Torque Calculator

Torque is T = F x r x sin(theta), where F is the applied force in newtons, r is the lever arm in metres, and theta is the angle between the force and the arm. The result is a moment in newton-metres (N x m).

Only the component of the force perpendicular to the arm twists the pivot. That part is F x sin(theta), so torque peaks at 90 degrees (sin = 1) and falls to zero when the force points straight along the arm at 0 degrees.

The Angle (theta) field defaults to 90 degrees, the everyday case of a wrench pushed at right angles to its handle. At 90 degrees the sine term becomes 1 and torque is simply force times lever arm.

Yes. Pick Force or Lever arm in the Solve for dropdown. The tool inverts the formula to F = T / (r x sin(theta)) or r = T / (F x sin(theta)) and returns the missing quantity.

sin(0) is zero, so torque is zero and no force or lever arm can produce a non-zero torque at that angle. In Force and Lever arm modes the calculator reports an error rather than dividing by zero.

You enter the angle in degrees; the engine converts to radians internally before taking the sine. There is no separate radian mode.

A negative force is accepted and flips the sign of the torque, representing a moment in the opposite rotational direction. The lever arm, however, must be zero or positive because a negative length has no physical meaning.

This tool reports newton-metres only. To convert, multiply the N x m value by about 0.7376 to get pound-feet, or divide by the same factor to go back.

No. The formula runs in plain JavaScript on your device, so your force, distance, and angle values stay in the browser.