Gears trade speed for torque. A small gear driving a large one turns the output slower but with more twisting force; a large gear driving a small one does the opposite. The trade is set by one number, the gear ratio. This calculator finds the ratio for a simple pair or a compound train, then works out the output speed, the output torque after friction, the power flowing through, and whether the output turns the same way as the input.
How to use the gear ratio calculator
- Choose Two gears or Compound gear train.
- For two gears, enter the driving (input) and driven (output) tooth counts, plus any idler gears between them.
- For a train, list each stage as driver:driven teeth separated by commas, for example 12:36, 15:45.
- Enter the input speed in rpm and, optionally, the input torque.
- Set the efficiency per mesh — about 98–99% for well-made spur and helical gears.
Gear ratio formulas
Meshing gears must have the same tooth size, so the number of teeth is proportional to the pitch diameter, and the ratio can equally be computed from pitch diameters. A ratio above 1 is a reduction (slower, stronger); below 1 is an overdrive (faster, weaker).
Worked examples
A 12-tooth pinion driving a 36-tooth gear (the default)
Ratio = 36 ÷ 12 = 3:1. At 1,800 rpm in, the output turns 1,800 ÷ 3 = 600 rpm, in the opposite direction.
With 10 N·m of input torque and a 98% efficient mesh, the output torque is 10 × 3 × 0.98 = 29.4 N·m. The input power is 10 N·m × 188.5 rad/s = 1.885 kW, of which 1.847 kW reaches the output.
A two-stage reduction. Stages of 12:36 and 15:45 give 3 × 3 = 9:1. At 1,800 rpm in, the intermediate shaft turns at 600 rpm and the output at 200 rpm. With two meshes, the output turns the same way as the input.
Ratios in everyday machines
| Machine | Typical ratio | What it does |
|---|---|---|
| Bicycle, 34-tooth chainring to 34-tooth sprocket | 1:1 | Easy climbing gear |
| Bicycle, 50 to 11 | 1:4.55 (overdrive) | Fast flat-road gear |
| Car differential | 3:1 to 4.1:1 | Final reduction to the wheels |
| Cordless drill gearbox | about 10:1 to 50:1 | High torque from a fast motor |
| Analog clock (minute to hour hand) | 12:1 | Hour hand turns once per 12 hours |
On a bicycle the chainring drives the rear sprocket, so a 50-tooth ring and 11-tooth sprocket give 11 ÷ 50 = 0.22 by this calculator’s convention, or 1:4.55 — the wheel turns 4.55 times per pedal stroke.
Choosing a ratio in practice
Start from the speed or torque the output needs and the motor’s rated speed, then divide. Single spur-gear stages are usually kept below about 6:1 or 7:1 so the pinion is not too small; larger reductions use two or three stages, planetary gearboxes or worm gears. Worm drives reach 20:1 to 100:1 in one stage but with efficiencies that can fall well below 90%, so set the efficiency field accordingly. Gear pairs whose tooth counts share no common factor (a “hunting tooth” ratio such as 13:37) spread wear evenly across all teeth.
For the torque produced by a force on a lever, or torque from horsepower and rpm, see the torque calculator. To convert between N·m, lb·ft and other torque units, use the torque converter, and to simplify a tooth ratio, the ratio simplifier.
Rotating machinery can cause serious injury. These figures are estimates; follow the gear manufacturer's ratings for load, speed and lubrication, and guard all moving parts.
Frequently asked questions
How do you calculate a gear ratio?
Divide the number of teeth on the driven (output) gear by the teeth on the driving (input) gear. A 12-tooth gear driving a 36-tooth gear has a ratio of 36 ÷ 12 = 3, written 3:1, so the output turns once for every three input turns.
How does a gear ratio affect torque and speed?
Speed divides by the ratio and torque multiplies by it, minus friction. With a 3:1 reduction, 1,800 rpm becomes 600 rpm and 10 N·m becomes 30 N·m in an ideal gearset, or 29.4 N·m at 98% mesh efficiency. Power stays the same apart from losses.
How do I calculate a compound gear train?
Multiply the ratios of each stage. Gears that share a shaft turn together, so each driven gear sets the speed of the next driver. Two stages of 12:36 and 15:45 give 3 × 3 = 9:1 overall.
Does an idler gear change the ratio?
No. An idler between two gears cancels out — its teeth appear in both the numerator and denominator — but it reverses the direction of rotation and adds one more mesh of friction loss.
Does this work for pulleys and sprockets?
Yes. Use sprocket tooth counts or pulley diameters in place of gear teeth. The difference is direction: a belt or chain keeps both shafts turning the same way, while two meshing external gears turn in opposite directions.