What Is Torque?
Torque (also called moment of force) is a measure of the turning force on an object. When you use a wrench, push a door handle, or turn a steering wheel, you’re applying torque. It depends on three things: how hard you push, how far from the pivot you push, and the angle of your push.
τ = Fr sin(θ)
Where F is the applied force, r is the distance from the axis of rotation to the point of force application (lever arm), and θ is the angle between the force vector and the lever arm. Maximum torque occurs when θ = 90°.
Torque Units
| Unit | Symbol | Conversion to N·m |
|---|---|---|
| Newton-metre | N·m | 1 (base) |
| Pound-foot | lb·ft | 1.3558 |
| Pound-inch | lb·in | 0.1130 |
| Kilogram-force metre | kgf·m | 9.8067 |
How to Use the Calculator
- Select what to find: torque, force, lever arm, or angle.
- Enter known values and select units.
- Click Calculate.
- View torque in multiple units with formula breakdown.
Example Calculations
100 N at 0.3 m, 90°
τ = 100 × 0.3 × 1 = 30 N·m
Wrench: 50 N at 25 cm
τ = 50 × 0.25 = 12.5 N·m
50 lb·ft bolt torque
50 × 1.3558 = 67.8 N·m
Common Mistakes
- Forgetting sin(θ) when force is not perpendicular to the lever arm.
- Confusing torque (N·m) with energy (J) even though they share dimensions.
- Using the total length instead of the perpendicular distance to the line of action.
- Mixing lb·ft with lb·in (a factor of 12 error).
Accuracy and Limitations
These calculations assume a rigid body, a well-defined axis of rotation, and a single point of force application. Real-world factors like material deformation, multiple forces, and friction at the pivot affect actual torque. Use for education and estimation.
FAQ
What is torque?›
Torque is the tendency of a force to rotate an object about an axis. It depends on force magnitude, lever arm length, and the angle between them.
What is the difference between torque and force?›
Force pushes or pulls in a straight line. Torque causes rotation. Torque = force × perpendicular distance from the axis.
Why is a longer wrench easier to use?›
A longer wrench increases the lever arm (r), so less force is needed for the same torque: F = τ/r.
Is N·m the same as joules?›
Dimensionally yes (both are kg·m²/s²), but they measure different things. N·m for torque and J for energy should not be interchanged.
What is the rotational equivalent of Newton’s second law?›
τ = Iα, where I is moment of inertia and α is angular acceleration.
How do I convert lb·ft to N·m?›
Multiply by 1.3558: 1 lb·ft = 1.3558 N·m.
Sources
Author & technical reviewer
Manish Kumar
PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.
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