Torque Calculator

Work out the rotational force a lever produces, for any force applied at any angle.

Angle should be between 0 and 180 degrees.
Torque
100 N·m
Rotational force generated at the pivot point
Pivotr = 1 mF90°

Force F applied at an angle of 90° to a lever of radius r.

How it was calculated

Formula:τ = r × F × sin(θ)
Sine of Angle:sin(90°) = 1
Calculation:τ = 1 × 100 × 1
Final Torque:100 N·m

About the Torque Calculator

Torque is the physics concept that explains why longer wrenches make it easier to loosen a stuck bolt. It measures how effectively a force causes an object to rotate around a pivot point.

Mathematical Formula & Logic

General Torque Formula tau = r * F * sin(theta) - tau = Torque (N\cdotm) - r = Lever arm length (m) - F = Force (N) - theta = Angle between force and lever arm (deg) Perpendicular Torque tau = r * F - tau = Torque (N\cdotm) - r = Lever arm length (m) - F = Force (N)

Step-by-Step Example

If you push perfectly perpendicular (90 degrees) on a 0.5 meter wrench with 100 Newtons of force, the torque is 0.5 × 100 = 50 N·m. If you push at a 30 degree angle on that same wrench with 100 N of force, the torque drops to 0.5 × 100 × 0.5 = 25 N·m, because half your effort is wasted pushing into the pivot.

Reference Data & Values

forceradiusangletorque
1029020
500.53012.5
100100
10011800
50900

Frequently Asked Questions

The general formula is τ = rF sin(θ). If you are pushing exactly perpendicular to the lever, it simplifies to just τ = r × F.
The standard SI unit is the Newton-meter (N·m). In the US customary system, it is often measured in pound-feet (lb-ft).
Because torque is force multiplied by distance (radius). If you double the length of the wrench, you double the torque without having to push any harder.
If you push parallel to the lever arm (an angle of 0° or 180°), the sin(0) is 0, so the torque is zero. You will just push the object, not rotate it.
No. While they share similar units (N·m vs Joules), work involves distance moved in the direction of the force. Torque is a static measure of rotational leverage. They are completely different concepts in physics.
You get maximum torque at 90 degrees (perpendicular). As the angle gets closer to 0 or 180 degrees, the useful rotating force decreases because more of your effort is wasted pushing or pulling directly against the pivot.
Yes, torque is a vector quantity. Its direction is perpendicular to both the force and the lever arm, determined by the 'right-hand rule' in physics.
Yes. In standard physics conventions, a counter-clockwise rotation is considered positive torque, while a clockwise rotation is negative torque.