Equal Spacing on a Circle Calculator
Place equally spaced points on a circle. Calculate every coordinate, angular step, adjacent chord and arc length, with a labelled layout.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Divide one full turn by the point count. Add or subtract that step from the entered starting angle. Convert each polar offset to Cartesian x/y and add the entered center.
θi=θ0±i×360°/n; x=cx+r cosθi; y=cy+r sinθi; adjacent chord=2r sin(π/n)
Worked example
Six points on a 100 mm diameter circle have a 60° step, 50 mm adjacent chord and 52.3599 mm adjacent arc. Starting at 0°, the first two coordinates are (50,0) and (25,43.3013) mm.
Assumptions and input details
Two to 360 points; the first point uses the starting angle and the closing point is not duplicated. Coordinates use a mathematical positive-y-up system; some screen/CAD conventions use a different axis. Starting angles are normalized modulo 360°. Diameter means the point-center circle, not the hole diameter or outer stock diameter. Adjacent arc length is not straight-line spacing. The table contains all points; the diagram labels only the first 12 for readability. This computes a layout, not machining clearances, tolerances or structural capacity.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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