Physics

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Torque Calculator.

Calculate torque magnitude from force, lever arm, and included angle.

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01

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Torque: 50 N·m

Torque

0.000000N·m

Results update automatically as you type.

Use Cases

Mechanical Engineering Design

Engineers use torque calculations to design rotating systems, such as shafts, gears, and levers, ensuring they can handle applied forces without failure.

Example: Calculate the torque on a wrench when a 200 N force is applied at a 90° angle to a 0.3 m handle.

Physics Education

Students and educators use this calculator to verify theoretical torque problems and understand the relationship between force, lever arm, and angle.

Example: Check the torque when a 50 N force is applied at 30° to a 0.5 m lever arm.

Frequently Asked Questions

What is torque and how is it calculated?
Torque is the rotational equivalent of force. It is calculated as the product of the force applied, the lever arm length, and the sine of the included angle between them. The formula is τ = r × F × sin(θ), where τ is torque, r is lever arm, F is force, and θ is the included angle.
What units does this torque calculator use?
This calculator uses newtons (N) for force, meters (m) for lever arm, and degrees (°) for the included angle. The resulting torque is expressed in newton-meters (N·m).
How does the included angle affect torque?
The included angle is the angle between the force vector and the lever arm. Torque is maximum when the angle is 90° (sin 90° = 1) and zero when the angle is 0° or 180° (sin 0° = sin 180° = 0). As the angle changes, the effective perpendicular component of force changes, altering torque.

Tips & Common Mistakes

Tips

  • Ensure the included angle is measured between the force vector and the lever arm, not the angle from the horizontal or vertical.
  • Use consistent units: force in newtons, lever arm in meters, and angle in degrees. The calculator handles the conversion to radians internally.
  • For maximum torque, apply the force perpendicular to the lever arm (90°). For zero torque, apply the force parallel to the lever arm (0° or 180°).
  • Double-check your input values for accuracy, especially the angle, as small errors can significantly affect the torque result.

Common Mistakes to Avoid

  • Using the angle between the force and the horizontal instead of the angle between the force and the lever arm.
  • Forgetting to convert units, such as using centimeters for lever arm instead of meters, which leads to incorrect torque values.
  • Assuming torque is always maximum regardless of angle; the angle must be 90° for maximum torque.

Last updated: August 13, 2026