How gear ratio works
The gear ratio is the number of teeth on the driven gear divided by the teeth on the driver gear. A 40-tooth driven gear paired with a 10-tooth driver gives 4.00 : 1, meaning the driver turns four times for each turn of the driven gear. A ratio above 1 trades speed for torque.
Teeth are used rather than diameters because the teeth must mesh — every tooth that leaves the driver arrives at the driven gear, so the tooth counts fix the relationship exactly. Diameters give the same answer for standard gears, but tooth counts are easier to check and are not affected by wear. A gear ratio is a ratio in the ordinary arithmetic sense, and the ratio calculator will reduce it to its simplest form.
How to use this calculator
Count the teeth on the driven gear (the output) and the driver gear (the input, connected to the power source), then enter both. The result is expressed as a ratio to 1. The driver must have at least one tooth, so a zero entry returns a dash.
Swapping the two entries is the classic mistake and gives the reciprocal — 0.25 : 1 instead of 4.00 : 1. If the answer looks inverted, check which gear is actually driven by the motor or pedals. Gearing trades speed for turning effort but never creates energy, so the power calculator shows what actually reaches the wheels.
Speed and torque trade-off
A ratio greater than 1 (gear reduction) increases torque and reduces output speed; a ratio under 1 does the opposite. This is why low gears help a vehicle climb hills. Torque at the output relates to the applied force and lever arm — see the torque calculator.
Gears never create energy — power is torque times rotational speed, so whatever a reduction gains in torque it gives back in speed.
Frequently asked questions
- How do I calculate gear ratio?
- Divide the driven gear's teeth by the driver gear's teeth. 40 ÷ 10 gives a 4.00 : 1 ratio.
- What does a 4:1 gear ratio mean?
- The driver gear turns four times for every single turn of the driven gear, increasing torque.
- Which gear is the driver?
- The driver is the input gear connected to the power source; the driven gear is the output.
- Does a higher ratio mean more speed?
- No — a higher ratio means more torque but lower output speed. A ratio below 1 increases speed.
- What about an idler gear between the two?
- An idler does not change the ratio at all — it only reverses the direction of rotation. The overall ratio still depends solely on the first driver and the final driven gear, so an idler can be ignored in the arithmetic.