Torque Calculator
Enter force, lever distance and angle to compute torque τ=r·F·sinθ. F=20 N, r=0.5 m, θ=90° → τ=10 N·m; at 30° → 5 N·m.
Input Data
Results
At a glance:Torque (moment of force) τ = r·F·sinθ measures how strongly a force tends to rotate an object about a pivot. F is the force (N), r is the lever-arm distance from the pivot (m), θ is the angle between the force direction and the lever arm. Only the component perpendicular to the lever (F·sinθ) produces rotation; when θ=90° torque is maximal (τ=rF), when θ=0° (force along the arm) torque is zero. Example: F=20 N at r=0.5 m, θ=90° → τ=20×0.5×1=10 N·m; at θ=30° → τ=20×0.5×0.5=5 N·m. Properties: (1) torque is a vector along the rotation axis (right-hand rule); (2) a 'couple' is two equal opposite parallel forces giving τ=F·d regardless of pivot; (3) rotational equilibrium needs net torque zero (Στ=0) — the basis of lever balance. Applications: (1) wrench and bolt tightening (longer handle → more torque); (2) seesaws and levers; (3) steering wheels and bicycle pedals; (4) motors and engines (rated in N·m); (5) DSE Physics rotational statics.
Formula
Torque: τ = r·F·sinθ
Max at θ=90°: τ = r·F
Zero at θ=0° (force along arm)
Equilibrium: Στ = 0
$$\tau = r F \sin\theta$$How to Use
- Enter force F (N).
- Enter lever-arm distance r (m).
- Enter angle θ (°); 90° gives maximum torque.
- The tool shows torque τ (N·m).
Case Studies
Loosening a bolt with a wrench
F=20 N at r=0.5 m, θ=90°.
τ = 20 × 0.5 × 1 = 10 N·m.
Pull at 30° instead → τ=20×0.5×0.5=5 N·m (half).
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.