Gear Backlash Effect Calculator

Work out gear backlash effect instantly with clear inputs, formula shown and shareable results.

About Gear Backlash Effect Calculator

Backlash is quoted at the gearbox output, so it converts straight into a tool position error of arm length times the angle in radians. Twelve arcminutes on a 400 mm arm is 1.4 mm of lost motion — visible every time the axis reverses direction, which is why precision axes use preloaded or harmonic drives.

Formula

Backlash error

error = arm length x backlash in radians; 1 arcmin = 0.29 mrad

Worked example

With the default values below, Gear Backlash Effect Calculator returns Position error at the tool of 1.40. Change any input above and every figure here is recalculated in your browser.

Inputs used

Gear backlash: 12 arcmin
Reduction ratio: 50 :1
Output arm length: 400 mm
Direction reversals per cycle: 2 reversals

Results

Position error at the tool: 1.40 mm
Backlash at the output: 12.00 arcmin
Error over the reversals: 2.79 mm
Output backlash: 3.49 mrad

Step by step

1Values used
2Backlash error
3Position error at the tool= 1.40 mm
4Backlash at the output= 12.00 arcmin
5Error over the reversals= 2.79 mm
6Output backlash= 3.49 mrad

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Can backlash be compensated in software?

Partly. A feedforward offset on reversal helps repeatable backlash, but it cannot fix the variability or the effect on servo stability.

Which gearboxes have least backlash?

Harmonic drives reach under 1 arcmin, precision planetary units 3-8 arcmin, and standard spur gearboxes 20-60 arcmin.