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 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.
Numbers may use either a comma , or a decimal point . separating 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 (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 are currently recognized.
You can use predefined constants and functions.
Multiple arguments to a function may be separated by either a semicolon 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.
You can reference an object by its Name or by its Label. In the case of a Label, it must be enclosed in double << and >> symbols, such as <<Label>>.
You can reference any numerical property of an object. For example, to reference a Cylinder's height, you may use Cylinder.Height or <<Long_name_of_cylinder>>.Height.
To reference list objects, use <<object_label>>.list[list_index] or object_name.list[list_index]. If you want for example to reference a constraint in a sketch, use <<MySketch>>.Constraints[16]. If you are in the same sketch you may omit its name and just use Constraints[16].
Note: The index starts with 0, therefore constraint 17 has the index 16.
For more information about referencing objects, see Reference to CAD_data.
The following constants are supported:
Constant Description
e Euler's number pi Pi
The following operators are supported:
Operator Description
+ Addition - Subtraction * Multiplication / Floating point Division % Remainder ^ Exponentiation
The mathematical functions listed below are available.
Trigonometric functions use degree as their default unit. For radian measure, add 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 1 deg, 1 ° or 1 rad as appropriate, e.g. (360 - X) * 1deg; (360 - X) * 1°; (0.5 + pi / 2) * 1rad.
These trigonometric functions are supported:
Function Description Value range
acos(x) Arc cosine -1 <= x <= 1 asin(x) Arc sine -1 <= x <= 1 atan(x) Arc tangent all atan2(x; y) Arc tangent of x/y all, except y = 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 = uneven 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 and y > 0, x >= y
These functions for exponentiation and logarithmization are supported:
Function Description Value 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
These functions for rounding, truncation and remainder are supported:
Function Description Value 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 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
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 {{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)}}.
These aggregate functions are supported:
Function Description Value 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
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>>
Strings can be concatenated using the '+' sign.
Following example <<MY>> + <<TEXT>> will be concatenated to "MYTEXT".
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--, following expression <<Cube length : %s>> % Box.Length will expand to "Cube length : 10.0 mm"
A limitation is that only one %-specifier is allowed in string, thus you have to use string concatenation if more than one is needed. With same above situation, expression <<Cube length is %s>> % Box.Length + << and width is %s>> % Box.Width 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
The following objects may be created in expressions via the create function:
- Vector
- Matrix
- Rotation
- Placement
The create function passes subsequent arguments to the underlying Python constructor when creating the object.
Various mathematical operations such as multiplication, addition, and subtraction are supported via standard mathematical operators (e.g. *, +, -).
When create is passed <<vector>> as the 1st argument, the next 3 arguments are the X, Y, and Z coordinates for the Vector respectively.
Example:
create(<<vector>>; 2; 1; 2)
When create is passed <<matrix>> as the 1st argument, the next 16 arguments are the elements for the Matrix in row-major order.
Example:
create(<<matrix>>; 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16)
When create is passed <<rotation>> as the 1st argument, there are two ways to create a Rotation:
1. Specify an axis vector and a rotation angle.
Example:
create(<<rotation>>; create(<<vector>>; 0; 1; 0); 45)
2. Specify 3 rotations about the X, Y, and Z axes as Euler angles.
Example:
create(<<rotation>>; 30; 30; 30)
When create is passed <<placement>> as the 1st argument, there are five ways to create a Placement.
These possible combinations are documented in the below table and are based on the Placement API page.
+++
| Number of arguments | Description |
+=====================+==========================================================+
| 2 | |
| | create(<<placement>>; Placement) |
| | |
+++
| 2 | |
| | create(<<placement>>; Matrix) |
| | |
+++
| 3 | |
| | create(<<placement>>; Base; Rotation) |
| | |
+++
| 4 | |
| | create(<<placement>>; Base; Rotation; Center) |
| | |
+++
| 4 | |
| | create(<<placement>>; Base; Axis; Angle) |
| | |
+++
The following example shows the syntax for creating a Placement from a Base (vector) and a Rotation:
create(<<placement>>; create(<<vector>>; 2; 1; 2); create(<<rotation>>; create(<<vector>>; 0; 1; 0); 45))
For readability, you can define vectors and rotations in separate cells, and then reference the cells in your expression.
Scale a Matrix with a given Vector.
mscale(Matrix; Vector)
mscale(Matrix; x; y; z)
Invert the given Matrix, Rotation, or Placement.
minvert(Matrix)
minvert(Rotation)
minvert(Placement)
You can create Python tuple or list objects via their respective functions.
tuple(2; 1; 2)
list(2; 1; 2)
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). Note that enclosing the conditional expression in parentheses is currently considered an error.
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
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
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
Energy/work:
Unit Description
J Joule 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
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
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 VA Volt-ampere
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
Volume:
Unit Description
l Liter
The following commonly used units are not yet supported:
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
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.
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 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, C, G, F, uF, µF, J, K, ''' ' ''', ''' ft ''', °, and many more! Characters and character sequences that are units #, !, ?, §, $, %, &, :, ;, \, |, ~, ∆, ¿, 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.
For spreadsheet cell aliases only alphanumeric characters and underscores (A to Z, a to z, 0 to 9 and _) are allowed.
It is possible to use data from the model itself in an expression. To reference a property useobject.property. If the property is a compound of fields, the individual fields can be accessed as object.property.field.
The following table shows some examples:
++++
| CAD data | Call in expression | Result |
+============================================+=======================================+==============================================================================================================================================================================+
| Parametric Length of a Part-Workbench Cube | | Length with units mm |
| | Cube.Length | |
| | | |
++++
| Volume of the Cube | | Volume in mm³ without units |
| | Cube.Shape.Volume | |
| | | |
++++
| Type of the Cube-shape | | String: Solid |
| | Cube.Shape.ShapeType | |
| | | |
++++
| Label of the Cube | | String: Label |
| | Cube.Label | |
| | | |
++++
| x-coordinate of center of mass of the Cube | | x-coordinate in mm without units |
| | Cube.Shape.CenterOfMass.x | |
| | | |
++++
| Value of constraint in a sketch | | Numeric value of the named constraint Width in the sketch, if the expression is used in the sketch itself. |
| | Constraints.Width | |
| | | |
++++
| Value of constraint in a sketch | | Numeric value of the named constraint Width in the sketch, if the expression is used outside of the sketch. |
| | MySketch.Constraints.Width | |
| | | |
++++
| Value of a spreadsheet alias | | Value of the alias Depth in the spreadsheet Spreadsheet |
| | Spreadsheet.Depth | |
| | | |
++++
| Value of a local property | | Value of the Length property in e.g a Pad object, if the expression is used in e.g Length2 in the same object. |
| | Length | |
| | | |
++++
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.
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.
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.
Unfortunately, the integrated checker sometimes claims that a valid name doesn't exist. Continue typing anyway. When you have completed the full reference, the OK button will become active.
Of course, it's up to you to load the corresponding documents later when you want to change anything.
- 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 the other for reporting.
- The expression parser does not handle parentheses well, and is unable to properly parse some expressions. For example:
<nowiki>=</nowiki> (A1 > A2) ? 1 : 0results in an error, while<nowiki>=</nowiki> A1 > A2 ? 1 : 0is accepted. The expression<nowiki>=</nowiki> 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 OK button will become active.
- 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 in the FreeCAD Bugtracker Expressions category
documentation index > Spreadsheet > Expressions