

String formatting

String formatting is supported using the (old) %-style Python way.

All %-specifiers as defined in Python documentation.

As an example, supposing you have a default 10mm-side cube named 'Box' (default FreeCAD naming), the following expression <<Cube length : %s>> % Box.Length will expand to "Cube length : 10.0 mm"

For more than one %-specifier use the following syntax: <<Cube length is %s and width is %s>> % tuple(Box.Length; Box.Width). Or use concatenation: <<Cube length is %s>> % Box.Length + << and width is %s>> % Box.Width. Both will expand to "Cube length is 10.0 mm and width is 10.0 mm".

A FreeCAD sample file using string formatting is available in the forum

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Object creation functions

The following objects may be created in expressions using the following functions:

Type Function Description
Tuple tuple(a; b; ...) Example: tuple(2; 1; 2)
List list(a; b; ...) Example: list(2; 1; 2)
Vector vector(x; y; z) Create a vector using three unit-less or Length unit values.

Example: vector(2; 1; 3)

create(<<vector>>; x; y; z)
Matrix
matrix(
  a11; a12; a13; a14;
  a21; a22; a23; a24;
  a31; a32; a33; a34;
  a41; a42; a43; a44
)
Create a 4x4 matrix in row-major order:

A minimum of 1 argument can be supplied such as matrix(1) which creates an identity matrix.

Example: matrix(1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16)

create(<<matrix>>; a11; a12; ...; a44)
Rotation rotation(axis; angle) Create a Rotation by specifying its axis (Vector) and angle (Angle unit or unit-less), or three Euler angles α, β, γ.

Examples:

  • rotation(vector(0; 1; 0); 45)
  • create(<<rotation>>; 30; 30; 30)
rotation(α; β; γ)
create(<<rotation>>; axis; angle)
create(<<rotation>>; α; β; γ)
Placement placement(base; rotation) Create a Placement with various parameters, including:
  • base: base location (Vector)
  • center: center location (Vector)
  • rotation: Rotation
  • axis: Rotation axis (Vector)
  • angle: Rotation angle (unit-less or Angle unit value)
  • matrix: Matrix

Examples:

  • placement(vector(2; 1; 3); rotation(vector(0; 0; 1); 45))
  • create(<<placement>>; create(<<vector>>; 2; 1; 2); create(<<rotation>>; create(<<vector>>; 0; 1; 0); 45))
placement(base; rotation; center)
placement(base; axis; angle)
placement(matrix)
create(<<placement>>; ...)

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Vector functions

Functions: introduced in version 0.22.

Function / Operator Description
v1 + v2 Add two vectors.
v1 - v2 Subtract two vectors.
v * s Uniformly scale a vector by s.
vangle(v1; v2) Angle between two vectors in degrees.
vcross(v1; v2) Cross product of two vectors .
v1 * v2 Dot product of two vectors .
vdot(v1; v2)
vlinedist(v1; v2; v3) Distance between vector v1 and a line through v2 in direction v3.
vlinesegdist(v1; v2; v3) Distance between vector v1 and the closest point on a line segment from v2 to v3.
vlineproj(v1; v2; v3) Project vector v1 on a line through v2 in direction v3.
vnormalize(v) Normalize a vector to a unit vector.
vplanedist(v1) Distance between vector v1 and a plane defined by a point v2 and a normal v3.
vplaneproj(v1) Project vector v1 on a plane defined by a point v2 and a normal v3.
vscale(v; sx; sy; sz) Non-uniformly scale a vector by sx in the X direction, sy in the Y direction, and sz in the Z direction.
vscalex(v; sx)
vscaley(v; sy)
vscalez(v; sz)

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Matrix functions

Rotation and Placement can each be represented by a Matrix. The following functions all take in a Matrix, Rotation, or Placement as their first parameter denoted in the table below by m. The type of the returned object is the same as the object supplied in the first argument except when using mtranslate on a Rotation, in which case a Placement will be returned.

