Gear Ratio Calculator
Gear ratio, output speed and output torque from the number of teeth on each gear.
Results
Ratio
3.0000
Rotational speed
483.33
rpm
Torque
150.00
N·m
What this tool does
A gear train trades speed for torque at a fixed exchange rate: whatever the ratio takes off the speed, it adds to the torque. The calculation ignores friction, so a real gearbox delivers slightly less torque than the ideal figure shown.
Formula
i = z₂ ÷ z₁ , n₂ = n₁ ÷ i , M₂ = M₁ × i
Variables
| Symbol | Meaning | Unit |
|---|---|---|
z1 | Teeth on driving gear | — |
z2 | Teeth on driven gear | — |
n1 | Rotational speed | rpm |
m1 | Torque | N·m |
i | Ratio | — |
n2 | Rotational speed | rpm |
m2 | Torque | N·m |
Worked example
- Teeth on driving gear20
- Teeth on driven gear60
- Rotational speed1450 rpm
- Torque50 N·m
- Ratio3.0000
- Rotational speed483.33 rpm
- Torque150.00 N·m
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.