What Is Shaft Torque and Why Does It Matter?
Any time power flows through a spinning shaft — an engine crankshaft, a gearbox output shaft, a wind turbine main shaft — that shaft is being twisted. Shaft torque is the size of that twist: the rotational force the shaft must carry to deliver the power at whatever speed it's spinning.
Engineers care about it because it drives real design decisions: a shaft, coupling or bearing that's too weak for its torque will fail, while one built far stronger than it needs to be wastes material and weight. Torque is also the number most drivers actually feel — it's what shoves you back in your seat, not the raw horsepower figure on a spec sheet.
The Shaft Torque Formula (T = P/ω)
Power, torque and rotational speed are linked by one compact relationship. For a rotating shaft:
[
P = T \times \omega
]
Rearranged to solve for torque, that becomes:
[
T = \frac{P}{\omega}
]
Where:
- T is torque, in Newton-meters (N·m)
- P is power, in watts (W)
- ω (omega) is angular velocity, in radians per second (rad/s)
Angular velocity isn't usually how shaft speed is reported, though — tachometers and spec sheets use revolutions per minute (RPM). So before applying the formula, RPM needs converting to rad/s:
[
\omega = \frac{2\pi \times N}{60}
]
Here N is the rotational speed in RPM. Each revolution sweeps through (2\pi) radians, and dividing by 60 turns "per minute" into "per second."
Worked Example
Say a shaft transmits 100 kW of power while spinning at 3,000 RPM.
First, convert speed to angular velocity:
[
\omega = \frac{2\pi \times 3{,}000}{60} = 314.16 \text{ rad/s}
]
Then convert power to watts (100 kW = 100,000 W) and apply the formula:
[
T = \frac{100{,}000}{314.16} = 318.31 \text{ N·m}
]
That shaft is carrying about 318 N·m of torque — plug those same numbers into the calculator above and you'll see the identical result.
Why the Same Power Gives Different Torque at Different Speeds
Because torque is power divided by angular velocity, the two move in opposite directions for a fixed power output. Spin a shaft slowly and it needs high torque to push that power through; spin it fast and the torque required drops.
This is exactly why a diesel engine — which makes peak power at low RPM — feels torquey and strong from a stop, while a high-revving motorcycle engine needs to be spun to high RPM before its (comparatively low) torque adds up to serious power.
| Power | Speed | Angular Velocity (ω) | Torque |
|---|---|---|---|
| 100 kW | 1,000 RPM | 104.72 rad/s | 954.93 N·m |
| 100 kW | 3,000 RPM | 314.16 rad/s | 318.31 N·m |
| 100 kW | 6,000 RPM | 628.32 rad/s | 159.15 N·m |
Same power, three very different torque figures — all because the shaft is spinning at a different speed each time.
Converting Power Units
Power is reported in different units depending on the field, so the calculator accepts three common ones and converts internally before running the formula:
| Unit | Conversion to Watts |
|---|---|
| Watts (W) | ×1 |
| Kilowatts (kW) | ×1,000 |
| Horsepower (hp) | ×745.7 |
Whichever unit you pick, the calculator converts it to watts first so the T = P/ω formula always works with consistent SI units.
Quick Recap
- T = P / ω — torque equals power divided by angular velocity.
- Convert RPM to rad/s first: ω = 2πN / 60.
- For a fixed power, torque falls as speed rises, and rises as speed falls.
- Use the calculator above with power in W, kW or hp and speed in RPM to get an instant torque reading in N·m.
If you want to go the other way and work out angular velocity on its own, the RPM to angular velocity calculator handles that conversion directly.