Gears & gear trains
A gear train is a mechanical computer. By choosing tooth counts, you can achieve any rational gear ratio — and the ratio is always exact, unlike friction drives. Click and drag the gold driver gear to spin the train. Add gears, change tooth counts, and watch power flow through the chain.
ωout / ωin = (−1)n · N1 / Nn • Gear ratio = ∏ (Ndriver / Ndriven)
How gear trains work
When two gears mesh, their teeth interlock. The gear with fewer teeth spins faster. If gear A has 20 teeth and gear B has 40, then A spins twice for every revolution of B. The gear ratio is the ratio of tooth counts: 40/20 = 2:1 reduction.
Compound gear trains
By chaining multiple pairs, you multiply gear ratios. Three stages of 5:1 each give 125:1 overall. This is how clocks, car transmissions, and industrial machinery achieve large speed changes in compact packages.
Why tooth count matters
Gear ratios are always exact rational numbers. A 37:13 gear pair gives precisely 37/13, repeating exactly after 37 × 13 = 481 teeth of engagement. This exactness is why mechanical clocks can keep time — each gear ratio is a precise fraction, and fractions compose perfectly. Gears are, in a real sense, mechanical computers that multiply rational numbers.
Direction of rotation
Each meshing pair reverses direction. An odd number of gears in a simple train means the output spins opposite the input; an even number means they spin the same way. Toggle the direction arrows to see this clearly.