Torque Calculator
Calculate torque from force, lever arm length, and the angle between them.
Torque (τ)
Calculation Details
Understanding Torque
Torque, also called the moment of force, is a measure of the rotational effect a force produces about an axis or pivot. It depends not only on how hard you push or pull, but also on how far from the axis the force is applied and the direction of that force. The relationship is expressed as τ = F × r × sin(θ), where the torque is greatest when the force is applied perpendicular to the lever arm.
Key Formula
- τ = F × r × sin(θ) — Torque equals force times lever arm length times the sine of the angle between them
- F — Applied force, measured in newtons (N)
- r — Lever arm length, the distance from the axis to the point of application, in metres (m)
- θ — Angle between the force vector and the lever arm, in degrees
Real-World Examples
Torque is central to engineering, mechanics, and everyday tasks. Here are some practical applications:
- Applying 50 N at the end of a 0.3 m wrench, perpendicular to the handle, produces 15 N·m of torque
- A force applied at 30° to the lever arm delivers only half the torque of the same force applied at 90°
- Loosening a tight bolt is easier with a longer wrench because the lever arm length r increases the torque
- A force directed straight along the lever arm (θ = 0°) produces zero torque, since sin(0°) = 0
References
The formula used in this calculator is based on established physics principles and verified sources:
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Note: This calculator assumes a rigid lever arm and a single applied force under ideal conditions. It does not account for multiple simultaneous torques, deformation, or dynamic effects. Results are based on classical mechanics and may differ from real-world scenarios.