Function Description
minvert(m) Calculate the Inverse matrix.
mrotate(m; rotation) Rotate by either:
  • a Rotation
  • an axis (Vector) and an angle (Angle unit or unit-less)
  • three Euler angles α, β, γ
mrotate(m; axis; angle)
mrotate(m; α; β; γ)
mrotatex(m; angle) Rotate around the X axis.
mrotatey(m; angle) Rotate around the Y axis.
mrotatez(m; angle) Rotate around the Z axis.
mtranslate(m; vector) Translate by a vector (Vector) or X, Y, Z values. If a Rotation is translated, the returned object is a Placement.
mtranslate(m; x; y; z)
mscale(m; vector) Scale by a vector (Vector) or X, Y, Z values.
mscale(m; x; y; z)

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Conditional expressions

Conditional expressions are of the form condition ? resultTrue : resultFalse. The condition is defined as an expression that evaluates to either 0 (false) or non-zero (true).

The following relational operators are defined:

Unit Description
== equal to
!= not equal to
> greater than
< less than
>= greater than or equal to
<= less than or equal to

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Units

Units can be used directly in expressions. The parser connects them to the previous value. So 2mm or 2 mm is valid while mm is invalid because there is no preceding value.

All values must have a unit. Therefore you must in general use a unit for values in spreadsheets.
In some cases it works even without a unit, for example if you have e.g. in spreadsheet cell B1 just the number 1.5 and refer to it for a pad height. This only works because the pad height predefines the unit mm that is used if no unit is given. It will nevertheless fail if you use for the pad height e.g. Sketch1.Constraints.Width - Spreadsheet.B1 because Sketch1.Constraints.Width has a unit and Spreadsheet.B1 has not.

Units with exponents can directly be entered. So e.g. mm^3 will be recognized as mm³ and m^3 will be recognized as m³.

If you have a variable whose name is that of a unit you must put the variable between << >> to prevent it from being recognized as a unit. For example if you have the dimension Sketch.Constraints.A it would be recognized as the unit ampere. Therefore you must write it in the expression as Sketch.Constraints.<<A>>.

The following units are recognized by the expression parser:

Amount of substance

Unit Description
mmol Millimole
mol Mole

Angle

Unit Description
° Degree; alternative to the unit deg
deg Degree; alternative to the unit °
rad Radian
gon Gradian
S Second of arc; alternative to the unit ″
Second of arc; alternative to the unit S
M Minute of arc; alternative to the unit ′
Minute of arc; alternative to the unit M

Current

Unit Description
mA Milliampere
A Ampere
kA Kiloampere
MA Megaampere

Electric capacitance

Unit Description
pF Picofarad
nF Nanofarad
uF Microfarad; alternative to the unit µF
µF Microfarad; alternative to the unit uF
mF Millifarad
F Farad; 1 F = 1 s^4·A^2/m^2/kg

Electric charge

Unit Description
C Coulomb; 1 C = 1 A*s

Electric conductivity

Unit Description
uS Microsiemens; alternative to the unit µS
µS Microsiemens; alternative to the unit uS
mS Millisiemens
S Siemens; 1 S = 1 s^3·A^2/kg/m^2
kS KiloSiemens
MS MegaSiemens

Electric inductance

Unit Description
nH Nanohenry
uH Microhenry; alternative to the unit µH
µH Microhenry; alternative to the unit uH
mH Millihenry
H Henry; 1 H = 1 kg·m^2/s^2/A^2

Electric potential

Unit Description
mV Millivolt
V Volt
kV Kilovolt

Electric resistance

Unit Description
Ohm Ohm; 1 Ohm = 1 kg·m^2/s^3/A^2
kOhm Kiloohm
MOhm Megaohm

Energy/work

Unit Description
mJ Millijoule
J Joule
kJ Kilojoule
eV Electronvolt; 1 eV = 1.602176634e-19 J
keV Kiloelectronvolt
MeV Megaelectronvolt
kWh Kilowatt hour; 1 kWh = 3.6e6 J
Ws Watt second; alternative to the unit Joule
VAs Volt-ampere-second; alternative to the unit Joule
CV Coulomb-volt; alternative to the unit Joule
cal Calorie; 1 cal = 4.184 J
kcal Kilocalorie

Force

Unit Description
mN Millinewton
N Newton
kN Kilonewton
MN Meganewton
lbf Pound of force

