Gear Backlash Calculator

Inputs

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Design forward from an allowance coefficient, or enter a backlash you measured (dial indicator at the pitch radius) and judge it against the common band.
Choose which gear tooth-size value you know.
Module in mm, diametral pitch in 1/in, or circular pitch in mm.
mm
Tooth count used to convert linear backlash into angular backlash at the pitch radius.
Used only for the approximate center-distance equivalent.
deg
Linear backlash allowance as a multiple of module. Early layout often starts around 0.03m to 0.05m.

Results

Default result
Edit inputs
Linear backlash (j)
0.08 mm
Pass

Allowance is inside the common early-design coefficient band.

Allowance at the pitch circle.

Also computed

Angular backlash (theta) Pass 0.2292 deg

j divided by pitch radius.

Angular backlash (theta) 13.75 arcmin

Reduction per gear (Delta s) 0.04 mm

If backlash is split equally between both gears.

Center-distance equivalent (Delta a) 0.1099 mm

Approximate only: backlash from center-distance change is estimated as j ~= 2*Delta a*tan(phi).

Approximate center-distance increase that produces the same backlash.

Pitch diameter (d) 40 mm

Module (m) 2 mm

Method notes 5 notes
  • Linear backlash allowance is j = c_j*m, where m is module and c_j is the entered allowance coefficient.
  • Angular backlash at the gear is theta = j/(d/2), with d = m*z.
  • If the pair splits backlash equally, each gear tooth thickness is reduced by j/2 at the pitch circle.
  • Approximate center-distance equivalent uses j ~= 2*Delta a*tan(phi) for external spur gears.
  • Production backlash is set by tooth-thickness tolerance, center-distance tolerance, profile shift, quality class, inspection method, heat treatment, thermal growth and lubrication conditions.

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