Gear Ratio Calculator
Calculate a gear ratio from tooth counts and see the output speed and torque for a given input, ideal and with an efficiency allowance.
What comes out of a gear pair when you know what goes in.
How the gear ratio calculator works
Two meshing gears turn at speeds inversely proportional to their tooth counts: a 20-tooth driver turning a 60-tooth driven gear gives a 3:1 ratio — the output turns a third as fast and, ideally, with three times the torque. Power in equals power out minus losses, so the calculator also shows the output torque at a chosen efficiency (spur gears run around 97–99% per stage).
A ratio above 1 is a reduction (more torque, less speed); below 1 an overdrive.
Formula: ratio = driven teeth ÷ driver teeth · output rpm = input rpm ÷ ratio · output torque = input torque × ratio × efficiency
Worked examples
| Inputs | Gear ratio | Note |
|---|---|---|
| 20 → 60 teeth at 1,500 rpm | 3 : 1 | 3:1, 500 rpm out |
| 60 → 20 teeth at 1,500 rpm | 0.333 : 1 | overdrive: 4,500 rpm |
| 11 → 34 teeth (bike) at 90 rpm | 0.324 : 1 | chainring drives the sprocket: wheel at 278 rpm |
FAQFrequently asked questions
Which gear is the driver?
The one connected to the power source — the motor, the pedals. The driven gear is on the output shaft.
Why does torque go up when speed goes down?
Power is torque × speed, and power is conserved (minus losses). Slow the output by three and the torque triples.
How do I combine several stages?
Multiply the ratios: 3:1 followed by 4:1 is 12:1. Efficiencies multiply too.
Do idler gears change the ratio?
No — an idler between driver and driven only reverses direction; the ratio is still driven teeth ÷ driver teeth.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Measurement Institute — Australia's measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.