Gear Ratio Calculator
Enter driver and driven teeth to get the ratio, output speed and output torque — with the mesh efficiency and multi-stage notes spelled out.
Last updated: 2026-09-15
How the calculation works
- Ratio is driven teeth ÷ driver teeth: a number above 1 means reduction (slower output, more torque).
- Output speed divides the input speed by the ratio; output torque multiplies it, reduced by a 97% single-mesh efficiency.
- Leave speed or torque blank if you only need the ratio itself.
Formula
Ratio = N_driven / N_driver Output RPM = Input RPM / Ratio Output torque ≈ Input torque × Ratio × 0.97
| Symbol | Meaning | Unit |
|---|---|---|
N | Number of teeth | — |
n | Rotational speed | RPM |
T | Torque | N·m |
Worked example
A 20-tooth pinion drives a 60-tooth gear at 1750 RPM with 10 N·m input. Ratio = 3:1. Output = 583 RPM with about 29.1 N·m — a classic 3:1 reduction stage.
Interpreting the result
Ratios above 1 reduce speed and multiply torque; below 1 they overdrive. Two-stage gearboxes multiply stage ratios (e.g. 3:1 × 4:1 = 12:1) and lose about 3% per mesh. For belt or chain drives the same math applies using diameter or tooth counts respectively.
Assumptions
- Single mesh per calculation; 97% efficiency per mesh for spur gears.
- Rigid mounting, no backlash dynamics considered.
Limitations
- Worm gears have much lower efficiency (30–70%) — do not apply 97% there.
- Bevel and helical meshes differ slightly; planetary systems need a different ratio method.
Frequently asked questions
How do I calculate gear ratio with three gears?
Idler gears in between don't change the ratio — only the first driver and last driven matter. For two stages (two shafts), multiply the stage ratios.
Does a bigger gear always mean more torque?
A larger driven gear multiplies torque and reduces speed. Power stays roughly constant (minus losses): you trade speed for torque.