Gear Ratio Calculator

Gear ratio compares the size of two meshing gears: ratio = driven teeth ÷ driver teeth. A 40-tooth gear driven by a 10-tooth pinion gives ratio 4:1 — the larger gear turns once for every four pinion revolutions, multiplying torque and reducing speed.

Output speed = input speed ÷ gear ratio (for a single stage). Multi-stage gearboxes multiply ratios across stages. Efficiency losses from friction are not modeled here.

Example: 1200 RPM input with a 3:1 reduction yields 400 RPM at the output shaft. Reverse the tooth counts to speed up instead of slow down.

Torque increases roughly by the gear ratio (minus losses) on the output side — a 4:1 reducer quadruples torque while quartering speed. That tradeoff is why vehicle differentials and drill gearboxes use reduction stages.

Compound gear trains multiply ratios: a 2:1 stage followed by a 3:1 stage gives 6:1 overall. Enter one mesh at a time or multiply ratios manually for multi-stage boxes.

Worked example with defaults: 10-tooth driver, 40-tooth driven, 1200 RPM in → ratio 4:1 → 300 RPM out. Swap tooth counts (40 driver, 10 driven) for a 0.25:1 speed-up to 4800 RPM.

Timing belts use pulley tooth counts like gear teeth: a 20-tooth driver and 60-tooth driven pulley gives the same 3:1 speed reduction as meshing gears with those counts, assuming no slip. Belt tension and wear introduce slip this ideal model ignores. Timing belt slip under load lowers effective reduction — tension and tooth wear matter on 3D printer drives even when tooth counts predict 3:1.

Automotive final-drive ratios multiply every transmission gear. A 4:1 axle ratio with a 3:1 first gear yields 12:1 overall reduction at the wheels — enter each stage separately or multiply ratios manually for compound trains beyond a single pair. Compound reductions multiply: 2:1 then 3:1 stages give 6:1 overall — enter one mesh at a time or multiply ratios for multi-stage boxes.

At 1200 RPM input with 10 driver and 40 driven teeth, output is 300 RPM. Need exactly 400 RPM instead? Solve backward: required ratio = 1200 ÷ 400 = 3:1, so pick tooth counts whose driven ÷ driver equals 3 (e.g., 30 ÷ 10). Need 400 RPM from 1200 RPM input? Target ratio 3:1 — pick 30 driven teeth on a 10-tooth driver instead of the default 4:1 pair.