Calculate gear ratio and speed change from tooth counts.
Gear ratio compares the number of teeth on the driven gear to the driver gear: ratio = driven teeth ÷ driver teeth. This ratio determines both the speed change and the torque change between the two gears — and the two always move in opposite directions.
A ratio greater than 1:1 means the output shaft turns slower than the input but with more torque (a mechanical advantage). A ratio less than 1:1 does the reverse — faster output, less torque.
This same relationship applies whether you're looking at bicycle gearing, a car's differential, or an industrial gearbox — the tooth-count math is identical.
A 12-tooth driver gear turning a 36-tooth driven gear gives a 3:1 ratio — the driven gear turns 3 times slower, with roughly 3 times the torque.
Energy is conserved in an ideal gear system (minus friction losses) — power = torque × speed stays roughly constant, so a gear trading speed for torque is just redistributing the same power differently.
Multiply the ratios of each stage together — a 3:1 first stage followed by a 2:1 second stage gives a combined 6:1 overall ratio.
A single pair of external gears reverses rotation direction between driver and driven. Adding an idler gear or using an internal gear can preserve the original direction instead.