About the Gear Ratio Calculator
This gear ratio calculator works out how a pair of gears — or a two-stage compound gear train — changes speed and torque. Enter the number of teeth on the driving (input) gear and the driven (output) gear, the input speed in RPM and the input torque, and it returns the ratio, the output speed, the output torque and whether the set is a reduction or an overdrive.
It is useful for robotics and maker projects, gearbox and conveyor design, bicycle and RC-car gearing, and mechanical engineering homework. The same math applies to chain sprockets and toothed-belt pulleys: just enter the sprocket or pulley tooth counts.
Speed and torque trade off against each other: a 3:1 reduction cuts speed to one third and multiplies torque by three, minus friction losses. Spur and helical gear meshes typically run at roughly 94–99% efficiency, so an efficiency per stage is applied to the output torque. Idler gears between the driver and driven gear change direction but not the ratio.
With the default inputs, the gear ratio (input : output) is 3 : 1. Change any value above to recalculate instantly.
How to use the gear ratio calculator
- 1Count the teeth on the driving (input) gear and the driven (output) gear.
- 2Turn on the second stage if your gearbox has an intermediate shaft, and enter those tooth counts.
- 3Enter the input speed in RPM and the input torque with its unit.
- 4Set the mesh efficiency (98% is typical for spur gears, 100% for the ideal case).
- 5Read the ratio, output speed and output torque, and check the stage-by-stage table.
Formula and method
The ratio of a gear pair is the driven gear tooth count divided by the driving gear tooth count. In a compound train, where two gears share an intermediate shaft, the stage ratios multiply. Idler gears cancel out and are ignored.
Output speed is input speed divided by the overall ratio. Ideal output torque is input torque multiplied by the ratio, because power (torque × angular speed) is conserved; the calculator then multiplies by the mesh efficiency once per stage to account for friction. Power in kW is torque (N·m) × RPM × 2π ÷ 60 ÷ 1000.
- GR
- Overall gear ratio (input turns per output turn)
- T₁, T₃
- Teeth on the driving gears
- T₂, T₄
- Teeth on the driven gears
- τ
- Torque
- η
- Efficiency per gear mesh
Worked examples
12-tooth pinion driving a 36-tooth gear
The ratio is 36 ÷ 12 = 3:1. A motor at 1,800 RPM drives the output at 600 RPM, and 10 N·m of input torque becomes 30 N·m ideally, or 29.4 N·m after a 98% efficient mesh. Input power is 10 × 1,800 × 2π ÷ 60 ≈ 1.885 kW.
Two-stage reduction, 12:36 then 15:45
Each stage is 3:1, so the overall ratio is 3 × 3 = 9:1. The output turns at 1,800 ÷ 9 = 200 RPM, and torque rises to 10 × 9 × 0.98² ≈ 86.4 N·m after losses in both meshes.
Overdrive: 40 teeth driving 20, lossless
With the larger gear driving, the ratio is 20 ÷ 40 = 0.5:1, so the output spins twice as fast at 2,000 RPM with half the torque, 25 lb-ft. 50 lb-ft at 1,000 RPM is about 7.1 kW (9.5 hp).
Frequently asked questions
How do you calculate gear ratio?+
Divide the number of teeth on the driven (output) gear by the number of teeth on the driving (input) gear. A 48-tooth gear driven by a 16-tooth pinion has a 3:1 ratio.
Does a higher gear ratio mean more torque or more speed?+
A higher ratio (driven gear larger than driver) gives more torque and less speed. A ratio below 1 is an overdrive: more speed and less torque. Power stays the same apart from friction.
Do idler gears change the gear ratio?+
No. An idler between the driver and the driven gear only reverses rotation direction and changes spacing; its teeth cancel out of the ratio. Gears on a shared shaft, however, do form a compound stage.
How efficient are gears?+
Well-made spur and helical gear meshes are typically about 94–99% efficient per stage. Worm gears can range from under 50% to about 90% depending on the lead angle, so use a lower efficiency for them.
Does this work for chains and sprockets or belts?+
Yes. For chain drives and toothed timing belts, enter the sprocket or pulley tooth counts. For smooth V-belt pulleys, use the pitch diameters in place of tooth counts — the ratio math is identical.