What this calculator does
Torque is a turning force: how hard something twists rather than how hard it pushes. It depends on the force applied and how far out from the pivot that force acts, which is why a longer spanner loosens a tight bolt that a short one cannot.
Power is torque combined with speed. An engine producing a given torque at 3,000 rpm delivers twice the power of the same torque at 1,500 rpm, which is why peak torque and peak power almost never occur at the same engine speed.
The formula
Multiply force by the lever arm and by the sine of the angle between them, which removes any part of the force pointing along the arm rather than across it. Power is that torque multiplied by angular velocity in radians per second, which is rpm times 2π divided by 60.
| Term | Meaning |
|---|---|
| Torque (τ) | Turning effect, in newton metres. A force of one newton at one metre from the pivot gives one newton metre. |
| Lever arm | The perpendicular distance from the pivot to the line of the force. |
| Angular velocity (ω) | Rotational speed in radians per second. One revolution is 2π radians. |
The inputs explained
| Field | What to enter |
|---|---|
| Force (N) | The force applied, in newtons. |
| Lever arm (m) | The distance from the pivot to where the force acts, in metres. |
| Angle (°) | The angle between the force and the lever arm. 90 degrees means the force acts straight across the arm, which gives maximum torque. |
| Rotational speed (rpm) | Rotational speed in revolutions per minute, used only for the power figures. |
When to use it
Tightening a fastener to specification
A torque figure and a spanner length together determine the force to apply, which is what a torque wrench automates.
Reading an engine specification
Torque and power figures describe the same engine at different speeds, and converting between them shows why each peaks where it does.
Sizing a motor for a load
A load that needs a certain torque at a certain speed needs a specific power, and that conversion is this calculation.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does power change with rpm at constant torque?
The same torque delivered at a range of rotational speeds.
| Speed | Torque | In horsepower |
|---|---|---|
| 1,000 rpm | 80.000 N·m | 11.235 |
| 2,000 rpm | 80.000 N·m | 22.469 |
| 3,000 rpm | 80.000 N·m | 33.704 |
| 5,000 rpm | 80.000 N·m | 56.173 |
Questions
Why does a longer spanner make a bolt easier to undo?
Because torque is force times distance. Doubling the length of the lever arm doubles the torque for the same hand force, which is why breaker bars exist.
Why does the angle matter?
Only the component of force acting perpendicular to the arm produces turning. Pulling along the arm instead of across it does nothing, and the sine term accounts for anything in between.
Is torque the same as power?
No. Torque is the twisting effort at an instant; power is torque combined with how fast it is turning. A low-speed winch can produce enormous torque at very little power.
Why do engines quote torque and power separately?
Because they peak at different speeds. Torque describes pulling ability at a given engine speed; power describes the rate of work. Both are the same physical behaviour viewed through different rpm.
For linear work and power, see the work, power and efficiency calculator. For the rotational equivalent of momentum, see the angular momentum calculator.