Spur Gear Calculator

Inputs

Size system

Specify gear size by metric module (mm) or imperial diametral pitch (teeth per inch).

Module / DP (m)

Module in mm (metric) or diametral pitch in 1/in (imperial), per the size system above.

Pressure angle (α)

Standard pressure angle. 20° is by far the most common.

Tooth count (z)

Number of teeth on this gear.

Mating tooth count (z₂)

Teeth on the mating gear — used for center distance. Set 0 if none.

Profile shift (x)

Profile-shift (addendum-modification) coefficient. Positive shifts the profile outward to avoid undercut.

Default result

Pitch diameter(d)

40mm

Also computed

Module (mm)2

Diametral pitch (1/in)12.7

Base diameter(d_b)37.59mm

Outside (tip) diameter(d_a)44mm

Root diameter(d_f)35mm

Addendum2mm

Method notes 2 notes

Standard full-depth involute teeth (addendum = m, dedendum = 1.25 m, clearance = 0.25 m).
Minimum teeth to avoid undercut at 20° is 18 without profile shift.