Torque Calculator
Torque is the rotational equivalent of force, the twisting effect that makes objects spin about an axis. This calculator finds torque from the force you apply, how far from the pivot you apply it, and the angle between them, or works backward to solve for the force, lever arm, or angle when you already know the torque. Force, distance, and torque each accept both metric and imperial units.
Formula
Worked example
50 N applied 0.3 m from the pivot at 90°: τ = 50 × 0.3 × sin(90°) = 50 × 0.3 × 1 = 15 N·m, which is about 11.06 lbf·ft. Working in reverse, to reach 15 N·m at 0.3 m and 90° you need 15 ÷ (0.3 × 1) = 50 N.
How torque works
Torque, also called the moment of force, measures how effectively a force rotates an object about a pivot or axis. It depends on three things: the magnitude of the force, the distance from the axis to the point where the force is applied (the lever arm), and the angle between the force and that lever arm. The formula τ = F · r · sin(θ) captures all three at once. Only the component of force acting perpendicular to the lever arm contributes to rotation, which is why the sine term appears, a force pointing straight along the arm produces no twist at all.
Forward and reverse solving
Use the "Solve for" selector to choose what you want to find. Leave it on Torque to get the standard result from force, lever arm, and angle. Switch it to Force, Lever arm, or Angle to work backward from a torque you already know. The same equation just gets rearranged: F = τ / (r · sin θ), r = τ / (F · sin θ), and θ = arcsin(τ / (F · r)). Solving for the angle has two valid answers, the one shown and its supplement (180° minus it), because sin(θ) and sin(180° minus θ) are equal. If the torque you ask for is larger than force times lever arm, no angle can deliver it and the calculator returns an empty result.
Units, metric and imperial
Force accepts newtons, kilonewtons, pound-force, or kilogram-force; distance accepts metres, centimetres, millimetres, feet, or inches; and known torque accepts newton-metres, kilonewton-metres, pound-force feet, pound-force inches, or kilogram-force metres. Everything is converted to SI internally, then the torque result is reported in newton-metres, pound-force feet, and kilogram-force metres at once. The key conversions are 1 lbf·ft ≈ 1.35582 N·m (so 1 N·m ≈ 0.73756 lbf·ft), 1 lbf ≈ 4.44822 N, and 1 ft = 0.3048 m. Newton-metres are dimensionally identical to joules but are never written as joules, because torque is a vector quantity describing rotation, not energy.
Why the angle matters
The sine of the angle scales the result between zero and one. At 90 degrees sin(θ) equals 1, so all of your force turns into rotation. At 0 or 180 degrees sin(θ) equals 0, meaning a force aimed directly toward or away from the axis produces no torque no matter how large it is. At 45 degrees only about 71 percent of the force is effective. This is the physical reason a wrench works best when you pull at a right angle to its handle, and why pushing a door near the hinge accomplishes very little compared with pushing at the edge.
Limitations
This calculator assumes a single force acting at one point with a rigid lever arm, and it reports the magnitude of the torque rather than its direction (clockwise or counterclockwise). When several forces act together, compute each torque separately and add them with the correct sign to find the net turning effect. For bolt tightening, motor shafts, or belt drives the geometry differs and a dedicated tool is more appropriate, but the underlying τ = F · r · sin(θ) relationship still governs the rotational effect of each force.
Effect of angle on torque
| Angle (θ) | sin(θ) | Fraction of max torque | Effectiveness |
|---|---|---|---|
| 0° / 180° | 0.00 | 0% | None |
| 30° | 0.50 | 50% | Low |
| 45° | 0.71 | 71% | Moderate |
| 60° | 0.87 | 87% | High |
| 90° | 1.00 | 100% | Maximum |
For a fixed force and lever arm, torque scales with sin(θ).
Frequently asked questions
What is the unit of torque?
The SI unit of torque is the newton-metre (N·m), the torque produced by a one-newton force acting one metre from the axis at a right angle. Although a newton-metre has the same dimensions as a joule, torque is never expressed in joules because it describes rotation rather than energy. In imperial units torque is often given in pound-feet, where 1 N·m ≈ 0.738 lbf·ft. This calculator reports newton-metres, pound-force feet, and kilogram-force metres together.
How do I solve for force, lever arm, or angle instead of torque?
Set the "Solve for" selector to the variable you want to find, then enter the known torque plus the other two values. The calculator rearranges τ = F · r · sin(θ): F = τ / (r · sin θ), r = τ / (F · sin θ), or θ = arcsin(τ / (F · r)). When solving for the angle, remember there is a second valid answer at 180° minus the one shown.
Why does the angle default to 90 degrees?
A force applied at 90 degrees to the lever arm is fully perpendicular, so sin(90°) = 1 and the entire force contributes to rotation. This is the most common and the most efficient case, think of pushing a door at right angles to its surface. Because it produces the maximum torque for a given force and distance, 90 degrees is the natural default.
How is torque different from force?
Force is a straight-line push or pull, while torque is the rotational effect that force creates about a pivot. The same force produces different torques depending on where and at what angle it is applied: far from the axis it produces a large torque, and directly toward the axis it produces none. Torque is what changes an object’s rotational motion, just as force changes its linear motion.