What Is Gear Torque?
Gear torque is the rotational force that comes out of a gear system once a driving gear has turned a driven gear. Gears don't create torque out of nothing — they trade speed for torque, and the exchange rate is set entirely by the gear ratio between the two gears.
Understanding this trade-off matters anywhere gears are used: a car's transmission and final drive, a bicycle's chainring and cassette, or an industrial gearbox. Pick the wrong ratio and a motor either stalls under load or spins uselessly fast without enough force to do the job.
The Gear Torque Formula
The relationship is a single multiplication:
[
\text{Output Torque} = \text{Input Torque} \times \text{Gear Ratio}
]
Where:
- Input Torque is the torque delivered to the driving gear (N·m or lb-ft)
- Gear Ratio is the driven gear's teeth count (or diameter) divided by the driving gear's teeth count (or diameter)
- Output Torque is the torque produced at the driven gear, in the same unit as the input
This is the ideal case, assuming no friction losses — a good approximation for most gear systems and the standard starting point for any mechanical design calculation.
Worked Example: Sizing a Gearbox
Say a motor delivers 150 N·m of torque into a gearbox with a 3.5:1 gear ratio:
[
\text{Output Torque} = 150 \text{ N·m} \times 3.5 = 525 \text{ N·m}
]
The gearbox triples-and-a-half the motor's torque at its output shaft — useful for driving a heavy load — but the output shaft will spin at only 1/3.5 of the motor's speed. Plug 150 and 3.5 into the calculator above and you'll get the same 525 N·m.
Gear Ratio and the Torque-Speed Trade-off
Because gears conserve power, any ratio that multiplies torque must divide speed by the same amount:
| Gear Ratio | Effect on Torque | Effect on Speed |
|---|---|---|
| 1:1 | No change | No change |
| 4:1 (step-down) | ×4 torque | ÷4 speed |
| 1:4 (step-up) | ÷4 torque | ×4 speed |
A step-down ratio (driven gear bigger than driving gear) is what you want for climbing a hill or moving a heavy load slowly. A step-up ratio (driven gear smaller than driving gear) trades torque away for higher speed, which is why a bicycle's smallest rear cog gives you top speed but the least pedaling leverage.
Typical Gear Ratios by Application
| Application | Typical Ratio | Why |
|---|---|---|
| Car 1st gear | 3.0–4.0:1 | Maximum torque for launching from a stop |
| Car final drive | 3.0–4.5:1 | Multiplies transmission output torque to the wheels |
| Bicycle low gear (climbing) | up to 4:1 | Torque over speed for steep grades |
| Industrial worm gearbox | 10:1–100:1 | Very high torque multiplication, low speed |
Quick Recap
- Output Torque = Input Torque × Gear Ratio, with both torques in the same unit.
- A ratio greater than 1 multiplies torque and divides speed by the same amount.
- The calculation assumes an ideal, lossless gear system — real gearboxes deliver slightly less.
- Use the calculator above to check any input torque and gear ratio combination instantly.
Once you've found your output torque, the RPM gear ratio calculator is a natural next step for working out the matching output speed.