Gear Ratio Calculator
Calculate the gear ratio between two gears from their teeth counts, and see how it changes speed and torque. The fundamental trade-off in every gearbox, bicycle and machine drive.
How to use this calculator
- Enter the driver (input) and driven (output) gear teeth counts.
- Optionally add input RPM and torque to see the output values.
- Ratio > 1 is reduction (more torque, less speed); < 1 is overdrive.
Formula used
A ratio above 1 is a reduction: the output turns slower but with more torque, multiplied by the ratio. Below 1 is overdrive: faster output, less torque. Speed and torque trade off inversely — their product is conserved apart from friction losses.
Example calculation
A 12-tooth driver turning a 36-tooth driven gear: ratio = 36 ÷ 12 = 3:1 reduction.
At 3,000 RPM input the output turns at 1,000 RPM but with 3× the torque — the classic trade a low gear makes to climb a hill.
The speed-torque trade-off
Gears exist to trade rotational speed for torque, and the ratio of their teeth counts sets the exchange rate. A reduction gear (larger driven gear) slows the output but multiplies torque by the same factor — which is why low gears help a car climb or a cyclist tackle a hill. An overdrive (smaller driven gear) does the reverse, spinning the output faster at the cost of torque, ideal for cruising speed.
The key insight is conservation: ignoring friction, power in equals power out, so whatever you gain in torque you lose in speed and vice versa. A 3:1 gear tripling torque also thirds the speed. Real gear trains chain several ratios together (multiply them), and the same teeth-ratio principle scales from a wristwatch to an industrial gearbox — which is why this one calculation underlies so much mechanical design.
Why use this calculator?
- Get the ratio, output speed and torque from teeth counts in one step.
- See instantly whether a pair is reduction or overdrive.
- Understand the speed-torque trade every gearbox makes.
Frequently asked questions
How do I calculate gear ratio?
Divide the driven (output) gear's teeth by the driver (input) gear's teeth. A 36-tooth gear driven by a 12-tooth gear gives 36/12 = 3:1. More teeth on the driven gear means more reduction.
Does a higher gear ratio mean more speed or more torque?
More torque, less speed. A high reduction ratio (like 4:1) multiplies torque fourfold but cuts output speed to a quarter. Overdrive ratios (below 1:1) do the opposite — more speed, less torque.
How do gear ratios combine in a gearbox?
Multiply them. Two stages of 3:1 and 2:1 give an overall 6:1 ratio. This lets compact gearboxes achieve large reductions by stacking modest ratios across several gear pairs.