Gear Ratio Calculator
Find the gear ratio by entering tooth counts for the driver and driven gears. Instantly see the speed and torque relationship between the two shafts.
Driven teeth ÷ Driver teeth — output rotates this many times per one input revolution
3
ratioDriver teeth
25%
Driven teeth
75%
- 1
Driver gear teeth (input)
20 - 2
Gear ratio = Driven ÷ Driver
60 ÷ 20 = 3
How does this calculator work?
Divide driven gear tooth count by driver tooth count: GR = T₂ ÷ T₁. A ratio above 1 slows the output by that factor and multiplies torque by the same factor. A ratio below 1 (overdrive) speeds up the output but reduces torque. Multiply individual ratios for compound gear trains.
Formula
How this is calculated
A gear ratio tells you how many times the driver gear (input shaft) must rotate for the driven gear (output shaft) to complete one full revolution. It is calculated by dividing the tooth count of the driven gear by the tooth count of the driver gear: GR = T₂ ÷ T₁. More teeth on the driven gear means a ratio greater than 1 — the output shaft turns more slowly than the input, but with proportionally more torque.
This speed–torque trade-off is fundamental to all gear systems. In an ideal (frictionless) gear pair, mechanical power (torque × angular velocity) is conserved across the mesh. A ratio of 3:1 means the driven shaft turns at one-third the driver speed but receives three times the driver torque. Real systems lose a few percent to gear-mesh friction and bearing drag, so the actual torque gain is slightly less than the theoretical multiplier.
For compound gear trains — several pairs connected in series — multiply each pair's ratio together to get the overall ratio. This applies equally to spur, helical and bevel gears. Worm gears typically produce very high ratios (40:1 to 100:1) in a single stage, though with higher friction losses.
Frequently asked questions
The driver gear must turn 3 times for the driven gear to turn once. The output shaft spins at one-third the input speed but delivers three times the input torque (ignoring friction losses).
A ratio greater than 1 (more driven teeth) reduces output speed and multiplies torque — used in gearboxes, winches and most machinery. A ratio less than 1 (fewer driven teeth) increases output speed while reducing torque — called overdrive, used in the top gear of many vehicle transmissions.
Multiply each pair's ratio together. If Stage 1 is 3:1 and Stage 2 is 4:1, the overall ratio is 12:1. Each pair's driven gear often shares a shaft with the next pair's driver gear.
Also known as
TG we-Calculate Editorial Team. (2026). Gear Ratio Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/gear-ratio-calculator
TG we-Calculate Editorial Team. "Gear Ratio Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/gear-ratio-calculator.
TG we-Calculate Editorial Team, "Gear Ratio Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/gear-ratio-calculator
@misc{wecalculate_gear_ratio_calculator, title = {Gear Ratio Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/gear-ratio-calculator}}, year = {2026}, note = {TG we-Calculate} }
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