Gear Ratio Formula
Calculate gear ratio from teeth count or shaft speeds.
Understand torque multiplication and speed reduction with worked examples.
The Formula
Gear Ratio = Speed of Driving Gear / Speed of Driven Gear
The gear ratio tells you how many times the driving gear must rotate for the driven gear to rotate once. A ratio greater than 1 reduces speed but increases torque. A ratio less than 1 increases speed but reduces torque.
Variables
| Symbol | Meaning |
|---|---|
| GR | Gear ratio (dimensionless) |
| N₁ | Number of teeth on the driving gear (input) |
| N₂ | Number of teeth on the driven gear (output) |
| ω₁ | Rotational speed of driving gear (RPM) |
| ω₂ | Rotational speed of driven gear (RPM) |
Torque Relationship
Output Speed = Input Speed / Gear Ratio
Example 1
A driving gear has 20 teeth and meshes with a driven gear of 60 teeth. What is the gear ratio?
GR = N₂ / N₁ = 60 / 20
GR = 3:1 (the driven gear turns 3 times slower with 3 times more torque)
Example 2
A motor spins at 3,000 RPM with a gear ratio of 5:1. The input torque is 10 N·m. Find the output speed and torque.
Output speed = 3,000 / 5 = 600 RPM
Output torque = 10 × 5 = 50 N·m
Output: 600 RPM at 50 N·m (slower but much stronger)
When to Use It
Use the gear ratio formula in mechanical design:
- Designing gearboxes and transmissions for vehicles
- Selecting gear pairs for speed reduction or torque multiplication
- Calculating bicycle gear ratios for different terrains
- Sizing motors and gears for robotics and machinery