About this calculator
Two meshing gears trade speed for turning force. The gear ratio is the teeth on the driven gear divided by the teeth on the driver.
Enter the number of teeth on each gear and the input speed in revolutions per minute (rpm). Add the input torque to see the output torque.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
20 teeth driving 40 teeth at 1,000 rpm
- Gear ratio (driven : driver)
- 2 : 1
- Output speed
- 500 rpm
- Speed change
- Slower, with more torque (a reduction)
- Output torque (ideal)
- 10
A 20-tooth driver turning a 40-tooth gear gives a ratio of 2:1, so 1,000 rpm in becomes 500 rpm out.
Show the working
- Ratio = teeth on the driven gear ÷ teeth on the driver = 40 ÷ 20 = 2.
- Output speed = input speed ÷ ratio = 1,000 ÷ 2 = 500 rpm.
- Torque goes up by the ratio (ignoring friction losses): 5 × 2 = 10.
Overdrive: 40 teeth driving 20
- Gear ratio (driven : driver)
- 0.5 : 1
- Output speed
- 2,000 rpm
- Speed change
- Faster, with less torque (an overdrive)
A 40-tooth driver turning a 20-tooth gear gives a ratio of 0.5:1, so 1,000 rpm in becomes 2,000 rpm out.
Show the working
- Ratio = teeth on the driven gear ÷ teeth on the driver = 20 ÷ 40 = 0.5.
- Output speed = input speed ÷ ratio = 1,000 ÷ 0.5 = 2,000 rpm.
- Torque multiplies by the ratio while speed divides by it (ignoring friction): you trade speed for turning force.
Bike: 50 teeth chainring, 25 sprocket at 60 rpm
- Gear ratio (driven : driver)
- 0.5 : 1
- Output speed
- 120 rpm
- Speed change
- Faster, with less torque (an overdrive)
A 50-tooth driver turning a 25-tooth gear gives a ratio of 0.5:1, so 60 rpm in becomes 120 rpm out.
Show the working
- Ratio = teeth on the driven gear ÷ teeth on the driver = 25 ÷ 50 = 0.5.
- Output speed = input speed ÷ ratio = 60 ÷ 0.5 = 120 rpm.
- Torque multiplies by the ratio while speed divides by it (ignoring friction): you trade speed for turning force.
The formulas
- Ratio = driven teeth ÷ driver teeth
- Output speed = input speed ÷ ratio
- Output torque = input torque × ratio (ideal, ignoring friction)
Reduction or overdrive
A ratio above 1 (a small gear driving a big one) is a reduction: the output turns slower with more torque, like a low gear on a car. A ratio below 1 is an overdrive: faster but weaker. A ratio of 1 changes nothing.
Chains and belts
The same calculation works for a chain or belt drive between two sprockets or pulleys, using teeth for sprockets or diameters for pulleys. For a bike, divide the chainring teeth by the rear sprocket teeth to compare gears.
Frequently asked questions
How do I calculate a gear ratio?
Divide the teeth on the driven gear by the teeth on the driver.
What does a 2:1 ratio mean?
The output turns half as fast with twice the torque.
Does the gear size or tooth count matter?
Teeth count gives the ratio. Meshing gears must have the same tooth size, so more teeth means a bigger gear.
Is the output torque exact?
It is the ideal value. Friction in real gearboxes reduces it by a few per cent.
Can I chain several pairs?
Yes: multiply the ratios of each pair.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.