Gear Ratio Simulator
Change how many teeth each gear has and watch them spin at their real relative speeds. It's the same trade-off as the lever — you're never getting more speed and more torque for free, only trading one for the other, which is exactly what happens inside a bicycle's gears or a car's transmission.
The math behind it
Where two gears mesh, their teeth move past that contact point at exactly the same speed — so a gear with fewer teeth has to spin faster to keep up with a bigger neighbor, the same way a small wheel has to spin faster than a big one to cover the same ground. That gives a simple ratio:
teeth(input) × speed(input) = teeth(output) × speed(output)
Torque works the opposite way. Ignoring friction, the power going in has to equal the power coming out — and power is torque times speed. So whatever speed a gear pair loses, it gains back in torque, in the same proportion: output torque = input torque × (output teeth ÷ input teeth). A small gear driving a big one trades speed for torque — more turning force, delivered slower. That's the entire idea behind a bicycle's low gear for climbing hills, or a car downshifting to accelerate.
This simulator ignores friction — real gear trains lose a little power to heat wherever the teeth rub — and draws teeth as simple straight spokes rather than the precisely curved shape (called an involute profile) real gear teeth use to mesh smoothly without slipping. The speed and torque trade-off it shows, though, is exact.
More on gears as a concept →