The torque calculator computes rotational force using τ = r × F × sin θ, where r is the lever arm length, F is the applied force, and θ is the angle between force and lever arm. Results are shown in both N·m and ft·lb simultaneously.
Inputs
90° = perpendicular (maximum torque)
Result
Enter values and click Calculate
How to Use the Torque Calculator
Torque is the rotational equivalent of linear force. It quantifies how effectively a force causes an object to rotate about an axis. This calculator uses the formula τ = r × F × sin θ to find any missing variable.
Example: Tightening a Bolt with a Wrench
A mechanic applies 50 N of force at the end of a 0.3 m wrench, perpendicular to the handle (θ = 90°): τ = 0.3 × 50 × sin(90°) = 0.3 × 50 × 1 = 15 N·m (= 11.06 ft·lb). If torque specifications require 20 N·m, the mechanic needs to either use more force or a longer wrench handle.
Solving for Force or Lever Arm
Use the "Solve For" dropdown to find an unknown variable. If you need 20 N·m with a 0.3 m wrench at 90°: required force = τ / (r × sin θ) = 20 / (0.3 × 1) ≈ 66.7 N. Or if you need 20 N·m with 50 N at 90°: required wrench length = τ / (F × sin θ) = 20 / (50 × 1) = 0.4 m (40 cm).
The Role of Angle
The sin θ term means only the perpendicular component of force creates rotation. A force applied at 45° creates 70.7% of maximum torque (sin 45° = 0.707). At 30°, only 50% (sin 30° = 0.5). Always apply force perpendicular to the lever arm for maximum torque — this is why wrench handles are designed to be gripped at a right angle to the bolt axis.
Unit Conversion
This calculator shows both N·m and ft·lb results simultaneously. The conversion factor is 1 N·m = 0.7376 ft·lb (or 1 ft·lb = 1.3558 N·m). Car engine torque specs are often listed in both units in owner's manuals — use this calculator to verify.
FAQ
What is torque in physics?
Torque (τ) is the rotational equivalent of linear force — it measures how much a force causes rotation about a pivot point. The formula is τ = r × F × sin θ, where r is the lever arm distance (meters), F is the applied force (newtons), and θ is the angle between the force vector and the lever arm.
What is a good example of torque?
A wrench tightening a bolt is the classic example. If you apply 50 N of force at the end of a 0.3 m wrench (perpendicular to the handle), torque = 50 × 0.3 × sin(90°) = 15 N·m. A longer wrench or more force increases torque proportionally.
How do I convert N·m to ft·lb?
1 N·m = 0.7376 ft·lb. So 15 N·m = 15 × 0.7376 = 11.06 ft·lb. This calculator shows both units simultaneously so you don't need to convert manually.
Why does angle matter in torque calculations?
The sin θ factor accounts for the direction of the force relative to the lever arm. Force applied perpendicular (90°) gives maximum torque — sin(90°) = 1. Force applied parallel to the lever arm (0° or 180°) gives zero torque because no rotation is produced.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted to any server.
What is the difference between torque and moment?
In physics and engineering, torque and moment (of force) are the same quantity — both describe the rotational effect of a force about a pivot. Engineers more often say 'moment' in structural analysis; physicists and mechanics more often say 'torque' in dynamics.