Torque Calculator
This torque calculator applies the formula for torque, T = F × r, to find the turning effect of a force acting at a distance from a pivot. Enter the force and the lever arm and the torque calculator returns the torque in newton meters and pound feet. It also works the other way, so you can calculate torque from power or from horsepower using the power torque formula.
Results
The Torque Calculator is part of our Rotation collection. Browse more rotation to size, convert, and check your work alongside this tool.
What the formula for torque describes
Torque is the rotational equivalent of force, and the formula for torque, T = F × r, measures how strongly a force twists an object around a pivot. This torque calculator applies that formula so you can torque calculate from a force and a lever arm without rearranging anything. The further the force acts from the center, the more torque it makes, which is why a long wrench loosens a stubborn bolt that a short one cannot.
The formula for torque
The formula for torque is force times the perpendicular lever arm:
When only the aligned component of a force matters, the formula for calculating torque adds the angle: T = F × r × sin θ. For rotating machinery the power torque formula relates torque to power and speed, which lets you calculate torque from hp:
The torque dimensional formula is [M L² T⁻²], the same dimensions as energy, which is why torque is stated in newton meters rather than joules to keep the two ideas distinct.
Formula for torque example
A force of 200 N on a wrench 0.3 m long, using the formula for torque:
To calculate torque from hp instead, a 10 kW motor at 1500 rpm gives T = 9550 × 10 ÷ 1500 = 63.7 N·m. Enter either set of values and the torque calculator returns the result and its unit conversion.
How to use the torque calculator
Enter the applied force and the length of the lever arm, the perpendicular distance from the pivot to the line of the force. The torque calculator multiplies them using the formula for torque and shows the result in newton meters and pound feet. To go from rotating machinery instead, switch inputs and the tool acts as a torque conversion calculator, letting you calculate torque from hp or from power directly.
Reading the torque calculator result
The torque figure tells you the twisting force available or required at the pivot. For a fastener, compare it against the manufacturer specification a bolt torque calculator would list, since over-torquing strips threads and under-torquing lets joints loosen. For a machine, the value from the power torque formula tells you whether a shaft or gearbox can carry the load. The torque calculator shows both metric and imperial units so it doubles as a torque conversion calculator.
When to use the torque calculator
- Sizing a wrench or lever with the formula for torque
- Tightening fasteners to spec, as a bolt torque calculator does
- Finding shaft torque from power with the power torque formula
- Working out motor output with an electric motor torque calculator using calculate torque from hp
Common formula for torque mistakes
- Using the wrong distance. The formula for torque needs the perpendicular lever arm, not the straight-line distance to the force.
- Confusing torque and energy. The torque dimensional formula matches energy, but torque is N·m of twist, not joules of work.
- Ignoring speed. To calculate torque from hp you must include rpm; power alone is not enough in the power torque formula.
Tips for accurate results
- Measure the lever arm perpendicular to the force before using the formula for torque.
- Keep units consistent, then let the torque calculator convert to lb·ft.
- For motors, pair the power torque formula with the rated rpm, not the maximum.
Understanding the formula for torque
The formula for torque hides a subtlety that trips people up: only the perpendicular part of the force and the distance count. Push straight along a lever toward the pivot and you make no torque at all, however hard you push, because the lever arm in that direction is zero. This is why the full formula for calculating torque includes sin θ, the angle between the force and the arm. When you pull a wrench at an awkward angle, the effective torque is less than the raw force times length suggests, and the torque calculator lets you check that instead of guessing.
From power to torque with the power torque formula
Rotating machinery is rated by power, but what turns a load is torque, so the power torque formula is where the two meet. Power is torque times rotational speed, which means the same power gives high torque at low speed or low torque at high speed. That trade-off is the whole reason gearboxes exist: gear down and you calculate torque from hp that is far higher at the output than at the motor, at the cost of speed. Understanding this link, and using the torque calculator to work both directions, turns a spec sheet into a real answer about whether a drive can move its load.
Torque conversion calculator chart
Common torque values across units, from the torque calculator:
| Newton meters (N·m) | Pound feet (lb·ft) | Pound inches (lb·in) |
|---|---|---|
| 1 | 0.738 | 8.85 |
| 10 | 7.38 | 88.5 |
| 50 | 36.9 | 443 |
| 100 | 73.8 | 885 |
| 200 | 147.5 | 1770 |
Torque Calculator FAQ
What is the formula for torque?
The formula for torque is T = F × r, force times the perpendicular lever arm. The torque calculator applies it directly, and adds the angle as T = F × r × sin θ when the force is not perpendicular.
How do I calculate torque from hp?
Use the power torque formula. In metric, T (N·m) = 9550 × power in kW ÷ speed in rpm. The torque calculator does this so you can calculate torque from hp without converting by hand.
What is the torque dimensional formula?
The torque dimensional formula is [M L² T⁻²], the same as energy. Torque is quoted in newton meters rather than joules to keep the twisting effect distinct from work done.
Which tool do I use for bolt tightening torque?
Use the Bolt Torque Calculator. It links the wrench torque to the bolt preload with T = K × F × d and also finds the clamp load from a known torque. This torque calculator covers torque from a force and a lever arm, or from power and speed.