Gear Design Calculator
Two Gears, One Ratio That Governs Everything Downstream
Mesh a small gear against a large one and the relationship between them is fixed the moment the tooth counts are chosen: speed drops, torque rises, and the trade-off between the two is exact rather than approximate. Getting the gear ratio right at the design stage is what keeps a motor's output matched to what the driven load actually needs.
The Formula
Output Speed = Input Speed / Gear Ratio
Output Torque = Input Torque × Gear Ratio × (Efficiency / 100)
Efficiency accounts for friction and mesh losses in the gear train — a value below 100% reduces the torque actually delivered at the output shaft below what a perfectly efficient mesh would provide.
Worked Examples
| Driver Teeth | Driven Teeth | Input Speed | Input Torque | Efficiency | Ratio | Output Speed | Output Torque |
|---|---|---|---|---|---|---|---|
| 20 | 60 | 1,800 rpm | 50 N·m | 95% | 3:1 | 600 rpm | 142.5 N·m |
| 15 | 45 | 3,000 rpm | 20 N·m | 90% | 3:1 | 1,000 rpm | 54.0 N·m |
A step-down in speed always produces a proportional step-up in torque before efficiency losses are applied — the gear ratio that cuts speed to a third multiplies ideal torque by three.
Where This Calculation Matters
- Motor-to-load matching — selecting a gear ratio so a motor's rated speed and torque land in the range a driven machine actually needs.
- Gearbox and gear train design — sizing individual mesh stages in a multi-stage reduction to hit a target overall ratio.
- Efficiency budgeting — estimating how much torque is lost to friction across a gear train so downstream components are sized with margin.
How to Use This Calculator
- Enter Driver Gear Teeth and Driven Gear Teeth.
- Enter Input Speed (RPM) and Input Torque (N.m).
- Enter Efficiency (%, default 100) if the mesh isn't ideal.
- Select Calculate to get the gear ratio, output speed, and output torque.
Related Calculations
For belt-and-pulley reductions instead of gears, see the Pulley Ratio Calculator. To size the shaft carrying the resulting output torque, use the Shaft Diameter Calculator.