Gear Ratio Calculator

Gear ratio is driven teeth divided by driver teeth. A 20-tooth driver turning a 60-tooth driven gear gives 60 / 20 = 3:1: the output turns once for every three turns of the input, at roughly three times the torque and one third the speed. Gears trade speed for torque (or the reverse); they cannot create power. The calculator below computes the ratio in both decimal and simplified form, the output RPM from an input speed, and the output torque with an efficiency allowance. It also fixes two defects in the previous version: the live tool was completely dead (a script error killed the whole calculator), and the simplified ratio was displayed backwards, contradicting the main result.

The Formulas

Gear ratio = driven teeth / driver teeth. Output RPM = input RPM / ratio. Output torque = input torque \u00d7 ratio \u00d7 efficiency. Worked example: 20-tooth driver, 60-tooth driven, 3,000 RPM in, 50 N\u00b7m in at 95% efficiency. Ratio = 60/20 = 3.000:1 (simplified 3:1). Output speed = 3,000/3 = 1,000 RPM. Output torque = 50 \u00d7 3 \u00d7 0.95 = 142.5 N\u00b7m.

Reduction vs Overdrive

Above 1:1 is reduction: slower output, multiplied torque, the right choice for winches, conveyors, and climbing gears. Below 1:1 is overdrive: faster output, reduced torque, used for cruising efficiency. Exactly 1:1 is direct drive. The common mistake is swapping driver and driven, which inverts the ratio; the driver is always the input side (motor or engine).

Why Efficiency Matters

The ideal formulas assume no friction. Real gear pairs lose roughly 5\u201315% per mesh to friction, heat, and noise, so budget about 90\u201395% efficiency for a well-lubricated spur pair. Ignoring it overstates output torque and can undersize the downstream components.

What Gears Cannot Do

Gears cannot increase power. Output power equals input power minus losses; the ratio only changes the balance between speed and torque. Claims of “torque multiplication” sometimes mislead beginners into thinking energy is created. It is not: the output turns proportionally slower.

Frequently Asked Questions

How do you calculate gear ratio from teeth?

Divide driven (output) teeth by driver (input) teeth. A 60-tooth gear driven by a 20-tooth gear is a 3:1 ratio.

Does gear ratio affect speed or torque?

Both, in opposite directions. Reduction lowers speed and raises torque by the same factor; overdrive does the reverse.

What is a good gear ratio?

It depends on the job: 3:1 to 5:1 for e-bikes, 5:1 to 50:1 for robot arms, 20:1 to 100:1 for winches. Match the ratio to whether you need speed or force.

Do idler gears change the ratio?

No. An idler between two gears reverses direction but the overall ratio depends only on the first and last gears.

How do compound gear trains work?

Multiply the stage ratios: a 2:1 stage followed by a 3:1 stage gives 6:1 overall. That is why large reductions are split across stages instead of one huge gear pair.