Gear Ratio Calculator
Find the gear ratio of a two-gear pair from the tooth counts. Enter the driver (input) and driven (output) teeth, plus an optional input rpm, to get the ratio, the output speed, and how much torque is multiplied.
Example: with Driver (input) gear teeth 12 · Driven (output) gear teeth 36 · Input speed (rpm, optional) 3000 → Gear ratio: 3.00:1.
- Output speed1,000 rpm output
- Torque / speed effect3.00× torque, 0.333× speed
Computed by the calculator below using its default values. Change any input to see your own numbers.
Gear ratio is driven teeth divided by driver teeth. A 36-tooth gear driven by a 12-tooth gear is a 3:1 reduction: a third of the speed, three times the torque.
What the ratio tells you
Gear ratio is the driven gear's tooth count divided by the driver's. A ratio above 1 is a reduction: the output turns slower than the input but with proportionally more torque. A 3:1 reduction spins the output at one-third the speed and roughly triples the torque. A ratio below 1 is an overdrive - faster output, less torque - which is how a top gear lets an engine loaf at highway speed.
Speed and torque always trade in opposite directions because power is conserved (minus friction). You never get more of both from a gear pair; you convert one into the other.
Single pairs and gear trains
This tool covers one meshing pair. In a multi-stage gear train, the overall ratio is the product of each stage's ratio, so two 3:1 reductions in series give 9:1. Idler gears between the driver and driven change rotation direction but not the ratio, since their teeth cancel out. Real drives also lose a few percent to friction and have backlash, so treat the output rpm as an ideal figure.
How it’s calculated
Gear ratio = driven (output) teeth / driver (input) teeth, reported as ratio:1. Output speed = input rpm / ratio. Torque multiplication equals the ratio; output-to-input speed equals 1 / ratio. Friction losses and backlash are ignored.
Covers a single gear pair. Compound gear trains multiply each stage, and real output loses a few percent to friction; this ignores backlash and efficiency.
What a gear ratio does
| Ratio | Type | Effect |
|---|---|---|
| 4.00:1 | Deep reduction (1st gear) | 4x torque, 1/4 output speed |
| 2.00:1 | Reduction | 2x torque, 1/2 speed |
| 1.00:1 | Direct drive | Torque and speed unchanged |
| 0.80:1 | Overdrive | 0.8x torque, 1.25x speed |
Output speed = input rpm / ratio; torque multiplies by the ratio, minus real-world friction losses.
Common mistakes
- Dividing driver by driven and inverting the ratio - it is driven over driver.
- Expecting more speed and more torque at once; a gear pair trades one for the other.
- Thinking an idler gear changes the ratio; it only reverses direction.
- Applying a single-pair result to a multi-stage train, where ratios multiply.
Frequently asked questions
What is the gear ratio formula?
Gear ratio = number of teeth on the driven (output) gear divided by the number of teeth on the driver (input) gear. A 36-tooth driven gear on a 12-tooth driver is 36/12 = 3:1.
Does a higher ratio mean more torque or more speed?
More torque and less speed. A ratio above 1 (reduction) multiplies torque by the ratio and divides output speed by it. A ratio below 1 (overdrive) does the reverse.
How do I find output rpm?
Divide input rpm by the ratio. At a 3:1 reduction, 3,000 input rpm becomes 1,000 output rpm.
Do idler gears change the ratio?
No. An idler gear between the driver and driven reverses the output's direction of rotation but leaves the overall ratio unchanged, because its teeth appear in both the numerator and denominator.
How do I handle multiple gears in series?
Multiply the individual ratios. Two 2:1 reductions in a row make an overall 4:1 reduction. This calculator handles one pair, so compute each stage and multiply.