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constants
Home > Constants & unit conversions
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Named values you can drop straight into the node graph - math constants and millimeter <-> working-unit conversions - just by typing their name.
In the node palette, type a constant's name and press Enter: Locus drops a Number node holding that value, named after the constant. The names are fuzzy-matched, so a few letters find them (gold -> goldenAngle, mmto -> the mm-to-unit family). See Adding & connecting nodes for the quick-entry palette.
| Name | Value | Notes |
|---|---|---|
pi |
3.14159... | π |
tau |
6.28319... | 2π - a full turn; tau / N divides the circle into N |
e |
2.71828... | Euler's number |
phi |
1.61803... | the golden ratio |
sqrt 2 |
1.41421... | |
sqrt 3 |
1.73205... | |
sqrt 5 |
2.23607... | |
silver |
2.41421... | the silver ratio, 1 + sqrt 2 |
goldenAngle |
137.50776 degrees | in degrees, matching Rotate's Angle |
Because node numbers are always millimeters, these constants convert to and from your working unit. Multiply a value by one to move it across units.
| Name | Value | Use |
|---|---|---|
intomm |
25.4 | inches -> mm |
mmtoin |
0.03937... | mm -> inches |
fttomm / mmtoft
|
304.8 / 0.00328... | feet <-> mm |
mtomm / mmtom
|
1000 / 0.001 | meters <-> mm |
sqintosqmm / sqmmtosqin
|
645.16 / 0.00155... | square inches <-> mm2 |
The same four (length both ways, area both ways) exist for every non-mm unit, and any new unit added to the app gets its set automatically.
Place each item goldenAngle further round than the last and the turns never line up - the even, non-repeating spread that packs a sunflower. Node setup: Series -> Math x goldenAngle (the angles) and Math ^ 0.5 x spacing (the radii) -> Point: Polar -> Place. Full walkthrough on the Phyllotaxis page.
A full turn is tau, so tau / N divides the circle into exactly N - no typing 60 and hoping. Node setup: Number tau -> Math (/ 6) -> Rotate (Angle from the result, Repeat 6, Center at the origin) -> a clean six-fold rosette.
The node graph is always in millimeters; multiply a value by mmtoin to read or export it in inches (intomm goes the other way, sqmmtosqin for areas). Node setup: the value -> Math (x mmtoin).
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