Calculate gear output torque, input torque, or required gear ratio from tooth counts or a known ratio, with efficiency losses, unit conversions, RPM, and power.
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Gear Torque Formula
Output torque equals input torque multiplied by the gear ratio and the efficiency of the mesh. The drivetrain mode chains a transmission ratio and a final drive ratio together.
- T_out = output torque (N·m, lb-ft, or kgf·m)
- T_in = input torque applied to the driver gear
- GR = gear ratio, driven teeth divided by driver teeth
- N_driver, N_driven = tooth counts on each gear
- RPM_in, RPM_out = shaft speeds before and after the mesh
- n = mesh efficiency expressed as a decimal (95% = 0.95)
- GR_trans, GR_final = transmission and final drive ratios
The Gear pair tab solves the first formula and lets you derive GR from teeth or from measured RPMs. The Known ratio tab skips that step when you already have the ratio. The Drivetrain tab applies the chained formula and, if you supply tire diameter, converts wheel torque into tractive force using F = T / r and vehicle speed from wheel RPM.
Typical Values
Use these as starting points if you do not have measured data.
| Gear type | Mesh efficiency |
|---|---|
| Spur | 96 to 99% |
| Helical | 95 to 98% |
| Bevel | 93 to 97% |
| Planetary stage | 96 to 98% |
| Worm (low ratio) | 70 to 90% |
| Worm (high ratio) | 40 to 70% |
| Chain drive | 95 to 98% |
| Drivetrain | Combined efficiency |
|---|---|
| Manual transmission, RWD | 85 to 90% |
| Manual, FWD | 88 to 92% |
| Automatic transmission | 75 to 85% |
| AWD or 4WD | 75 to 85% |
| Direct drive EV | 90 to 95% |
Worked Examples
1. Single gear pair. A 12 tooth pinion drives a 36 tooth gear. Input torque is 10 N·m at 95% efficiency.
GR = 36 / 12 = 3.0
T_out = 10 × 3.0 × 0.95 = 28.5 N·m
2. Drivetrain to wheels. An engine produces 250 N·m. The transmission is in a 3.50:1 gear, the final drive is 4.10:1, and drivetrain efficiency is 85%.
Total ratio = 3.50 × 4.10 = 14.35
T_wheel = 250 × 14.35 × 0.85 = 3,049 N·m
FAQ
Does a higher gear ratio always mean more torque? Yes, ignoring losses. A 4:1 reduction multiplies input torque by four and divides speed by four. Real hardware gives back a few percent to friction.
Driver or driven first? The gear ratio for torque multiplication is driven teeth divided by driver teeth. Flip it and you get the speed ratio instead.
What efficiency should I enter if I do not know it? Use 95% for a single spur or helical mesh, 90% for a typical manual gearbox plus axle, and 80% for an automatic. Drop worm gears to 50 to 80% depending on lead angle.
Why does the calculator show output torque in N·m even if I entered lb-ft? Inputs are converted internally to N·m for the math, then the result is shown in all three units so you can pick the one you need.
