Spur Gear Module and Diameter Calculator

What is the module?

The module is the number that defines tooth size in metric gears: pitch diameter divided by the number of teeth, in millimetres. m = d / z. A larger module means a bigger tooth that carries more load. Two gears that mesh must have the same module.

Spur gear dimensions

For a standard spur gear without profile shift, every dimension follows from the module and the tooth count:

• Pitch diameter: d = m × z
• Tip diameter: d_a = m × (z + 2)
• Root diameter: d_f = m × (z − 2.5)
• Circular pitch: p = π × m
• Tooth depth: h = 2.25 × m
• Centre distance of a pair: a = m × (z₁ + z₂) / 2

How do I find the module of a gear I have?

Count the teeth and measure the outside diameter with calipers. m = d_a / (z + 2) gives the module. The result should land very close to a standard value. If it does not, the gear may be an inch size or have profile shift.

Example

A gear with a 2.5 mm module and 40 teeth has a pitch diameter of 100 mm, a tip diameter of 105 mm, a root diameter of 93.75 mm and a circular pitch of 7.854 mm. A 20 tooth gear measuring 66 mm across the tips has a module of 66 / 22 = 3 mm.

Limits

The tool gives the geometry of a standard spur gear only. Helical gears, profile shift, backlash and strength calculations are outside the scope. At a 20 degree pressure angle, undercut begins below 17 teeth.