Gear Ratio Output Torque

Formula

Description

A gear train multiplies torque by the gear ratio N while dividing speed by the same ratio, with efficiency losses reducing the actual output. A gear ratio of 10:1 means the output shaft rotates 10 times slower but with 10 times more torque (minus losses). The output speed is ωout = ωin / N. Gear efficiency depends on the type: spur gears 95-98%, helical gears 96-99%, worm gears 50-90% (highly dependent on lead angle), planetary gears 90-97% per stage. Multi-stage gearboxes multiply both ratios and efficiencies.

Variables

• τout — Output torque (N·m)
• τin — Input torque from motor (N·m)
• N — Gear ratio (output teeth / input teeth)
• η — Gear train efficiency (0 to 1)

Practical Notes

Backlash (the play between gear teeth) affects positioning accuracy and is critical for servo applications. Zero-backlash gearboxes (harmonic drives, cycloidal reducers) are used in robotics. For high reduction ratios, multi-stage planetary gearboxes or harmonic drives (100:1+ in a single stage) are preferred over spur gear trains. Always account for the reflected inertia: J_reflected = J_load / N².