How do I calculate a gear ratio?

Divide the teeth on the driven (output) gear by the teeth on the driver (input) gear. A 42-tooth gear driven by a 14-tooth pinion is 42 ÷ 14 = 3:1. A ratio above 1 means the output turns slower than the input and with more torque; below 1 means faster and with less.

How does gearing change speed and torque?

They trade off. A 3:1 reduction turns the output at a third of the input speed but multiplies the torque roughly threefold, minus losses. Overdrive works the other way — an output faster than the input gives back speed at the cost of torque. The tool shows both from your input figures.

What is a compound or two-stage ratio?

When two gear pairs sit in series, the overall ratio is the two multiplied together. A 3:1 followed by a 2:1 is 6:1 overall. Fill in the second pair here and the tool multiplies them; leave it blank and it just uses the first stage.

Which gear is the driver?

The one the power comes in on — the motor or engine side. The driven gear is the one it turns, on the output side. Getting them the right way round matters, because swapping them inverts the ratio and turns a reduction into an overdrive.

Gear ratio calculator

Dents, roue menante (étage 1)

Dents, roue menée (étage 1)

Dents, roue menante (étage 2, facultatif)

Dents, roue menée (étage 2, facultatif)

Vitesse d’entrée (facultatif)

RPM

Couple d’entrée (facultatif)

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This is the arithmetic of tooth counts and an ideal, loss-free drive. Real gearboxes lose a few percent to friction, and torque a shaft can actually carry is a mechanical limit this tool says nothing about. Use it to plan the ratio, not to rate the hardware.

Enter the tooth counts for the driver and driven gears and the tool gives the ratio. Add a second pair for a compound drive, and an input speed or torque, to see how the output turns and pulls once the gearing has had its say.

Exemple détaillé

A 14-tooth pinion driving a 42-tooth gear is 42 ÷ 14 = 3:1. Feed it 1,800 RPM and the output turns 1,800 ÷ 3 = 600 RPM, while 10 N·m in becomes about 30 N·m out. Add a 2:1 second stage and the overall ratio is 6:1 — 300 RPM and roughly 60 N·m. In imperial it is the same sum: 7.4 ft·lb in (10 N·m) is about 22 ft·lb out at 3:1 and 44 ft·lb at 6:1.

Sur le chantier

Chain drive on a conveyor. A 12-tooth sprocket on a 1,725 RPM motor driving a 48-tooth on the head shaft: 48 ÷ 12 = 4:1, so the shaft turns 431 RPM. Type the teeth as driver and driven; the input speed is off the motor plate.

Belts and pulleys — same sum, different numbers. The tool asks for teeth, but a pulley drive works on diameters: a 2 in motor pulley to an 8 in driven pulley is 8 ÷ 2 = 4:1, exactly as if they were 2 and 8 teeth. Metric pulleys are no different — 50 mm to 200 mm is 200 ÷ 50 = 4:1; keep both in the same unit. Type the diameters in the teeth fields and everything downstream is right.

Torque goes up as speed comes down. The 4:1 chain drive that quarters the speed quadruples the torque: 10 N·m in, 40 N·m out (7.4 ft·lb in, 29.5 ft·lb out) — less what the chain and bearings eat. That is the whole point of the reduction, and why the output shaft and its key are bigger than the motor's.

Exercez-vous

Quick referencefor drives

Rapport: driven ÷ driver — teeth, or pulley diameters
Speed: output RPM = input ÷ ratio
Couple: output = input × ratio, less losses
Stages: multiply — 3:1 then 2:1 is 6:1
Common motor speeds: 1,725 and 3,450 RPM (60 Hz nameplates) · 1,425 and 2,850 (50 Hz)
Belt speed: π × pulley diameter × RPM — ft/min with the diameter in feet, m/min with it in metres
Torque units: out in the unit you put in · 1 ft·lb = 1.356 N·m = 12 in·lb

Mistakes to catchbefore you trust the number

Swapping driver and driven — if the ratio comes out under 1 when you expected a reduction, the tooth counts are in the wrong fields.
Multiplying stage ratios by adding them: a 3:1 stage into a 3:1 stage is 9:1, not 6:1.
Reading output torque from the ratio alone without allowing for the losses; the tool's torque is the ideal figure and a real gearbox delivers a little less.

La formule

ratio = driven ÷ driver · output RPM = input ÷ ratio · output torque = input × ratio

Speed and torque are inverse across a gear pair: whatever the ratio takes off the speed it adds to the torque, in an ideal drive. Stages in series multiply, so a compound ratio is simply the product of each pair's driven-over-driver.

Questions

How do I calculate a gear ratio?: Divide the teeth on the driven (output) gear by the teeth on the driver (input) gear. A 42-tooth gear driven by a 14-tooth pinion is 42 ÷ 14 = 3:1. A ratio above 1 means the output turns slower than the input and with more torque; below 1 means faster and with less.
How does gearing change speed and torque?: They trade off. A 3:1 reduction turns the output at a third of the input speed but multiplies the torque roughly threefold, minus losses. Overdrive works the other way — an output faster than the input gives back speed at the cost of torque. The tool shows both from your input figures.
What is a compound or two-stage ratio?: When two gear pairs sit in series, the overall ratio is the two multiplied together. A 3:1 followed by a 2:1 is 6:1 overall. Fill in the second pair here and the tool multiplies them; leave it blank and it just uses the first stage.
Which gear is the driver?: The one the power comes in on — the motor or engine side. The driven gear is the one it turns, on the output side. Getting them the right way round matters, because swapping them inverts the ratio and turns a reduction into an overdrive.

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