Torque is the turning effect of a force, from opening a door to tightening a bolt. Enter the force, the distance from the pivot and the angle to get the torque in newton-metres.
Enter the force and the distance from the pivot.
Enter the angle (90° for a perpendicular push).
Read the torque.
Torque: τ = F × r × sin θ
Torque is the turning effect of a force. This calculator multiplies the force by its distance from the pivot and by the sine of the angle between the force and the lever, giving the torque in newton-metres. It answers questions such as how hard a spanner turns a nut, how much twist a door handle gives, or why a push at a slant is less effective than a push at right angles.
Class 9 and Class 11 physics introduce torque as the moment of a force, and it is basic to rotational motion in JEE. Outside exams it shows up everywhere: in motorcycle and car wheel-nut specifications printed in N·m, in cycle pedals and cranks, in construction cranes and in the design of hand tools. Getting the torque right matters, because too little leaves bolts loose and too much can strip threads.
1. Find the force F in newtons.
2. Measure the lever arm r in metres, from the pivot to the point where the force is applied.
3. Measure the angle θ between the direction of the force and the line of the lever.
4. Multiply: τ = F × r × sin θ. The result is in N·m.
5. Check the special cases: at 90°, sin θ = 1 and τ = F × r; at 0° or 180°, sin θ = 0 and there is no turning effect.
6. For several forces, give clockwise and anticlockwise torques opposite signs and add them.
Split the force into two parts: one along the lever, F cos θ, and one perpendicular to it, F sin θ. The part along the lever pulls or pushes on the pivot and cannot rotate anything. Only the perpendicular part turns the lever, and its turning effect grows with distance, so τ = r × F sin θ. Equivalently, you can keep the full force and use the perpendicular distance from the pivot to the force's line of action, r sin θ. Both views give the same number.
In full form torque is a cross product, τ = r × F, with a direction along the axis of rotation given by the right-hand rule. For flat problems we simply label torques clockwise or anticlockwise. A body is in rotational equilibrium when the total torque about any point is zero; this is the principle of moments behind see-saws, beam balances and the placement of loads on cranes. Newton's second law for rotation is τ = Iα, where I is the moment of inertia.
Torque and energy share the base units kg·m²/s², but they are different quantities. Energy is force times distance moved along the force; torque is force times a perpendicular distance, with no motion needed. A spanner can apply torque to a stuck nut without doing any work. When torque does turn something through an angle φ in radians, the work done is τφ in joules. Writing torque in N·m and energy in J keeps the two clear.
Vikram tightens a wheel nut on his car with a 0.4 m wrench, pushing with 200 N at an angle of 60° to the wrench handle because the wheel arch is in the way.
τ = F × r × sin θ: = 200 × 0.4 × sin 60° = 69.282 N·m
Answer: Torque 69.282 N·m
Measuring the distance to the hand from the wrong point, instead of from the centre of the nut or pivot.
Using cos θ instead of sin θ when θ is measured between the force and the lever.
Entering centimetres for the lever arm, which makes the torque 100 times too large.
Assuming a longer spanner adds force; it adds torque for the same force.
Ignoring the direction of torques when balancing several forces.
Tightening vehicle and machine bolts to the torque printed in service manuals.
Class 9, 11 and JEE problems on moments, levers and rotational motion.
Balancing see-saws, beam balances and loads on cranes.
Choosing motors and gearboxes for fans, pumps and conveyors.
Designing door handles, taps and tools that are easy to turn.
Why is a longer spanner easier?
A larger r gives more torque for the same force.
Is N·m the same as joules?
They have the same base units, but torque is written in N·m to avoid confusion with energy.