Gear Ratio Calculator

Gear ratio is calculated by dividing the number of teeth on the driven gear (the output gear) by the number of teeth on the driving gear (the input gear): GR = N2 / N1. For example, if a driving gear has 20 teeth and the driven gear it meshes with has 60 teeth, the gear ratio is 60 / 20 = 3, written as 3:1. This means the driving gear must turn 3 full revolutions to make the driven gear turn once.

A 3:1 gear ratio means the driving (input) gear rotates 3 times for every 1 rotation of the driven (output) gear. This is a reduction gear train — it slows down rotational speed while multiplying torque by the same factor of 3. Conversely, if the ratio were written 1:3, the output would spin 3 times faster than the input, trading torque for speed.

Output speed is found by dividing the input speed by the gear ratio: Output Speed (RPM) = Input Speed (RPM) / GR. For example, with a 3:1 gear ratio and an input speed of 300 RPM, the output speed is 300 / 3 = 100 RPM. If the gear ratio is less than 1 (an overdrive or step-up gear train), the output speed will be higher than the input speed.

Gear ratio and torque are directly proportional in an ideal (frictionless) gear train: Output Torque = Input Torque × GR. A gear ratio greater than 1, such as 3:1, multiplies torque by 3 while dividing speed by 3 — this is why low gears in a car or bicycle make it easier to climb hills. The trade-off is fundamental: you can gain torque or gain speed, but not both, from a single gear pair.

A gear reduction occurs when the driven gear has more teeth than the driving gear (GR > 1), which slows down output speed and increases torque — common in winches, conveyor drives, and low gears. A gear increase, or overdrive, occurs when the driven gear has fewer teeth than the driving gear (GR < 1), which speeds up the output shaft but reduces torque — common in high gears used for fuel-efficient highway cruising.

Only the number of teeth (or the pitch diameter, which is proportional to tooth count for gears of the same module/pitch) determines the gear ratio — physical diameter alone is not enough unless you know the gears share the same tooth pitch. Since teeth must mesh evenly, gears of the same pitch have tooth counts proportional to their diameters, so N2/N1 and pitch-diameter ratios give the same result. This is why gear ratio calculators ask for tooth counts rather than raw size.