How to use this calculator
- Choose pitch system. Select module, diametral pitch or circular pitch.
- Enter pitch value. Enter the pitch value for the selected system.
- Enter tooth count. Enter the number of teeth on the gear.
- Read pitch diameter. Read pitch diameter plus equivalent module, DP and circular pitch.
How it works
Pitch diameter is the diameter of the gear's pitch circle, the theoretical rolling
circle where tooth spacing is defined. For module gears:
d = m · z
For diametral-pitch gears in inches:
d = z / DP
Circular pitch converts through m = p/π.
Worked example
Verified against the live calculator
A 20-tooth module 2 gear has pitch diameter
d = 2 × 20 = 40 mm. The same tooth size is
DP = 12.7 and circular pitch 6.28 mm. Its standard
outside diameter is about 44 mm, not 40 mm.
Frequently asked questions
How do you calculate gear pitch diameter?
For a module gear, pitch diameter d = m·z, where m is module and z is tooth count. For a diametral-pitch gear in inches, d = z/DP.
Is pitch diameter the same as outside diameter?
No. Pitch diameter is the theoretical rolling circle. Outside diameter is the tip diameter. For a standard full-depth spur gear, outside diameter is approximately d + 2m.
Can I use circular pitch?
Yes. Circular pitch p converts to module with m = p/π, then pitch diameter is d = m·z.
What pitch diameter do mating gears use for center distance?
For standard unshifted external spur gears, center distance is half the sum of the pitch diameters: a = (d1 + d2)/2.
Does this work for timing pulleys or sprockets?
This page is for gear pitch diameter from module, DP or circular pitch. For chain sprockets and belt pulleys, use the sprocket, pulley or timing-belt calculators.
Method & assumptions
- External spur gear pitch diameter, not tip diameter or base diameter.
- Profile shift changes working geometry and center distance, but not the reference pitch diameter d = m·z.
- Helical gears require normal/transverse module handling; this page assumes spur gear pitch.