What is the difference between module and circular pitch?

Question

Accepted Answer

Module and circular pitch describe the same basic tooth size in different ways. Module is reference diameter divided by tooth count; circular pitch is the arc distance between corresponding points on adjacent teeth along the reference circle. For spur gears, p = πm. Both use length units, so a circular pitch of 5 mm is not module 5.

Module and circular pitch use different formulas

For a spur gear with reference diameter d and z teeth, use consistent millimeter units:

Quantity	Formula
Module, m	d ÷ z
Circular pitch, p	πd ÷ z = πm
Module from circular pitch	p ÷ π

Measure pitch along the reference circle, not as a straight gap between tooth tips. The reference circle is a geometric datum rather than a visible machined edge.

Diagram identifying circular pitch along a gear reference circle — Circular pitch follows the reference-circle arc between corresponding tooth positions.

Tooth geometry diagram locating circular pitch and other tooth dimensions — Tooth thickness, tooth height and circular pitch are different drawing dimensions.

Worked comparison: module 2 and CP 5

Module 2: p = π × 2 ≈ 6.2832 mm.
CP 5: m = 5 ÷ π ≈ 1.5915 mm.

A 20-tooth CP 5 pinion advances a matched straight rack by 20 × 5 = 100 mm per full revolution in ideal geometry. CP racks can therefore make nominal travel per turn convenient to specify.

The calculation does not include backlash, positioning errors or elastic deflection.

Keep the reference plane consistent

For helical gears, distinguish normal and transverse values: p_n = πm_n and p_t = πm_t. Do not mix the two planes. Matching tooth size also requires compatible pressure angle, tooth form and other mating geometry.

When sending PairGears a drawing, identify the pitch system and units. See the spur gear pitch and measurement guide.

Module and circular pitch use different formulas

Worked comparison: module 2 and CP 5

Keep the reference plane consistent

Related questions