How to use this calculator
- Enter the tooth counts. Enter the driving (input) and driven (output) tooth counts. The ratio is driven ÷ driving.
- Enter the input speed and torque. Enter the driving-gear RPM and, optionally, the input torque.
- Enter the tire diameter. For road speed, enter the drive-wheel diameter.
- Read the results. Read the gear ratio, output RPM, output torque and vehicle speed.
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).
The same ratio logic drives belts and chains — see the
pulley and sprocket
calculators. To turn that torque into tooth loads for shafts and bearings, use
the gear mesh force calculator.
For a longer derivation and vehicle examples, see
how to calculate gear ratio.
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.
Horsepower is useful after the ratio is chosen, but it is not an input to the tooth-count ratio itself. For power-limited drivetrain work, pair this page with wheel torque, road-load horsepower and engine RPM.
Horsepower, RPM & Gear Ratio Workflow
Use horsepower as a constraint check after the ratio, speed and torque targets are defined. The gear ratio calculator answers the geometry; the adjacent tools below answer whether the engine or motor can carry the load at that speed.
| Question | Use this input or page | Decision it supports |
|---|---|---|
| What speed do I want at target RPM? | Engine RPM, tire diameter and tooth counts | Choose an initial ratio from road speed and operating RPM. |
| Will the ratio multiply enough torque? | Torque input and wheel torque | Check launch, grade, pulling force or tire-contact force. |
| Is horsepower enough at that speed? | Road-load horsepower | Compare required power with available engine or motor power. |
| What happens across multiple gears? | Gear speed table | Check shift spacing, top speed and RPM drop between ratios. |
| Does the final drive change the answer? | Final drive ratio | Combine transmission and axle ratios before comparing speed and torque. |
Worked example
Verified against the live calculator
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.
Can I calculate gear ratio by horsepower?
Horsepower does not determine gear ratio by itself. Use horsepower to check whether the vehicle or machine has enough power for the speed or load, then choose ratio from target RPM, tire or pulley diameter, torque multiplication and road speed. Pair this with the wheel torque or road-load horsepower calculators when power is the limiting question.
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.