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Free Gear Ratio Calculator

This gear ratio calculator finds the ratio between two meshing gears from their tooth counts, then uses it to work out the output shaft speed and the torque multiplication of the gear pair. Enter the number of teeth on the driver (input) gear and the driven (output) gear, and optionally an input speed in RPM, and the calculator returns the gear ratio in reduced 'A : B' form, its decimal value, the output speed and the ideal torque multiplier. Gear ratios are central to almost every mechanical drivetrain — from bicycles, drills and conveyor belts to car gearboxes and clock movements — because they let a designer trade rotational speed for torque (or the reverse) without changing the input power.

Enter the driver (input) and driven (output) gear tooth counts. RPM is optional. Ratio = driven ÷ driver.

Results
Gear ratio3 : 1
Ratio (decimal)3 : 1
Torque multiplier× 3
Output speed500 RPM

Gear ratio = driven teeth ÷ driver teeth. A ratio above 1 is a reduction (more torque, lower speed); below 1 is an overdrive (less torque, higher speed). Output RPM = input RPM ÷ ratio, and ideal output torque = input torque × ratio (frictionless).

Quick answer

Gear ratio equals the number of teeth on the driven (output) gear divided by the number of teeth on the driver (input) gear: ratio = driven ÷ driver. For example, a 12-tooth driver turning a 36-tooth driven gear gives 36 ÷ 12 = 3, a 3:1 reduction. The output speed is the input speed divided by the ratio (1500 RPM ÷ 3 = 500 RPM), and the ideal output torque is the input torque multiplied by the ratio (×3), since power is conserved.

Formula & method

ratio = N_driven ÷ N_driver
  • N_driver — Number of teeth on the driver (input) gear
  • N_driven — Number of teeth on the driven (output) gear

N_driver = teeth on the input (driver) gear, N_driven = teeth on the output (driven) gear. A ratio > 1 is a speed reduction (torque gain); a ratio < 1 is an overdrive (speed gain, torque loss). Driver teeth cannot be 0.

RPM_out = RPM_in ÷ ratio    •    Torque_out = Torque_in × ratio

Output speed falls and output torque rises by the same factor in an ideal (lossless) gear set, because power = torque × angular speed is conserved. Real gears lose a few percent to friction.

ratio_total = ratio_1 × ratio_2 × … × ratio_n

For a compound gear train (gears in series), multiply the individual stage ratios. Idler gears between two gears change direction but not the overall ratio.

Examples

Example 1: Speed-reduction gear pair (default)
Input
Driver = 12 teeth, Driven = 36 teeth, Input = 1500 RPM
Result
Ratio = 3 : 1, Output = 500 RPM, Torque ×3
Why
Gear ratio = driven ÷ driver = 36 ÷ 12 = 3, written 3 : 1. Output speed = 1500 ÷ 3 = 500 RPM, so the output shaft turns slower. Because power is conserved, the output torque is multiplied by 3. This is a classic reduction used to drive a heavy, slow-moving load from a fast motor.
Example 2: Overdrive gear pair (small driven gear)
Input
Driver = 40 teeth, Driven = 20 teeth, Input = 3000 RPM
Result
Ratio = 0.5 : 1, Output = 6000 RPM, Torque ×0.5
Why
Ratio = 20 ÷ 40 = 0.5, an overdrive because the driven gear is smaller. Output speed = 3000 ÷ 0.5 = 6000 RPM, so the output spins twice as fast as the input. Torque is multiplied by 0.5, meaning it is halved — you trade torque for speed.
Example 3: Bicycle-style ratio with a different input speed
Input
Driver = 15 teeth, Driven = 45 teeth, Input = 1750 RPM
Result
Ratio = 3 : 1, Output = 583.333 RPM, Torque ×3
Why
Ratio = 45 ÷ 15 = 3 (3 : 1). Output speed = 1750 ÷ 3 = 583.333 RPM. The torque multiplier is 3. Note that 15:45 reduces to the same 1:3 tooth proportion as 12:36, so the ratio is identical even though the gears are larger.
Example 4: Compound (two-stage) gear train
Input
Stage 1: 14 → 42 teeth, Stage 2: 12 → 48 teeth, Input = 2400 RPM
Result
Total ratio = 12 : 1, Output = 200 RPM, Torque ×12
Why
Stage 1 ratio = 42 ÷ 14 = 3; stage 2 ratio = 48 ÷ 12 = 4. Multiply the stages: total ratio = 3 × 4 = 12. Output speed = 2400 ÷ 12 = 200 RPM and torque is multiplied by 12. To get this in the calculator, enter one stage at a time (e.g. 14 and 42), then feed the resulting 800 RPM into the second stage.

