Torque Calculator

About the Torque Calculator

Torque is the rotational equivalent of force, it measures how much a force tends to rotate an object about an axis. It depends on the force, the distance from the axis, and the angle between them.

Enter the force (N), the lever-arm length r (m) and the angle θ between the force and the lever arm in degrees (90° for a perpendicular force). Torque is returned in newton-metres (N·m).

How to use this calculator

1. Enter the lever-arm length \(r\), the force \(F\), and the angle \(\theta\) between the lever arm and the force.
2. Make sure the angle is in degrees or radians to match the calculator setting.
3. Click calculate to find the torque \(\tau\).
4. Use the result to compare turning effects or to solve for an unknown force, distance, or angle.

The formula explained

The formula \(\tau = rF\sin\theta\) computes torque, which is the rotational effect of a force about a pivot. Only the part of the force perpendicular to the lever arm contributes to the turning.

• \(\tau\) = torque
• \(r\) = lever-arm length, the distance from the pivot to where the force is applied
• \(F\) = force
• \(\theta\) = angle between the lever arm and the force
• \(\sin\theta\) = the factor that gives the turning portion of the force

Step by step method

1. Identify the pivot, the distance \(r\), the force \(F\), and the angle \(\theta\).
2. Compute \(\sin\theta\).
3. Multiply \(r\), \(F\), and \(\sin\theta\) to get \(\tau\).
4. Check the units, torque is usually in newton-meters, written \(\text{N} \cdot \text{m}\).

Worked example

Problem. A wrench is \(0.30\) m long, and you apply a force of \(40\) N at an angle of \(60^\circ\) to the wrench. Find the torque.

1. Use \(\tau = rF\sin\theta\).
2. Substitute the values, \(\tau = 0.30 \times 40 \times \sin 60^\circ\).
3. Since \(\sin 60^\circ \approx 0.866\), \(\tau \approx 0.30 \times 40 \times 0.866 = 10.392\).

Tips and common mistakes

• If the force is perpendicular to the lever arm, \(\theta = 90^\circ\), and torque is maximized because \(\sin 90^\circ = 1\).
• If the force points along the lever arm, \(\theta = 0^\circ\), and torque is \(0\) because that force does not cause rotation.

Frequently asked questions