Sprocket Pitch Diameter
Calculator
Calculate the pin-center pitch circle diameter of a sprocket from tooth count and chain pitch using regular-polygon geometry.
Your setup
Your results
CalculatedPitch diameter passes through chain pin centers; outside tooth diameter is a different dimension.
Geometry does not specify tooth profile, roller seating, bore, strength or manufacturing tolerances.
How the calculation works
Follow the formula and keep the input units consistent at every step.
pitch diameter = pitch / sin(π / teeth)- Enter chain pin-to-pin pitch and integer tooth count.
- Treat adjacent pin centers as a chord on a circle.
- Solve chord = diameter × sin(π/N) for the pitch diameter.
A Worked Example
For 0.5-inch pitch and 12 teeth, sin(15°) = 0.258819. Pitch diameter is 0.5/0.258819 = 1.93185 inches.
What Your Result Means
Pitch diameter passes through chain pin centers; outside tooth diameter is a different dimension.
Assumptions & Limitations
Geometry does not specify tooth profile, roller seating, bore, strength or manufacturing tolerances.
Common Mistakes
Do not use outside diameter for chain engagement geometry or degrees in a radians-only sine function.
Questions about this calculation
Which values should I enter?
Enter chain pin-to-pin pitch and integer tooth count. Do not use outside diameter for chain engagement geometry or degrees in a radians-only sine function.
How should I interpret the result’s precision?
Displayed results are rounded for readability. Intermediate calculations retain floating-point precision; extra displayed decimals do not improve your input accuracy.
Can I use metric units?
Yes. Select Metric above the calculator to convert your inputs. Results always state their units. Tire-size designations keep their conventional mm and inch units.
What are the main limitations?
Geometry does not specify tooth profile, roller seating, bore, strength or manufacturing tolerances.
Method, sources & relevant guides
Two-sprocket chain approximation and even-pitch selection. Sprocket geometry is independently derived from the regular polygon chord.
Renold — Transmission chain installation & designer guideMethod documentation updated October 18, 2026. Independent professional review has not been claimed. Read the calculation and review policy.