Gear Teeth Ratio Calculator
Compute the gear ratio from driver and driven tooth counts, plus the output speed and torque change of the pair.
How it works
Gear ratio = driven teeth ÷ driver teeth · Output rpm = input rpm ÷ ratio · Torque ×= ratio
The gear ratio is the ratio of the driven (output) gear’s teeth to the driver (input) gear’s teeth. A ratio above 1 is a reduction: the output turns slower but with proportionally more torque, since power (speed × torque) is conserved apart from friction. A ratio below 1 is an overdrive, trading torque for speed. Idler gears between the two change direction but not the overall ratio.
Worked example
A 15-tooth driver turning a 45-tooth driven gear gives a ratio of 45 ÷ 15 = 3:1. At 1,500 rpm in, the output spins at 1,500 ÷ 3 = 500 rpm, while torque is multiplied by 3 — slower but three times stronger.
Sources: Gear train — Wikipedia
Frequently asked questions
Which gear is the driver?
The driver is the input gear connected to the power source (motor, pedal, engine); the driven gear is the output that does the work. Swapping which is which inverts the ratio, turning a reduction into an overdrive.
Why does a reduction increase torque?
Because mechanical power (speed × torque) is roughly conserved. If a 3:1 reduction cuts the output speed to a third, the torque must roughly triple to keep the power the same, minus small friction losses.
Do idler gears change the ratio?
No. An idler gear placed between the driver and driven gears reverses the output’s direction but leaves the overall ratio unchanged, because its own ratios cancel out across the train.
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This calculator is for educational purposes. Double-check important results before acting on them.