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MachineCalcs

Gear Ratio Calculator

Gear ratio from tooth counts, plus the output RPM, torque and road speed it produces. For drivetrains, cars, motorcycles and machine design. Metric and imperial.

Inputs

rpm
N·m
mm

Results

Gear ratio(i) ✓
3

3.00:1 — reduction (torque up, speed down).

driven ÷ driving (n:1).

Output speed(n₂)
1 000 rpm

Output torque(T₂)
300 N·m

Ideal, before losses.

Vehicle speed
119.3 km/h

At the output speed, from tire diameter.

  • Ratio i = driven teeth ÷ driving teeth. Output speed = input ÷ i; output torque = input × i.
  • Torque is ideal (100% efficient); real gear trains lose a few percent per mesh.
  • Vehicle speed assumes the driven gear turns the wheel directly — for a full drivetrain, multiply the transmission and final-drive ratios first.

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.

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