Torque Calculator
Calculate torque, force, lever arm, angle, net torque, and rotational equilibrium with diagrams and step-by-step explanations.
Background
Torque measures how strongly a force tends to rotate an object around a pivot. It depends on the force, the distance from the pivot, and the angle between the force and the lever arm. This calculator helps students see why pushing farther from the pivot and pushing more perpendicular to the lever arm creates more rotation.
How to use this calculator
- Choose Basic torque, Multiple forces, Rotational equilibrium, or Where should I push?
- Enter force in newtons, distance in meters, angle in degrees or radians, and torque in N·m.
- Click Calculate to see the answer, sign convention, torque diagram, and steps.
- Use quick examples to compare doors, wrenches, seesaws, beams, and zero-torque cases.
How this calculator works
The calculator uses the magnitude equation for torque, τ = rFsinθ. The force creates maximum torque when it is perpendicular to the lever arm and zero torque when it points directly toward or away from the pivot.
For multiple forces, it calculates each torque separately, assigns clockwise or counterclockwise direction, then adds the signed torques to find the net torque. For equilibrium, it uses Στ = 0, meaning clockwise torque equals counterclockwise torque.
Formula & Equation Used
Torque magnitude: τ = rFsinθ
Lever-arm form: τ = F × lever arm
Rotational dynamics: Στ = Iα
Net torque: τnet = Στccw − Στcw
Rotational equilibrium: Στ = 0
Perpendicular lever arm: r⊥ = r sinθ
Example Problems & Step-by-Step Solutions
Example 1: Door torque
A 35 N push applied 0.70 m from the hinge at 90° gives τ = (0.70)(35)sin(90°) = 24.5 N·m.
Example 2: Wrench at an angle
An 80 N force on a 0.25 m wrench at 60° gives τ = (0.25)(80)sin(60°) ≈ 17.3 N·m, less than the 20 N·m maximum.
Example 3: Seesaw balance
If a 392 N child sits 1.0 m from the pivot and a 245 N child sits on the other side, equilibrium requires 392 × 1.0 = 245 × r, so r = 1.6 m.
Example 4: Beam with multiple forces
For a beam, calculate each torque separately, assign clockwise or counterclockwise sign, then add the signed torques to find the net rotation tendency.
Example 5: Crowbar lifting
A longer crowbar increases the lever arm, so the same force produces more torque around the contact point.
Frequently Asked Questions
When is torque maximum?
Torque is maximum when the force is perpendicular to the lever arm, so θ = 90° and sinθ = 1.
Why does pushing at the hinge produce zero torque?
At the hinge, the lever arm distance is zero. Since τ = rFsinθ, zero distance gives zero torque.
What does negative torque mean?
Negative torque usually means clockwise rotation if counterclockwise is chosen as positive. It is a sign convention, not a bad result.
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