About the Torque Calculator
This torque calculator helps you find the torque arising in a rotating object. Whether you need to find torque, force, or lever arm length, simply enter the values you know and let the calculator do the rest.
What Is Torque?
Torque (also called the moment of force) is the tendency of a force to rotate an object around a pivot point. Imagine trying to open a door — the further you push from the hinges (the pivot point), the less force you need, because a longer lever arm produces greater torque.
Torque depends on three factors:
- r — Lever arm: the perpendicular distance from the pivot point to the line of action of the force.
- F — Force: the magnitude of the force applied.
- θ — Angle: the angle between the force vector and the lever arm. At 90° (perpendicular), torque is maximized. At 0° or 180°, the force is parallel to the lever arm and produces no torque.
Torque Equation
τ = r × F × sin(θ)
| Symbol | Quantity | Metric unit | US unit |
|---|---|---|---|
| τ | Torque | N·m (newton-metre) | ft·lbf (foot-pound) |
| r | Lever arm | m (metre) | ft (foot) |
| F | Force | N (newton) | lbf (pound-force) |
| θ | Angle | degrees (°) | |
Three Ways to Use This Calculator
1. Find Torque (τ)
Calculate torque when you know the lever arm length, the applied force, and the angle.
Formula: τ = r × F × sin(θ)
Example: r = 0.5 m, F = 120 N, θ = 90° → τ = 60 N·m
2. Find Force (F)
Calculate the required force when you know torque, lever arm, and angle.
Formula: F = τ / (r × sin(θ))
Example: τ = 60 N·m, r = 0.5 m, θ = 90° → F = 120 N
3. Find Lever Arm (r)
Calculate the required lever arm length when you know torque, force, and angle.
Formula: r = τ / (F × sin(θ))
Example: τ = 60 N·m, F = 120 N, θ = 90° → r = 0.5 m
How to Calculate Torque — Step by Step
- Determine the force acting on the object. For example, F = 120 N.
- Measure the lever arm — the distance from the pivot to the point where the force is applied. For example, r = 0.5 m.
- Find the angle between the force vector and the lever arm. For maximum torque, θ = 90° (perpendicular force).
- Apply the formula: τ = r × F × sin(θ) = 0.5 × 120 × sin(90°) = 60 N·m.
Unit Systems Supported
This calculator supports both the metric (SI) system and the US customary system:
Metric (SI)
- Torque: N·m (newton-metres)
- Force: N (newtons)
- Length: m (metres)
US Customary
- Torque: ft·lbf (foot-pounds)
- Force: lbf (pound-force)
- Length: ft (feet)
Results always include automatic conversions between N·m, ft·lbf, N·cm, and kgf·m for torque, plus N/lbf/kgf for force and m/cm/ft/in for lever arm.
Key Conversion Factors
| From | To | Multiply by |
|---|---|---|
| N·m | ft·lbf | 0.737562 |
| ft·lbf | N·m | 1.35582 |
| N·m | kgf·m | 0.101972 |
| N·m | N·cm | 100 |
| N | lbf | 0.224809 |
| lbf | N | 4.44822 |
Frequently Asked Questions
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What is the difference between torque and force?
Force is a push or pull in a straight line (measured in N or lbf). Torque is the rotational effect of that force around a pivot point. The same force produces more torque if applied further from the pivot (longer lever arm) or at a more perpendicular angle.
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Why is the angle important?
Only the component of force perpendicular to the lever arm contributes to rotation. sin(θ) captures this: at θ = 90° the full force acts rotationally (maximum torque); at θ = 0° or 180° the force is parallel to the lever arm and produces zero torque.
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What is a practical example of torque?
Opening a door: the hinges are the pivot. Pushing near the hinges requires much more force than pushing at the far edge (handle). A longer lever arm reduces the force needed for the same torque. Another example: tightening a bolt with a wrench — a longer wrench handle lets you apply the same torque with less force.
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Is torque the same as energy?
Numerically, 1 N·m of torque has the same units as 1 joule (J) of energy, but they are different physical quantities. Torque is a vector quantity describing a rotational tendency; energy is a scalar describing work done. Do not confuse them in physical calculations.
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How does the torque calculator handle the angle?
Enter the angle in degrees between the force vector and the lever arm. The default is 90°, which gives maximum torque. If you enter 0° or 180°, the formula yields zero torque — and the calculator will show an error when trying to find force or lever arm from a zero result.