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
For steady power transmission from input to output, output torque magnitude equals input torque magnitude multiplied by the reduction ratio and efficiency. For a simple gear pair, the ratio is driven teeth divided by driver teeth. For a transmission and final drive in series, multiply their ratios and use the combined efficiency of that path.
- 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 = input and output shaft-speed magnitudes in revolutions per minute; rotation direction is not represented
- n = efficiency of the selected mesh or complete drivetrain path, expressed as a decimal (95% = 0.95)
- GR_trans, GR_final = transmission and final drive ratios
Choose the quantity to solve: output torque, input torque, or required ratio. Determine a simple gear-pair ratio from teeth or enter a known overall ratio. Shaft speed follows RPM_out = RPM_in / GR, and mechanical power is P = T × 2π × RPM / 60 in watts when torque is in N·m. At consistent input and output boundaries, output power equals input power multiplied by efficiency. These calculations estimate operating values; the hardware torque rating comes from the manufacturer.
Typical Values
The ranges below are retained as illustrative efficiency assumptions, not verified typical values or equipment ratings. Actual efficiency depends on design, stage count, ratio, speed, temperature and losses within the selected input/output boundary. Use manufacturer data or measurements for the relevant operating conditions; compare assumed scenarios when those data are unavailable.
| Gear type | Illustrative 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 | Illustrative 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 = 3,049.375 N·m ≈ 3,049 N·m
FAQ
Does a higher gear ratio always mean more torque? At the same input torque and efficiency, output torque is proportional to the reduction ratio. An ideal 4:1 reduction multiplies torque by four and divides speed by four. Actual efficiency can change with gear design and operating conditions, so losses are not always just a few percent.
Driver or driven first? For a simple gear pair, use driven teeth divided by driver teeth for the reduction ratio. Its reciprocal equals output-speed magnitude divided by input-speed magnitude. For a worm pair, use wheel teeth divided by worm starts; for a compound or planetary arrangement, use its actual overall ratio.
What efficiency should I enter if I do not know it? Prefer manufacturer data or measurements for the actual drive and operating conditions. If those are unavailable, use an explicitly assumed value and compare a range: 95%, 90% and 80% are example scenarios, not universal recommendations for particular gearboxes. For a complete drivetrain, use the combined efficiency and count each loss only once.
Why does the calculator show output torque in N·m even if I entered lb-ft? Inputs are converted internally to N·m. Select the result torque unit in Speed and display options; secondary results show all four supported torque units.
