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Gears transfer rotation between shafts while changing speed and torque. The ratio of tooth counts sets the speed change: a driven gear with twice as many teeth turns at half the speed but delivers roughly twice the torque.
Output speed and torque from gear tooth counts.
ratio = N_driven / N_driver ω_out = ω_in / ratio τ_out = τ_in × ratio
N is the tooth count. A ratio above 1 is a reduction: lower speed, higher torque. Real gear trains lose 1–3% per stage to friction.
| Symbol | Meaning |
|---|---|
| N_driver, N_driven | Tooth counts of the input and output gears. |
| ω_in, ω_out | Input and output angular speeds. |
| τ_in, τ_out | Input and output torques. |
The ratio is 2, so the output turns at 500 rpm with twice the input torque, minus friction losses. This is a typical first gear in a gearbox.
Continue with the Lever Calculator, Mechanical Advantage Calculator, or the Pulley System Calculator — or browse more simple machines tools and all physics calculators.
It increases speed and reduces torque. A ratio below 1 is an overdrive, useful for cruising at low engine rpm.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026