October 25, 2026 · DIY & Workshop · 6 min read

Gear Ratios Explained: Trading Torque for Speed

A gear train is a torque-speed marketplace: you can buy more torque with speed, or more speed with torque, but you never get a discount. Understanding the exchange rate — the gear ratio — is the key to sizing every drive from a bicycle to an industrial gearbox.

The basic ratio

When two gears mesh, the ratio is simply the tooth counts:

A 12-tooth pinion driving a 48-tooth gear gives a ratio of 4:1. The output turns at one quarter of the input speed — and, ignoring losses, delivers four times the input torque. Because meshing gears share the same tooth pitch, you can just as well use the pitch diameters: i = D₂ ÷ D₁.

Speed and torque after the gears

• Output speed: n₂ = n₁ ÷ i. At 1,750 RPM input with a 4:1 reduction, the output turns 437.5 RPM.
• Output torque: T₂ = T₁ × i × η, where η is transmission efficiency. Real gears are not free: spur gear pairs run about 96–98% per mesh, so a 4:1 pair typically delivers closer to 3.8× the torque.
• Transmitted power (P = T × ω) stays roughly constant — that's the whole point. Gears reshape power between speed and torque; they don't create it.

Compound gear trains

When you stack pairs of gears, multiply the ratios. A 3:1 first stage feeding a 4:1 second stage gives 12:1 overall, and efficiency multiplies too: 0.97 × 0.97 ≈ 0.94. This is why gearboxes with many stages run warm and why worm drives (single mesh, big reduction) can be dramatically inefficient — 60–70% is common, though they gain the ability to self-lock.

Choosing a ratio in practice

Start from the load, not the motor. Work out the torque and speed your application actually needs — a winch, a conveyor, a mixer — then pick a motor whose continuous torque and speed bracket the target and use the gears to make up the difference. Leaving margin matters: running a gear train near its torque limit shortens life through tooth wear and backlash growth.

Watch for the classic mistakes: forgetting a second mesh reverses rotation direction (idlers flip it back), mixing module or diametral pitch between gears that must mesh, and trusting nameplate motor torque at startup — most motors deliver far less before they reach speed.

If your power gets to the load through pulleys instead of meshing teeth, Pulley Belts: How to Calculate the Right Belt Length covers the belt side of the same trade-off.