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Introduction to Gear Ratio Calculations

Learn how to calculate gear ratios for simple and compound gear trains, with worked examples and practical design tips.

2026-03-05
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What Is a Gear Ratio?

The gear ratio is the ratio of the number of teeth on the driven gear to the number of teeth on the driving (input) gear:

Gear Ratio (GR) = N_driven / N_driving

A higher gear ratio means more torque output and lower output speed; a lower ratio means higher speed with less torque multiplication.

Simple Gear Train

For a two-gear system:

ParameterFormula
Gear ratioGR = N₂ / N₁
Output speedω₂ = ω₁ / GR
Output torqueT₂ = T₁ × GR × η

Where η is the mesh efficiency (typically 0.97–0.99 per stage).

Compound Gear Train

When multiple gear stages are in series, multiply the individual stage ratios:

GR_total = GR₁ × GR₂ × GR₃ × ...

Example: A 3-stage gearbox with ratios 3:1, 4:1, and 2:1 gives a total ratio of 24:1.

Practical Design Tips

  1. Keep individual stage ratios below 6:1 to avoid excessive tooth load differences.
  2. Use standard module sizes (1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8 mm) for interchangeability.
  3. Check centre distance: for two external spur gears, centre distance = m(N₁ + N₂)/2.
  4. Profile shift can be used to avoid undercutting when the pinion has fewer than 17 teeth.

Try the Calculator

Use the Gear Ratio Calculator on this site to quickly compute output speed, torque, and efficiency for your gear train.