Gear Ratio Calculator
The ratio of two gears or pulleys and the output speed and torque, a bicycle's gear inches and speed at your cadence, or a car's engine rpm at a road speed.
Result…
How it's calculated
Gear ratio = driven teeth (or diameter) ÷ driving teeth (or diameter) Output rpm = input rpm ÷ ratio · Output torque = input torque × ratio × efficiency Bicycle: gear inches = wheel diameter (in) × chainring ÷ cog; speed = π × diameter × chainring ÷ cog × cadence Car: engine rpm = road speed ÷ (π × tyre diameter) × gear ratio × final drive
Two meshing gears move the same number of teeth past each other, so the speeds are in the inverse ratio of the teeth: a 12-tooth gear driving a 36-tooth gear turns it at a third of the speed. Pulleys work the same way with diameters. Power is speed times torque, so with no losses the torque rises by the same ratio as the speed falls; the efficiency takes off what friction loses. On a bicycle the chainring drives the cog, so the wheel turns chainring ÷ cog times per pedal turn; gear inches multiplies that by the wheel diameter in inches, and the distance per pedal turn (development) by its circumference. In a car the wheels turn once per tyre circumference, and the engine turns gear ratio × final drive times for each wheel turn. 1 inch = 25.4 mm and 1 mile = 1.609344 km exactly.
Your numbers, step by step
About the Gear Ratio calculator
This gear ratio calculator covers three jobs in one place. For two gears or pulleys it gives the ratio from the teeth or diameters, then the output speed and the output torque after the efficiency you enter. For a bicycle it turns the chainring, rear cog and wheel diameter into gear inches, the distance per pedal turn and your speed at a cadence. For a car it works out the engine rpm at a road speed from the gear ratio, final drive and tyre diameter. Metric and imperial units are both supported, in millimetres and km/h or inches and mph. Makers, mechanics, cyclists choosing a cassette and drivers checking motorway revs after a tyre change all use the same idea: speed and torque trade against each other in the ratio. The working is shown for every answer.
How to use it
- Choose what to “Work out”: “Gears or pulleys”, “Bicycle gearing” or “Car engine rpm”.
- For gears, enter the “Driving gear or pulley” and “Driven gear or pulley”, the “Input speed”, and optionally the “Input torque” and “Efficiency”.
- For a bicycle, enter the “Chainring teeth”, “Rear cog teeth”, “Wheel diameter with tyre” and your “Cadence”.
- For a car, enter the “Gear ratio”, “Final drive ratio”, “Tyre diameter” and “Road speed”.
- Pick metric or imperial “Units” for the bicycle and car modes, then read the results and the chart.
Worked example
A 15-tooth motor gear drives a 45-tooth gear: the ratio is 45 ÷ 15 = 3 : 1. At 1,450 rpm in, the output turns at 1,450 ÷ 3 = 483.3 rpm, and 20 N·m in becomes 20 × 3 × 95% = 57 N·m out. On a bicycle, a 50-tooth chainring and 17-tooth cog on a 670 mm wheel give 77.6 gear inches and 6.19 m per pedal turn, so 90 rpm is 33.4 km/h (20.8 mph). A car in a 0.85 gear with a 3.73 final drive on 26.5 in tyres turns at about 2,815 rpm at 70 mph.
Updated
Questions people ask
How do I calculate a gear ratio?
Divide the teeth on the driven gear by the teeth on the driving gear. For pulleys, divide the driven pulley's diameter by the driving pulley's. A ratio above 1 slows the output and multiplies the torque.
What are gear inches on a bicycle?
Gear inches = wheel diameter in inches × chainring teeth ÷ cog teeth. It is the size of a penny-farthing wheel that would travel as far per pedal turn, and it lets riders compare gears across wheel sizes.
What is the formula for engine rpm at a given speed?
Engine rpm = road speed in metres a minute ÷ tyre circumference × gear ratio × final drive. The tyre circumference is π × the tyre's outside diameter, which the tyre size calculator works out from the sidewall size.
Do idler gears change the ratio?
No. A gear placed between the driving and driven gears only reverses the direction; the overall ratio is still driven teeth ÷ driving teeth. Only compound gears, two gears fixed on one shaft, multiply ratios together.
How accurate are the speed and rpm results?
They assume no slip and the tyre's full unloaded diameter. Belt slip, clutch or torque-converter slip and a loaded, worn tyre all change the real figures a little, and the torque result is only as good as the efficiency entered. The horsepower and torque calculator relates the engine's torque and rpm to its power.