Gear Ratio Calculator
Work out the ratio of a simple or compound gear train and see the output speed and torque, including mesh losses. Switch to vehicle mode to find road speed at any rpm from gear ratios, final drive and tire size.
Stages (driven gear of one stage shares a shaft with the next driver)
| Stage | Driver → driven | Stage ratio | Cumulative | Shaft speed | Torque |
|---|
Speed in each gear (mph)
How to use the Gear Ratio Calculator
- Enter the input speed and torque of the motor or engine and the efficiency per gear mesh.
- Enter the teeth on the driver and driven gear for each stage; add stages for a compound train.
- Press Calculate ratio to see the total ratio, output rpm, torque and direction.
- For a car or bike, open Vehicle speed and enter engine rpm, gear ratios, final drive and tire size.
- Read the speed in the selected gear, the rpm at cruise speed and the full gear speed chart.
Gear ratio, speed and torque formulas
- Stage ratio = driven teeth ÷ driver teeth
- Total ratio = ratio₁ × ratio₂ × … × ratioₙ
- Output speed = input rpm ÷ total ratio
- Output torque = input torque × total ratio × efficiencyⁿ
- Direction: each external mesh reverses rotation, so an odd number of stages reverses the output.
Worked example: a motor at 1,800 rpm and 10 N·m drives a 12→36 stage and then a 15→45 stage. Total ratio = (36 ÷ 12) × (45 ÷ 15) = 9:1. Output = 1,800 ÷ 9 = 200 rpm, torque = 10 × 9 × 0.98² = 86.4 N·m, turning the same way as the input.
Vehicle speed from rpm
mph = rpm × π × tire diameter (in) × 60 ÷ (transmission ratio × final drive × 63,360). For km/h multiply by 1.609. Tire diameter from a metric size W/A R D is D + 2 × W × A ÷ 100 ÷ 25.4 inches.
Example: a 225/45R17 tire is 17 + 2 × 225 × 0.45 ÷ 25.4 = 24.97 in tall. At 3,000 rpm in 4th (1.00) with a 3.73 axle: 3,000 ÷ 3.73 × π × 24.97 × 60 ÷ 63,360 = 59.8 mph, and 70 mph needs about 3,514 rpm.
Typical ratios
| Application | Typical ratio | Notes |
|---|---|---|
| Car 1st gear | 3.0–4.5 : 1 | Most torque for pulling away |
| Car top gear (overdrive) | 0.6–0.85 : 1 | Output faster than engine for low cruise rpm |
| Rear axle / final drive | 2.7–4.1 : 1 | Lower numbers favor economy, higher favor acceleration |
| Bicycle (50T chainring, 25T cog) | 0.5 : 1 | Wheel turns twice per pedal turn |
| Single spur gear pair | up to about 6 : 1 | Use more stages for bigger reductions |
| Worm gearbox | 5–100 : 1 | Large reduction in one stage, lower efficiency |
Frequently asked questions
How do you calculate a gear ratio?
Divide the number of teeth on the driven gear by the number on the driver gear. A 12-tooth gear driving a 36-tooth gear gives 36 ÷ 12 = 3:1, so the output turns 3 times slower with 3 times the torque (minus friction losses).
How do I calculate the ratio of a compound gear train?
Multiply the ratios of each stage. Stages of 12→36 (3:1) and 15→45 (3:1) give 3 × 3 = 9:1. An input of 1,800 rpm becomes 200 rpm at the output.
How is output torque calculated?
Output torque = input torque × gear ratio × efficiency for each mesh. With 10 N·m in, a 9:1 ratio and two meshes at 98%, the output is 10 × 9 × 0.98 × 0.98 = 86.4 N·m.
How do I calculate speed from rpm and gear ratio?
Speed (mph) = rpm × tire diameter (in) × π × 60 ÷ (gear ratio × final drive × 63,360). For example 3,000 rpm in a 1.00 gear with a 3.73 axle and 24.97 in tires is about 59.8 mph.
Does an idler gear change the ratio?
No. An idler gear between two gears only reverses the direction of rotation; the ratio still depends only on the first driver and last driven gear of that mesh.
What is a good gear efficiency to use?
Spur and helical gears are typically 97–99% efficient per mesh, bevel gears 95–98% and worm gears much lower, often 50–90% depending on the lead angle.