Length

Unit Description
nm Nanometer
um Micrometer; alternative to the unit µm
µm Micrometer; alternative to the unit um
mm Millimeter
cm Centimeter
dm Decimeter
m Meter
km Kilometer
mil Thousandth of an inch; alternative to the unit thou
thou Thousandth of an inch; alternative to the unit mil
in Inch; alternative to the unit "
" Inch; alternative to the unit in
ft Foot; alternative to the unit '
' Foot; alternative to the unit ft
yd Yard
mi Mile

Luminous intensity

Unit Description
cd Candela

Magnetic flux

Unit Description
Wb Weber; 1 Wb = 1 kg*m^2/s^2/A

Magnetic flux density

Unit Description
G Gauss; 1 G = 1 e-4 T
T Tesla; 1 T = 1 kg/s^2/A

Mass

Unit Description
ug Microgram; alternative to the unit µg
µg Microgram; alternative to the unit ug
mg Milligram
g Gram
kg Kilogram
t Tonne
oz Ounce
lb Pound; alternative to the unit lbm
lbm Pound; alternative to the unit lb
st Stone
cwt Hundredweight

Power

Unit Description
W Watt
kW Kilowatt

Pressure

Unit Description
Pa Pascal
kPa Kilopascal
MPa Megapascal
GPa Gigapascal
uTorr Microtorr; alternative to the unit µTorr
µTorr Microtorr; alternative to the unit uTorr
mTorr Millitorr
Torr Torr; 1 Torr = 133.32 Pa
psi Pound-force per square inch; 1 psi = 6.895 kPa
ksi Kilopound-force per square inch

Temperature

Unit Description
uK Microkelvin; alternative to the unit µK
µK Microkelvin; alternative to the unit uK
mK Millikelvin
K Kelvin

Time

Unit Description
s Second
min Minute
h Hour
Hz (1/s) Hertz
kHz Kilohertz,
MHz Megahertz
GHz Gigahertz
THz Terahertz

Volume

Unit Description
ml Milliliter
l Liter
cft Cubicfoot

Special imperial units

Unit Description
mph Miles per hour
sqft Square foot

Unsupported units

The following commonly used units are not yet supported, for some an alternative is provided:

Unit Description Alternative
°C Celsius [°C] + 273.15 K
°F Fahrenheit; ([°F] + 459.67) × ​5/9
u Atomic mass unit; alternative to the unit Da 1.66053906660e-27 kg
Da Dalton; alternative to the unit u 1.66053906660e-27 kg
sr Steradian not directly
lm Lumen not directly
lx Lux not directly
px Pixel not directly

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Invalid characters and names

The expression feature is very powerful but to achieve this power it has some limitations concerning some characters. To overcome this, FreeCAD offers to use labels and reference them instead of the object names. In labels you can use almost all special characters.

In cases where you cannot use a label, such as the name of a sketch's constraints, you must be aware what characters are not allowed.

Labels

For labels there are no invalid characters, however some characters need to be escaped:

Characters Description
', \, " Need to be escaped by adding \ in front of them.

For example, the label Sketch\002 must be referenced as <<Sketch\\002>>.

Names

Names of objects like dimensions, sketches, etc. may not have the characters or character sequences listed below, otherwise the name is invalid:

Characters / Character sequences Description
+, -, *, /, ^, _, <, >, (, ), {, }, [, ], ., ,, = Characters that are math operators or part of mathematical constructs
A, kA, mA, MA, J, K, ' , ft , °, and many more! Characters and character sequences that are units (see the Units paragraph)
#, !, ?, §, $, %, &, :, ;, \, |, ~, , ¿, and many more! Characters used as placeholder or to trigger special operations
pi, e Mathematical constants
´, `, ' , " Characters used for accents
space A space defines the end of a name and can therefore not be used

For example, the following name is valid: <<Sketch>>.Constraints.T2üßµ@. While these are invalid names: <<Sketch>>.Constraints.test\result_2 (\r means "carriage return") or <<Sketch>>.Constraints.mol (mol is a unit).

Since shorter names (especially if they have only one or two characters) can easily result in invalid names, consider using longer names and/or establishing a suitable naming convention.

Cell aliases

See Spreadsheet SetAlias.

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Reference to CAD data

It is possible to use data from the model itself in an expression. To reference a property use object_name.property or <<object_label>>.property, labels must be enclosed in << and >>. If you want to use labels they must be unique.

