How to use the gear ratio calculator
- Choose 1 stage (one pair of gears) or 2 stages (two pairs, with a compound gear in the middle).
- Enter the number of teeth on each gear. The driver is the gear turned by the motor; the driven gear is the one it turns.
- Enter the motor's speed in RPM and its torque (N·m, N·cm, mN·m or kgf·cm — hobby motor sellers in India often quote kg·cm).
- Set the efficiency per stage. 95 % is typical for good spur gears; cheap plastic gearboxes may be 80–90 %.
- Read the gear ratio, output speed, output torque, direction and power. The drawing shows the gears to scale and turning at the correct relative speeds.
Formula
A ratio above 1 is a reduction: the output turns slower with more torque. A ratio below 1 is a speed-up (overdrive): faster, with less torque. Gears can never create power — with friction, the output power is always a little less than the input.
Rotation direction
Every time two external spur gears mesh, the direction reverses.
| Gear pairs in the train | Output direction |
|---|---|
| 1 | Opposite to the motor |
| 2 | Same as the motor |
| 3 | Opposite to the motor |
| 1 pair with an idler gear between | Same as the motor (the idler does not change the ratio) |
Typical efficiencies
| Gear type | Typical efficiency per stage |
|---|---|
| Metal spur gears, well lubricated | 95–98 % |
| Plastic spur gears (hobby gearboxes) | 85–95 % |
| Planetary stage | about 90–97 % |
| Worm gear | often 40–80 %, low for high ratios |
These are rough planning figures; check the datasheet for real gearboxes.
Common mistakes
- Swapping driver and driven. 12 → 36 is a 3 : 1 reduction; 36 → 12 is a 1 : 3 speed-up. The driver is always the gear on the motor side.
- Adding the ratios of two stages. Stage ratios multiply: 3 : 1 and 4 : 1 give 12 : 1, not 7 : 1.
- Using no-load RPM as running speed. A motor's rated RPM is usually measured with no load; under load it runs slower.
- Forgetting efficiency. A five-stage plastic gearbox at 90 % per stage passes on only about 59 % (0.9⁵) of the torque you would calculate without losses.
- Counting an idler gear in the ratio. An idler between two gears only changes direction, not the ratio.
Related tools and guides
Turn output RPM into robot speed with the wheel RPM and speed calculator. For 3D printers and CNC axes, use the stepper steps per mm calculator, and to control motor speed see the PWM duty cycle calculator. Learn how gear motors are driven in our L298N robot car guide and stepper motor guide. Want gears and motors to experiment with? Explore our robotics kits and workshops.
