Gear Ratio Calculator
Enter teeth counts for the driver (input) and driven (output) gears to get the gear ratio, output speed and output torque. Add up to three stages for a gear train, and optionally compute vehicle speed from engine RPM and tire size.
Vehicle speed (optional)
Gear ratio formulas
N is the number of teeth, n is rotational speed, T is torque and η is efficiency (about 0.98 per spur or helical mesh, much lower for worm gears). A ratio above 1 is a reduction: the output turns slower with more torque. Below 1 is an overdrive. Idler gears between driver and driven do not change the ratio, only the direction. In a compound train, each stage's driven gear shares a shaft with the next stage's driver, so the stage ratios multiply. For sprockets and toothed belts use tooth counts the same way; for plain pulleys use diameters.
Worked examples
Single stage: a 12-tooth pinion drives a 36-tooth gear. i = 36/12 = 3:1. A 1750 rpm motor gives 1750/3 = 583.3 rpm and 10 N·m becomes 30 N·m (ideal).
Two stages: 15→45 then 12→48: i = 3 × 4 = 12:1. At 1750 rpm the output is 145.8 rpm; with 98% efficiency per mesh (η ≈ 0.96) 10 N·m becomes 10 × 12 × 0.96 = 115.2 N·m.
Vehicle: 265/70R17 tires are 17 + 2 × 265 × 0.70/25.4 = 31.61 in tall. With a 3.73 axle in a 1:1 top gear at 2000 rpm: 2000 × 31.61 × π × 60 / (3.73 × 63,360) = 50.4 mph (81.1 km/h).
Gear ratio reference table
| Driver teeth | Driven teeth | Ratio | Output @ 1750 rpm in | Torque @ 10 N·m in |
|---|---|---|---|---|
| 12 | 36 | 3:1 | 583 rpm | 30 N·m |
| 15 | 45 | 3:1 | 583 rpm | 30 N·m |
| 20 | 40 | 2:1 | 875 rpm | 20 N·m |
| 10 | 50 | 5:1 | 350 rpm | 50 N·m |
| 17 | 51 | 3:1 | 583 rpm | 30 N·m |
| 24 | 72 | 3:1 | 583 rpm | 30 N·m |
| 30 | 15 | 0.5:1 | 3,500 rpm | 5 N·m |
| 40 | 20 | 0.5:1 | 3,500 rpm | 5 N·m |
Ideal gears (100% efficiency).
Frequently asked questions
How do you calculate gear ratio?
Divide the number of teeth on the driven (output) gear by the number of teeth on the driver (input) gear. A 12-tooth gear driving a 36-tooth gear is 36/12 = 3:1.
How does gear ratio affect speed and torque?
Output speed is input speed divided by the ratio, and output torque is input torque multiplied by the ratio (minus friction losses). Power stays the same apart from losses.
How do I calculate the ratio of a gear train?
Multiply the ratios of each stage. Idler gears are ignored because their teeth cancel out.
What does a 3.73 gear ratio mean?
In a car axle, 3.73 means the driveshaft turns 3.73 times for each wheel revolution. Higher numbers give quicker acceleration and lower top speed at a given RPM.
Does tire size change the effective gear ratio?
Yes. Larger tires travel farther per revolution, so the vehicle goes faster at the same RPM, which acts like a numerically lower (taller) gear ratio.