All next examples reference the object by its name, but in all cases the object label can also be used.

If the property is a compound of fields, the individual fields can be accessed as object_name.property.field.

To reference list objects use object_name.list[list_index]. If you want to reference a constraint in a sketch, use Sketch.Constraints[16]. If you are in the same sketch you may omit its name and just use Constraints[16]. Note that the index starts with 0, therefore Constraint17 has to be referenced as Constraints[16].

To reference the object itself use the _self pseudo property: object_name._self.

The following table shows some more examples:

CAD data Call in expression Result
Length of a Part Box Box.Length Length with units (mm)
Volume of the Box Box.Shape.Volume Volume in mm³ without units
Shape type of the Box Box.Shape.ShapeType String: Solid
Label of the Box Box.Label String: Label
X-coordinate of center of mass of the Box Box.Shape.CenterOfMass.x X-coordinate in mm without units
X-coordinate of the Box placement Box.Placement.Base.x X-coordinate with units (mm)
X-component of the rotation axis of the Box placement Box.Placement.Rotation.Axis.x X-component of the unit vector in mm without units
Rotation angle of the Box placement Box.Placement.Rotation.Angle Rotation angle with units (deg)
Full Box object Box._self Object of type <Part::PartFeature>
Value of constraint in a sketch Constraints.Width Numeric value of the named constraint Width in the sketch, if the expression is used in the sketch itself.
Value of constraint in a sketch MySketch.Constraints.Width Numeric value of the named constraint Width in the sketch, if the expression is used outside of the sketch.
Value of a spreadsheet alias Spreadsheet.Depth Value of the alias Depth in the spreadsheet Spreadsheet
Value of a local property Length Value of the DataLength property in e.g a Pad object, if the expression is used in e.g DataLength2 in the same object.

Cyclic dependencies

FreeCAD checks dependencies based on the relationship between document objects, not properties. This means that you cannot provide data to an object and query that same object for results. For example, even though there are no cyclic dependencies when the properties themselves are considered, you may not have an object which gets its dimensions from a spreadsheet and then display the volume of that object in the same spreadsheet. You have to use two spreadsheets, one to drive your model and the other for reporting.

As a workaround it is possible to display a cell range from the second spreadsheet in the first (or vice versa) by creating a cell binding with the Hide dependency of binding option.

Another way to workaround cyclic dependencies is to hide the reference by using the href or hiddenref function for individual expressions, for example: href(Box.Length).

Please note that both mentioned workarounds should be used with caution, and that they do not work if the properties that are reported depend on dimensions that are driven from the same spreadsheet.

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Document-wide global variables

There is no concept of global variables in FreeCAD at the moment. Instead, arbitrary variables can be defined as cells in a spreadsheet using the Spreadsheet workbench, and then be given a name using the alias property for the cell (right-click on cell). Then they can be accessed from any expression just as any other object property.

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Cross-document linking

It is possible (with limitations) to define a Property of an object in your current document (".FCstd" file) by using an Expression to reference a Property of an object contained in a different document (".FCstd" file). For example, a cell in a spreadsheet or the DataLength of a Part Cube, etc. in one document can be defined by an Expression that references the X Placement value or another Property of an object contained in a different document.

A document's name is used to reference it from other documents. When saving a document the first time, you choose a file name; this is usually different from the initial default "Unnamed1" (or its translated equivalent). To prevent links being lost when the master document is renamed upon saving, it is recommended that you first create the master document, create a spreadsheet inside it, and save it. Subsequently, you can still make changes to the file and its spreadsheet but you should not rename it.

Once the master document with the spreadsheet is created and saved (named), it is safe to create dependent documents. For example, assuming you name the master document master, the spreadsheet modelConstants, and give a cell an alias-name Length, you can then access the value as:

master#modelConstants.Length

Note that the master document must be loaded for the values in the master to be available to the dependent document.

Of course, it's up to you to load the corresponding documents later when you want to change anything.

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Known issues / remaining tasks

  • FreeCAD does not yet have a built-in expression manager where all expressions in a document are listed, and can be created, deleted, queried, etc. But an addon is available: fcxref expression manager.
  • Open bugs/tickets for Expressions can be found on GitHub.

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