Gear Ratio Calculator

Gear ratio: i = Z_driven / Z_driver

The gear ratio ties together the tooth counts, speeds and torques of two meshing gears: i = Zdriven / Zdriver = Ndriver / Ndriven = Tdriven / Tdriver. When the ratio is above 1 you have a reduction, which multiplies torque and slows the output. Below 1 it's a multiplication (overdrive). Power barely changes (P = T · ω), apart from mechanical losses of roughly 95–98% per stage on spur gears. Example: a road bike with a 53-tooth chainring driving a 12-tooth sprocket sits at i = 12/53 ≈ 0.226 at the wheel, so one turn of the pedals spins the rear wheel 53/12 ≈ 4.4 times — that's the fast top end. Feed 1800 rpm at 5 N·m into a 20/60 reducer (i = 3) running at 95% efficiency and you get 600 rpm and 5 · 3 · 0.95 = 14.25 N·m out the other side.

Applications: gearboxes, bicycles, robotics

You'll find it in automotive transmissions (1st gear is often around 3.5:1, the final drive near 4:1), industrial worm and planetary reducers, bicycle drivetrains (Shimano, SRAM), and DC motors with gearbox for robotics. Take a small motor at 10 000 rpm behind a 100:1 gearhead: it puts out 100 rpm with 100× the torque, losses aside, which is plenty to turn a robot wheel or a 3D-printer extruder.

FAQ

Reduction or multiplication? More teeth on the driven gear than on the driver gives you a reduction: more torque, less speed. Fewer teeth on the driven gear flips it to overdrive, with more speed and less torque.

Why isn't power conserved exactly? Friction, oil churn and losses at the meshing teeth eat up 2–5% on each stage. So a 3-stage reducer at 95% per stage only passes through 0.95³ ≈ 86% of the input power.

Compound trains? Just multiply the ratios. A 3:1 stage in series with a 4:1 stage gives 12:1 overall, which helps when a single stage would call for gears that are too big to be practical.