Gear Ratio Formula
Calculate the gear ratio between two meshing gears.
Determines speed reduction and torque multiplication in machines.
The Formula
Gear Ratio = N_driven / N_driver = ω_driver / ω_driven
The gear ratio determines how speed and torque are exchanged between gears. A ratio greater than 1 means the output turns slower but with more torque.
Variables
| Symbol | Meaning |
|---|---|
| N_driver | Number of teeth on the driving gear (input) |
| N_driven | Number of teeth on the driven gear (output) |
| ω_driver | Rotational speed of the driving gear (RPM) |
| ω_driven | Rotational speed of the driven gear (RPM) |
Example 1
A 20-tooth gear drives a 60-tooth gear. The motor spins at 3000 RPM.
Gear ratio = 60 / 20 = 3:1
Output speed = 3000 / 3 = 1000 RPM
Output turns 3x slower with 3x more torque
Example 2
A bicycle: front sprocket has 44 teeth, rear has 11 teeth
Gear ratio = 44 / 11 = 4:1
Each pedal revolution turns the wheel 4 times (high gear = more speed)
When to Use It
Use the gear ratio formula when:
- Designing gear trains for motors and machinery
- Calculating output speed and torque in transmissions
- Choosing bicycle gears for different terrain
- Understanding how clocks, robots, and vehicles work