Gear Module, Pitch Diameter & Center Distance Calculator
Spur-gear geometry from module (or diametral pitch) and tooth counts — pitch, outside, root and base diameters, addendum and dedendum, center distance, gear ratio, circular pitch and tooth thickness, output speed and pitch-line velocity, plus the interference check for small pinions and the module ↔ DP conversion.
How it works
d = m × z · C = m (z₁ + z₂) ÷ 2 · d_a = m (z + 2), d_f = m (z − 2.5), d_b = d cos α · p = π m, DP = 25.4 ÷ m · z_min = 2 ÷ sin²α (17 at 20°) · v = π d₁ n₁ ÷ 60,000 m/s
The module is the millimetres of pitch diameter per tooth, so every dimension of a standard spur gear is a multiple of it: pitch diameter is module times teeth, the addendum is one module, the dedendum one and a quarter, and two gears mesh when their centre distance equals half the sum of their pitch diameters — which is why gears of the same module and pressure angle are interchangeable. The base circle, set by the pressure angle, is where the involute tooth flank is generated, and the contact ratio counts how many tooth pairs share the load on average. Pinions with too few teeth get their roots gouged by the cutter, the undercut that the minimum-tooth rule and profile shift exist to avoid.
Worked example
A module-2 pair with 20 and 60 teeth has pitch diameters of 40 and 120 mm, a centre distance of 80 mm and a 3:1 ratio, turning 1,450 rpm into 483 rpm. Tip diameters are 44 and 124 mm, whole depth 4.5 mm, contact ratio about 1.67, pitch-line speed 3.0 m/s. Twenty teeth clears the 17-tooth undercut limit at 20°; module 2 corresponds to 12.7 DP.
Frequently asked questions
Can I mesh a module-2 gear with a 12 DP gear?
No — 12 DP is module 2.117. Even a few percent of pitch mismatch prevents proper meshing. Convert with DP = 25.4 ÷ m and use matching cutters.
What if my centre distance is fixed and not equal to m(z₁+z₂)/2?
Use profile-shifted gears: positive shift on both increases the working centre distance slightly (and strengthens teeth); large gaps need a different module or tooth count.
Related calculators
Textbook machine-design formulas (Shigley, Roark, Eurocode 3 / VDI conventions) with idealised assumptions. Use manufacturer data, material certificates and a qualified engineer's check for anything safety-related.