# Torque Calculator (τ = rF sinθ)

Calculate torque from applied force, lever arm, and angle using τ = rF sinθ. Instant results in N·m and ft·lbs with formula explanation.

## What this calculates

Torque is the rotational equivalent of force. It measures how effectively a force causes an object to rotate about an axis. This calculator uses the formula τ = rF sin(θ), where r is the lever arm distance, F is the applied force, and θ is the angle between the force vector and the lever arm.

## Inputs

- **Applied Force** (N) — min 0
- **Lever Arm Distance** (m) — min 0
- **Angle Between Force and Lever Arm** (°) — min 0, max 180

## Outputs

- **Torque** (N·m) — τ = rF sin(θ)
- **Torque** (ft·lbs) — Torque in foot-pounds
- **Effective Moment Arm** (m) — r·sin(θ): perpendicular distance from pivot to line of force

## Frequently Asked Questions

**Q: What is torque?**

A: Torque (or moment of force) is a measure of the turning force on an object. It depends on three factors: the magnitude of the force, the distance from the pivot point (lever arm), and the angle at which the force is applied. Maximum torque occurs when the force is perpendicular to the lever arm (sin 90° = 1).

**Q: Why does angle matter for torque?**

A: Only the component of force perpendicular to the lever arm produces torque. When you push along the lever arm (0°), no rotation occurs. When you push perpendicular (90°), all the force contributes to rotation. The sin(θ) factor accounts for this geometry.

**Q: How do I convert N·m to ft·lbs?**

A: Multiply Newton-meters by 0.7376 to get foot-pounds. For example, 100 N·m ≈ 73.76 ft·lbs. This conversion is commonly needed when working with automotive torque specifications, which are often given in ft·lbs in the United States.

**Q: What is the difference between torque and work?**

A: Both torque and work have units of force times distance, but they are different concepts. Torque is a rotational force applied at a distance from a pivot (a vector/pseudovector quantity). Work is energy transferred by a force through a displacement (a scalar quantity). Torque can exist without motion, but work requires displacement.

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Source: https://vastcalc.com/calculators/physics/torque
Category: Physics
Last updated: 2026-04-21