Calculate gearbox efficiency, input torque, output torque, or gear ratio from any three values using N-m, lb-ft, or kg-m units with unit conversion.
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Gearbox Efficiency Formula
The gearbox efficiency calculation compares actual output torque to the ideal output torque produced by the input torque and gear ratio.
\eta = \frac{T_{out}}{T_{in} \times GR} \times 100Rearranged formulas used to solve the other fields:
T_{out} = \frac{\eta}{100} \times T_{in} \times GRT_{in} = \frac{T_{out}}{(\eta/100) \times GR}GR = \frac{T_{out}}{(\eta/100) \times T_{in}}- η = gearbox efficiency, as a percent
- Tout = output torque
- Tin = input torque
- GR = gear ratio
The calculator converts torque values to N-m before applying the formula, then converts the result back to the selected torque unit. You can enter any 3 of the 4 values: output torque, input torque, gear ratio, and efficiency. The missing value is calculated from the same relationship.
Typical Gearbox Efficiency Ranges
Actual efficiency depends on gear type, lubrication, load, speed, temperature, bearing losses, and manufacturing quality. These ranges are typical reference values.
| Gearbox type | Typical efficiency range | Notes |
|---|---|---|
| Spur gear | 95% to 98% | High efficiency when aligned and lubricated well |
| Helical gear | 94% to 98% | Smooth operation, with some extra axial-load losses |
| Bevel gear | 90% to 97% | Used when shaft direction changes |
| Worm gear | 50% to 90% | Efficiency varies widely with ratio, lead angle, and lubrication |
| Planetary gearbox | 90% to 97% | Compact design with good torque density |
Torque Unit Conversions
The calculator supports N-m, lb-ft, and kg-m. Internally, torque is converted to N-m.
| Unit | Conversion to N-m |
|---|---|
| 1 N-m | 1 N-m |
| 1 lb-ft | 1.35582 N-m |
| 1 kg-m | 9.80665 N-m |
Example Calculations
Example 1: Calculate gearbox efficiency
You have an input torque of 50 N-m, a gear ratio of 4, and an output torque of 180 N-m.
\eta = \frac{180}{50 \times 4} \times 100\eta = \frac{180}{200} \times 100 = 90\%The gearbox efficiency is 90%.
Example 2: Calculate output torque
You have an input torque of 75 N-m, a gear ratio of 3, and an efficiency of 92%.
T_{out} = \frac{92}{100} \times 75 \times 3T_{out} = 0.92 \times 225 = 207\text{ N-m}The output torque is 207 N-m.
FAQ
What does gearbox efficiency mean?
Gearbox efficiency is the percentage of input mechanical power that reaches the output after losses. In this torque-based calculation, it compares the actual output torque to the ideal output torque expected from the input torque and gear ratio. An efficiency of 90% means 10% is lost to friction, heat, bearings, seals, oil churning, and other losses.
Can gearbox efficiency be over 100%?
No. A real gearbox cannot produce more mechanical power than it receives. If your result is over 100%, check the gear ratio direction, torque units, measured torque values, and whether the input and output torques were measured under the same operating condition.
Is gear ratio the same as torque multiplication?
Not exactly. Gear ratio gives the ideal torque multiplication before losses. Actual output torque is lower because gearbox efficiency is less than 100%. For example, a 5:1 gearbox with 80 N-m input torque has an ideal output torque of 400 N-m, but at 90% efficiency the actual output torque is 360 N-m.
