# Gear Ratio Calculator

URL: https://speedycalculator.com/calculators/physics/gear-ratio/
Last updated: 2026-10-30

> The gear ratio calculator finds the gear ratio from the number of teeth on the driving and driven gears, and the output speed and torque from the input values and efficiency.

## Inputs

- Teeth on the driving (input) gear
- Teeth on the driven (output) gear
- Input speed (rpm, rad/s, Hz (rev/s))
- Input torque (N·m, lbf·ft, kgf·m, N·mm)
- Efficiency (%)

## Results

- Gear ratio
- Output speed
- Output torque
- Type

## Formula

```
i = N_driven / N_driving,  n_out = n_in / i,  T_out = T_in·i·η
```

## Explanation

Gears trade speed for torque. A small gear driving a large one slows the output and multiplies torque – how a bicycle's low gear helps you climb. Swap them and you get speed at the cost of force.

### How to use the Gear Ratio Calculator

- **Teeth on the driving (input) gear**
- **Teeth on the driven (output) gear**
- **Input speed**
- **Input torque**
- **Efficiency (%)**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the tooth counts and, optionally, the input speed, input torque and efficiency.

### Inputs explained

FieldWhat to enterTeeth on the driving (input) gearA numberTeeth on the driven (output) gearA numberInput speedUnits: rpm, rad/s, Hz (rev/s)Input torqueUnits: N·m, lbf·ft, kgf·m, N·mmEfficiency (%)A number

### What each result means

- **Gear ratio** = [Teeth on the driven (output) gear]÷[Teeth on the driving (input) gear]
- **Output speed** = [Input speed]÷([Teeth on the driven (output) gear]÷[Teeth on the driving (input) gear])
- **Output torque** = [Input torque]×[Teeth on the driven (output) gear]÷[Teeth on the driving (input) gear]×[Efficiency (%)]÷100

### Example values

How the main result changes when **Teeth on the driving** changes and everything else stays at the example values above:

Teeth on the driving (input) gearGear ratio (:1)6694123152.4182241.5

## Worked example

Inputs — Teeth on the driving (input) gear: 12; Teeth on the driven (output) gear: 36; Input speed: 1,500 rpm; Input torque: 10 N·m; Efficiency (%): 98.

Results — **Gear ratio = 3 :1**; Output speed = 500 rpm; Output torque = 29.4 N·m; Type = Reduction (more torque).

## Key terms

- **Gear train**: A set of meshing gears.

## FAQ

**What does a 3:1 ratio mean?**
The input turns three times for each output turn.

**Does the direction change?**
Yes – two meshing external gears rotate in opposite directions.

**Why is torque multiplied?**
Power is conserved (minus losses), so lower speed gives higher torque.

**How do I combine stages?**
Multiply the stage ratios.


## Sources

- [Shigley's Mechanical Engineering Design (Budynas & Nisbett) – reference text](https://www.mheducation.com/highered/product/shigley-s-mechanical-engineering-design-budynas/M9780073398204.html)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)