Gear Ratio Calculator — speed, torque and compound trains

Ratio, output speed and torque multiplication for single and compound gear trains.

Example: 12:60 over 1 stage gives 5:1 — 600 rpm at 0.475 N·m.

Inputs

Driver teeth

The gear attached to the motor.

Driven teeth

The output gear.

Stages

Identical stages in series. Ratios multiply.

Input speed(rpm)

Input torque(N·m)

Efficiency per stage

Around 0.95 for good spur gears, lower for worm drives.

Result

Total ratio

5 : 1

Output speed: 600 rpm
Output torque: 0.475 N·m
Ratio per stage: 5 : 1
Total efficiency: 95%
Input power: 31.42 W
Output power: 29.85 W

Torque and speed trade exactly: 5× more torque means 5× less speed. Gearing cannot create power — the 1.57 W difference here is friction.
The tooth counts share a common factor of 12, so the same teeth mesh repeatedly — every 5 turns of the driver. Coprime counts (a "hunting tooth") spread wear evenly across every tooth pair instead.

Compounding across stages

Stages	Total ratio	Output rpm	Output torque	Efficiency
1	5 : 1	600	0.475 N·m	95%
2	25 : 1	120	2.2563 N·m	90.3%
3	125 : 1	24	10.7172 N·m	85.7%
4	625 : 1	4.8	50.9066 N·m	81.5%
5	3125 : 1	1	241.8065 N·m	77.4%

Formula

ratio = driven teeth / driver teeth    torque out = torque in × ratio × efficiency

Worked example

12:60 over 1 stage gives 5:1 — 600 rpm at 0.475 N·m.

stage ratio = driven teeth / driver teeth
60 / 12
5 : 1
total ratio = stage ratio ^ stages
5^1
5 : 1
output speed = input speed / ratio
3000 / 5
600 rpm
output torque = input torque × ratio × efficiency
0.1 × 5 × 0.95
0.475 N·m

Frequently asked questions

How do I calculate a gear ratio?

Divide the driven gear's tooth count by the driver's. A 12-tooth pinion driving a 60-tooth gear is 5:1 — the output turns five times slower with roughly five times the torque, less friction losses.

How do compound gear trains work?

Ratios multiply. Three stages of 5:1 give 125:1, not 15:1, which is why compact gearboxes reach large reductions. Efficiency multiplies too, in the other direction: 95% per stage becomes 86% across three.

Does gearing increase power?

No. It trades speed for torque at constant power, minus friction. Multiplying torque by ten divides speed by ten, and the output power is always slightly below the input — the difference is heat in the mesh and bearings.

Why should tooth counts be coprime?

So wear spreads evenly. If the counts share a common factor, the same tooth pairs mesh repeatedly and wear together. Coprime counts — sometimes achieved with a deliberate 'hunting tooth' — make every driver tooth eventually meet every driven tooth.

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