Units and Expressions#

Overview#

Every value in Fusion has a unit type: length, angle, or unitless. Expressions are evaluated with dimensional analysis: you can add lengths to lengths, multiply a length by a number, and divide a length by a length to get a unitless ratio. You cannot add a length to an angle.

Understanding this removes most "mysterious" red fields.

Where to find it#

• Document units: in the Browser, expand the design node and the Document Settings entry; set Units (mm, cm, m, in, ft). This sets the default unit for bare numbers in length fields (Autodesk's API documentation states that a bare number is read in the document's default units, while a unit typed in the expression overrides it).
• Parameter units: the Unit column or dropdown in Change Parameters.
• Any numeric field: type an expression with explicit units, such as 1.5 in or 25.4 mm.

Step by step#

Mix units safely#

1. In a length field, type 1 in + 5 mm. Fusion evaluates to 30.4 mm (in a mm document).
2. In an angle field, type 45 deg or 0.785 rad.
3. For unitless numbers (counts, ratios) choose "No Unit" for the parameter.

Bare numbers#

A bare number in a length field takes the document's default unit. If your document is in mm, 10 means 10 mm. In a user parameter, a bare number is read in the document default unit according to the API documentation, and the parameter's unit is the unit of the result; if these differ (an inch parameter in a mm document), test with 4 and check the Value column before relying on it. To avoid surprises, always type units in important expressions.

Convert units#

1. Create a parameter length_in with unit in and expression 4.
2. Create length_mm with unit mm and expression length_in. The value displays as 101.6 mm.

Fusion converts automatically. If the parameter's unit and the expression's dimension disagree (angle versus length), you get an error.

Use ratios#

1. ratio (no unit) = box_l / box_w.
2. diag (mm) = sqrt((box_l / 1 mm) ^ 2 + (box_w / 1 mm) ^ 2) * 1 mm. Autodesk's reference says sqrt takes a unitless argument and returns a unitless value, so strip the units first and restore them afterwards.

Trigonometry#

1. Functions take angles; sin(30 deg) gives 0.5.
2. Always write deg or rad explicitly inside trig functions rather than relying on a default for a bare number (not specified in the parameters reference).
3. Inverse functions (asin, acos, atan) return angles.

Options reference#

The function list above follows Autodesk's Parameters reference. Do not use a comma between arguments, because it conflicts with the decimal delimiter in some locales. If a function is not accepted, Fusion flags the expression in red.

Order of operations, highest first: parentheses, exponentiation, negation, multiplication and division, addition and subtraction. Because negation ranks below exponentiation in that list, -2 ^ 2 evaluates as -(2^2) = -4; write (-2) ^ 2 when you mean 4.

Tips and pitfalls#

Tip: When an expression is red, break it into two parameters and inspect the Value of each. The first one that goes red or shows wrong units is the culprit.

Tip: Write * 1 mm to turn a unitless count into a length when needed (for example n * 1 mm). Use sparingly.

Tip: To get a unitless number from a length, divide by 1 mm in the same expression: box_l / 1 mm.

Warning: Changing document units does not change the stored geometry (internally cm), but bare-number fields reinterpret. A bare 25 in an inch document means 25 inches. Retype with units when copying between designs.

Warning: Imperial fractions: 1/4 in is a division and should work. A mixed number such as 1 1/4 in contains a space and may not parse as intended, so write (1 + 1/4) * 1 in or 1.25 in. I could not confirm this edge case in Autodesk's help, so test it.

Warning: Integer division is not an issue (values are floating point), but rounding display precision hides small differences. Increase the displayed precision (Document Settings has a Precision setting) if you need to inspect.

Unit conventions to adopt:

• Keep document units equal to your manufacturing units (mm for metric work).
• Store thread sizes, counts, and ratios as No Unit parameters.
• Put units in every literal inside expressions (2 mm, 45 deg), so nothing depends on settings.
• Name angle parameters with an _a or _ang suffix, and length parameters in a consistent way.

Precision and tolerances#

Display precision is a setting; the stored values are full double-precision. For fits, represent tolerance explicitly: shaft_d = 10 mm, hole_d = shaft_d + 0.1 mm.

Worked calculations with dimensional analysis#

Each of these shows how the unit of the result is determined, so you can predict it before pressing Enter.

A particular trap is a parameter whose unit is set to mm while the expression has an area (a * b): the dialog flags it because the dimensions disagree. Set the parameter's unit to match the dimension of the expression, or change the expression.

Use if for switching#

Autodesk's reference lists if, and, or and not. A minimum wall check is if(wall < 1.2 mm; 1.2 mm; wall), equivalent to max(wall; 1.2 mm). A condition on a count: if(n > 8; 8; n). Use if when the alternative is not a simple min or max, for example a different boss diameter for steel versus plastic. Nested if handles three cases: if(n < 4; 3 mm; if(n < 8; 4 mm; 5 mm)).

Worked example: a hole row#

For box_l = 80 mm, margin = 6 mm and n = 5 holes:

• hole_pitch = (box_l - 2 * margin) / (n - 1) gives (80 - 12) / 4 = 17 mm.
• Hole x-positions: 6, 23, 40, 57 and 74 mm.
• If n becomes 1 the denominator is zero. Guard it with (box_l - 2 * margin) / max(n - 1; 1) so a single hole stays at the margin instead of failing.

Unit conventions across a team#

Display precision#

Displayed values are rounded for readability but stored at full precision. A hole_pitch that reads 17 mm might be 17.0000001. When comparing values in an if, round first. round takes a unitless argument, so strip the unit: round(hole_pitch / 1 mm * 100) / 100. If a comparison such as == fails unexpectedly, display precision is almost certainly the cause. Rounding functions accept and return unitless values only.

Failure modes and fixes#

Practice exercise#

1. Set document units to mm. Create d_in (in) = 0.5, d_mm (mm) = d_in. Confirm 12.7 mm.
2. Create circ (mm) = PI * d_mm. Check ~39.9 mm.
3. Create tilt (deg) = atan(10 mm / 40 mm). Check ~14.04 deg.
4. Create bad = d_mm + tilt and read the error.
5. Create box_l, margin (mm) and n (no unit), then hole_pitch = (box_l - 2 * margin) / (n - 1) with a unitless n and confirm the unit is mm.

Expected result: you can predict the unit and value of any expression before pressing Enter.

Related#

• User parameters and equations
• The Change Parameters dialog
• Design-for-change patterns