Engineering & mechanics
Spur gear pitch geometry
Translate module and tooth count into common involute gear reference diameters.
A clear answer. Here’s how.
Pitch diameter=m×z, circular pitch=πm and base diameter=pitch diameter×cos(pressure angle). Also shows unshifted full-depth reference outside diameter=m(z+2) and approximate root diameter=m(z−2.5). These reference dimensions do not specify tooth shape, fillet, backlash, undercut, profile shift or manufacturing tolerances.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Metric module (mm)
- 2
- Whole tooth count
- 30
- Pressure angle (degrees)
- 20
Example result
- Pitch diameter (mm)
- 60
- Outside diameter (mm)
- 64
- Approximate root diameter (mm)
- 55
- Base-circle diameter (mm)
- 56.3815572472
- Circular pitch (mm)
- 6.28318530718
- Diametral pitch (teeth/inch)
- 12.7