Gear Ratio Calculator
Find gear ratio, output speed and output torque for a pair of gears.
About the Gear Ratio Calculator
Enter the teeth on the driving gear and the driven gear, the input speed and torque, and the efficiency. The calculator gives the gear ratio and the output speed and torque.
The gear ratio is driven teeth ÷ driving teeth. Speed divides by the ratio and torque multiplies by it, less friction losses (spur gears are typically 94–98% efficient). For a train of gears, multiply the individual ratios.
The formula
Ratio = driven ÷ driver; rpm out = rpm in ÷ ratio; torque out = torque in × ratio × efficiency
Worked example
A 12-tooth gear driving a 36-tooth gear at 1,500 rpm and 10 N·m
- Ratio: 36 ÷ 12 = 3 : 1
- Output speed: 1,500 ÷ 3 = 500 rpm
- Output torque: 10 × 3 × 0.98 = 29.4 N·m
Questions people ask
Do idler gears change the ratio?
No, only the direction of rotation.
What about pulleys?
Use diameters in place of tooth counts.
What about bicycle gears?
Chainring teeth ÷ sprocket teeth gives wheel turns per pedal turn: 48 ÷ 16 = 3.