How to use this calculator
- Choose pitch basis. Enter module, diametral pitch or circular pitch.
- Enter tooth count. Use the gear tooth count so pitch diameter and pitch radius are known.
- Set pressure angle. Use the operating pressure angle for the center-distance equivalent estimate.
- Set allowance coefficient. Start with a module-based allowance such as 0.04, then adjust to your tolerance target.
- Read backlash results. Use linear backlash, angular backlash, tooth-thickness split and center-distance equivalent as layout values.
How it works
Backlash is the clearance between mating gear teeth at the pitch circle.
For a quick spur-gear layout, this calculator uses a module-based allowance:
j = c_j x m
where j is linear backlash, c_j is the entered
backlash coefficient and m is module. Diametral pitch converts
with m = 25.4 / DP; circular pitch converts with
m = p / pi.
The pitch diameter is d = m x z. Angular backlash is the linear
clearance divided by pitch radius:
theta = j / (d / 2)
The page also reports arcminutes because small gear-backlash angles are often
easier to read that way.
If the backlash allowance is split evenly, each gear gives up
j/2 of tooth thickness at the pitch circle. If you create backlash
by opening the center distance, the rough relation for external spur gears is
j ~= 2 x Delta a x tan(phi), so the calculator reports
Delta a ~= j/(2 tan phi).
For tooth-depth proportions, use the addendum dedendum calculator. For tooth thickness and undercut, use the gear tooth calculator. For mesh overlap, use the gear contact ratio calculator, and for full geometry and DXF export use the involute gear calculator.
Worked example
Verified against the live calculator
A 20-tooth module 2 mm spur gear with coefficient
0.04 has linear backlash 0.08 mm. Its pitch diameter
is 40 mm, so pitch radius is 20 mm and angular
backlash is 0.229 deg, or about 13.8 arcmin. If split
equally, each gear gives up 0.04 mm of tooth thickness at the pitch
circle.
Frequently asked questions
How do you calculate gear backlash from module?
A first-pass spur-gear backlash allowance can be written as j = c_j x m, where m is module and c_j is an entered allowance coefficient. A common early layout band is roughly 0.03m to 0.05m, but production drawings should use the required tolerance and inspection method.
How do I convert backlash to angular backlash?
Angular backlash at the gear is theta = j / r, where j is linear backlash at the pitch circle and r = d/2 is pitch radius. The calculator reports the same angle in degrees and arcminutes.
What is tooth thickness reduction per gear?
If backlash is shared equally between the two gears, each gear tooth thickness is reduced by j/2 at the pitch circle. Some designs put more allowance on one member, so treat the split as a planning value.
Can I create backlash by increasing center distance?
For a rough external spur-gear screen, backlash from a center-distance increase is approximated as j ~= 2 x Delta a x tan(phi). The calculator rearranges that to Delta a ~= j/(2 tan phi).
Is this an AGMA or ISO gear tolerance calculator?
No. This page is an early backlash allowance screen. Final production backlash depends on tooth thickness tolerance, center distance tolerance, profile shift, gear quality, inspection method, heat treatment, lubrication and operating temperature.
Method & assumptions
- External spur-gear backlash allowance only; helical, bevel, worm and internal gears need separate treatment.
- The default coefficient is a starting value, not an AGMA, ISO, DIN or manufacturer tolerance class.
- The center-distance equivalent uses the approximation
j ~= 2 x Delta a x tan(phi). - Production backlash, tooth-thickness tolerances, center-distance tolerances, profile shift, cutter geometry, quality class, inspection method, heat treatment, lubrication, thermal growth and gear strength are outside this screen.