Pulley & Gear Ratio Calculator

About Pulley & Gear Ratio Calculator

This calculator works out how speed and torque change between two shafts linked by a belt or by meshing gears. Enter pulley diameters or gear tooth counts, optionally the driver's speed in rpm and its torque, and it returns the ratio, the driven shaft's speed and torque, and whether the drive speeds up or slows down.

The principle fits in one line. A belt, chain or pair of meshing teeth moves at the same surface speed on both wheels, so driver size × driver rpm = driven size × driven rpm. A big wheel turning a small one speeds it up; a small wheel turning a big one slows it down and multiplies force.

Speed and torque trade one for the other

Rotational power is torque times angular speed (P = τω). An ideal belt or gear pair neither creates nor loses power, so if the driven shaft turns 2.5 times slower it delivers 2.5 times the torque, and if it turns faster it delivers proportionally less. That's the whole reason gearboxes exist: an electric motor is efficient at high rpm and low torque, while a conveyor, winch or wheel needs the opposite.

The torque the tool reports assumes no losses. Real gears and belts lose some power to friction, bearing drag and belt flexing, so the actual output torque is somewhat lower. When sizing a motor, treat the calculated torque as an upper bound and leave a margin.

The ratio is displayed as 1 : (driven ÷ driver). A reading above 1 means reduction (slower, more torque); below 1 means overdrive (faster, less torque). Mechanics often quote the same thing as “2.5:1 reduction,” so don't be thrown by the order.

A bicycle as a gear-ratio lab

On a bicycle the front chainring drives and the rear cog is driven. With a 50-tooth chainring and an 11-tooth cog at a cadence of 90 rpm, the rear wheel turns 90 × 50 ÷ 11 ≈ 409 rpm. A 700×25C tire sits on a 622 mm bead seat and adds roughly 25 mm of height on each side, for an outer diameter near 672 mm and a circumference near 2.11 m. That gives 409 × 2.11 m × 60 ≈ 51.8 km/h, or about 32 mph.

Shift to a 34-tooth ring and 34-tooth cog, a common climbing gear, and the ratio is 1:1: the wheel turns at 90 rpm and you're doing about 11.4 km/h (7 mph). You're 4.5 times slower, but the same force on the pedals now puts about 4.5 times as much torque on the rear wheel, which is what gets you up a steep grade. Cyclists often compare gears by development, the distance covered per crank revolution: about 9.6 m for 50/11 and 2.1 m for 34/34. The older “gear inches” figure is the same idea using wheel diameter.

A chain drive turns both sprockets in the same direction. The "reversed rotation" shown in gear mode refers to two gears meshing directly, and the result line adds that a chain or timing belt keeps the same direction. You can also enter tooth counts in pulley mode, which shows same-direction rotation. The ratio is identical whether you use teeth or pitch diameters.

Belts slip; gears and timing belts don't

Flat belts and V-belts transmit power by friction, so under load they creep and slip slightly. The driven pulley therefore turns a little slower than the calculated rpm, and the gap grows with heavy loads and loose tension. That's why applications that need an exact ratio, such as 3D-printer axes or engine camshafts, use toothed timing belts, and why a squealing V-belt on start-up is a sign of slip rather than a noisy bearing.

For V-belts, use the pitch diameter, where the belt actually rides, not the pulley's outside diameter. The difference matters most on small pulleys, where it can noticeably shift the ratio. Gears mesh positively, so the tooth-count ratio is exact.

Worked examples

How to use it

1. Choose pulley (diameters) or gear (tooth counts).
2. Enter the driver and driven sizes.
3. Add driver rpm and torque if you want the driven shaft's values.

Frequently asked questions