Classical Mechanics
Torque Calculator
Solve τ = rFsinθ for torque, force, or lever arm. Enter angle between force and lever arm.
Result
τ = rFsinθ
Step-by-Step Solution
What is Torque?
Torque (or moment of force) is the rotational equivalent of linear force. It measures the tendency of a force to rotate an object about an axis. The greater the lever arm (distance from the axis) and the force, the greater the torque. The angle between force and lever arm also matters.
τ = rFsinθ
τ = torque (N·m) | r = lever arm (m) | F = force (N) | θ = angle between force and lever arm
💡 Maximum torque occurs when the force is applied perpendicular to the lever arm (θ = 90°, sin90° = 1). A force along the lever arm produces zero torque.
Real-World Applications
Spanners & Wrenches
A longer spanner handle increases the lever arm r, requiring less force F to achieve the same torque on a bolt.
Car Engines
Engine torque (in N·m) determines pulling power. High-torque engines accelerate heavy vehicles effectively.
Cranes
The boom arm creates torque about the crane base. Counterweights balance it to prevent tipping.
Door Hinges
Pushing a door near the hinge (small r) needs far more force than pushing near the edge (large r).
Frequently Asked Questions
Why does a longer spanner make it easier to loosen bolts?
A longer spanner increases the lever arm r. Since τ = rFsinθ and the required torque is fixed (to loosen the bolt), a larger r means you need less force F. This is simple mechanical advantage.
What is the SI unit of torque?
Newton-metre (N·m). It has the same dimensions as energy (Joule = N·m), but torque is not energy — it is a vector (has direction). They are different physical quantities despite sharing units.
What is the difference between torque and work?
Both are measured in N·m but are fundamentally different. Work W = F·d (dot product, scalar), while torque τ = r×F (cross product, vector). Work involves force along displacement; torque involves force perpendicular to the radius.