When to use this tool

  • Designing or checking a gearbox, drivetrain or speed reducer to hit a target output RPM from a known motor speed.
  • Estimating how much a gear pair multiplies (or reduces) torque before selecting a motor or sizing a shaft.
  • Choosing sprocket or pulley sizes for bicycles, chain drives or belt drives, where the tooth-count ratio works the same way.
  • Calculating the overall ratio of a compound gear train by combining the ratios of each stage.
  • Teaching or learning the relationship between gear teeth, rotational speed and torque in physics or engineering classes.

Common mistakes

  • Inverting the formula. The gear ratio is driven ÷ driver (output teeth over input teeth). Dividing driver by driven gives the speed ratio instead and will report a reduction as an overdrive.
  • Confusing the driver and driven gears. The driver is the gear receiving power (connected to the motor or input shaft); the driven gear delivers the output. Swapping them inverts the ratio.
  • Expecting torque and speed to both increase. A gear set conserves power, so any gain in torque comes at an equal loss of speed, and vice versa. You cannot multiply both at once.
  • Adding stage ratios in a compound train instead of multiplying them. Two 3:1 stages give 3 × 3 = 9:1 overall, not 6:1.
  • Counting an idler gear as part of the ratio. An idler between the driver and driven gear reverses the rotation direction but does not change the overall gear ratio.

Frequently asked questions

How do you calculate a gear ratio from teeth?

Divide the number of teeth on the driven (output) gear by the number of teeth on the driver (input) gear. For instance, a 36-tooth gear driven by a 12-tooth gear has a ratio of 36 ÷ 12 = 3, written as 3:1. The ratio tells you how many turns of the driver are needed for one turn of the driven gear.

What does a 3:1 gear ratio mean?

A 3:1 ratio means the driver gear must rotate three times for the driven gear to rotate once. The output shaft therefore turns at one-third of the input speed but delivers three times the torque (minus small friction losses). It is a speed reduction, commonly used to drive heavy or slow loads from a fast motor.

Does a higher gear ratio mean more torque or more speed?

A higher ratio (greater than 1) means more torque and less speed — the output turns slower than the input. A ratio below 1, called an overdrive, means more speed and less torque. Because power is conserved through the gears, you always trade one for the other; you can never gain both at the same time.

How do I find the output RPM from a gear ratio?

Divide the input RPM by the gear ratio: output RPM = input RPM ÷ ratio. With a 4:1 reduction and a 2000 RPM motor, the output is 2000 ÷ 4 = 500 RPM. For an overdrive ratio like 0.5, the output spins faster: 2000 ÷ 0.5 = 4000 RPM.

How do you calculate the ratio of a compound gear train?

Multiply the ratios of each gear pair in the train. If the first stage is 3:1 and the second is 4:1, the total ratio is 3 × 4 = 12:1. Idler gears placed between two gears change the direction of rotation but do not affect the overall ratio.

Is the gear ratio the same as the speed ratio?

They are reciprocals of each other. The gear ratio (driven ÷ driver) describes torque multiplication, while the speed ratio (driver ÷ driven) describes how output speed relates to input speed. A 3:1 gear ratio corresponds to a 1:3 speed ratio, meaning the output runs at one-third of the input speed.

Sources & references

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