How it works
The gear ratio is the driven tooth count divided by the driving tooth count:
i = z₂ / z₁
A ratio above 1:1 is a reduction — the output turns slower than
the input but with proportionally more torque. The output speed and torque are
n₂ = n₁ / i and T₂ = T₁ · i (ideal, before mesh losses).
If the driven gear turns a wheel, the road speed is the wheel speed
times the tire circumference: v = n₂ · π · d_tire. For a complete
drivetrain, multiply the transmission ratio by the final-drive ratio to get the
overall ratio, then apply it here.
Worked example
A 15-tooth pinion driving a 45-tooth gear is a 3:1 reduction. At 3,000 RPM in, the output turns 1,000 RPM; 100 N·m in becomes 300 N·m out. With a 633 mm (≈ 25 in) tire, that 1,000 RPM is about 119 km/h (74 mph). Those are the numbers the calculator shows for these inputs.
Frequently asked questions
- How do I calculate a gear ratio?
- Divide the driven (output) tooth count by the driving (input) tooth count: ratio = z₂ / z₁. For example 45 driven teeth over 15 driving teeth is a 3:1 reduction.
- How does gear ratio affect RPM and torque?
- A reduction ratio (greater than 1:1) lowers the output speed and multiplies torque by the same factor: output RPM = input ÷ ratio, output torque = input × ratio. An overdrive ratio (less than 1:1) does the opposite.
- How do I find vehicle speed from the gear ratio?
- Speed = output (wheel) RPM × tire circumference. Enter the tire diameter above. For a full drivetrain, multiply the transmission gear ratio by the final-drive ratio first, then use that as the overall ratio.
- What is the difference between a reduction and an overdrive ratio?
- A reduction (ratio > 1, e.g. 3:1) turns the output slower than the input but with more torque — good for acceleration and pulling. An overdrive (ratio < 1) turns the output faster with less torque — good for top speed and economy.
- How do I use this for a car, motorcycle or go-kart?
- Enter the driving and driven gear or sprocket teeth (pinion/ring, or front/rear sprocket), the engine RPM, and the tire diameter. The calculator returns the wheel RPM and road speed.
- Does this work in metric and imperial?
- Yes — tire diameter in mm or inches, and road speed in km/h or mph. Toggle SI/Imperial in the header.
Method & assumptions
- Torque transfer is ideal (100% efficient); real gear trains lose a few percent per mesh.
- Road speed assumes the driven gear drives the wheel directly — combine transmission and final-drive ratios for a full drivetrain.
- Tire diameter is the loaded rolling diameter; published tire sizes are slightly larger than the rolling diameter under load.
Related calculators
- Involute Gear Calculator — Tooth geometry from module/DP and pressure angle, with a tooth-profile render and DXF export.
- Gear Module Calculator — Module from pitch diameter and teeth, with diametral and circular pitch.
- Gear Tooth Ratio Calculator — Single- or two-stage gear-train ratio and output speed from tooth counts.
- Planetary Gear Calculator — Epicyclic gear ratio for ring-, sun- or carrier-fixed arrangements.
- Worm Gear Calculator — Worm drive ratio, center distance, lead angle and self-locking check.