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physics

Torque Calculator

Calculate the torque (rotational force) produced by a force applied at a distance from a pivot point using τ = r × F × sin(θ). Essential for understanding rotation, levers, and mechanical systems.

Reviewed by Christopher FloiedUpdated

This free online torque calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Torque Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Torque Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Torque Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • Use the Torque Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
  • Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
  • Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
  • Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.

About This Calculator

The Torque Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate the torque (rotational force) produced by a force applied at a distance from a pivot point using τ = r × F × sin(θ). Essential for understanding rotation, levers, and mechanical systems. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.

About Torque Calculator

The Torque Calculator computes the rotational effect of a force applied at a distance from a pivot point. Torque is the rotational analog of force — just as force causes linear acceleration, torque causes angular acceleration. The magnitude depends on three factors: the force applied, the distance from the pivot (moment arm), and the angle of application. Maximum torque occurs when force is perpendicular to the lever arm (θ = 90°). Torque explains why long wrenches are easier to turn, why doors have handles far from hinges, and how engines generate rotational power.

The Math Behind It

Torque (τ) is defined as the cross product of position vector and force: τ = r × F. Its magnitude is τ = rF sin θ, where θ is the angle between r and F. **Maximum torque**: When θ = 90° (force perpendicular to lever arm), sin θ = 1, giving τ = rF. This is why you push a door handle perpendicular to the door. **Zero torque**: When θ = 0° or 180° (force along the lever arm). Pushing directly toward or away from the pivot produces no rotation. **Moment arm**: The perpendicular distance from the pivot to the line of action of the force: d = r sin θ. Torque can be written as τ = Fd, where d is the moment arm. **Rotational analog of Newton's second law**: τ_net = Iα, where I is moment of inertia and α is angular acceleration. Just as F = ma governs translation, τ = Iα governs rotation. **Equilibrium**: A system is in rotational equilibrium when net torque is zero: Στ = 0. This is the principle behind balance scales, seesaws, and structural engineering. **Units**: N·m (newton-meters). Not the same as joules, even though dimensionally identical, because torque and energy are fundamentally different concepts. **Power and torque**: P = τω. A car engine producing 300 N·m at 3000 RPM outputs P = 300 × (3000 × 2π/60) = 94.2 kW (126 hp).

Formula Reference

Torque

τ = rF sin θ

Variables: r = distance from pivot (m), F = force (N), θ = angle between r and F

Worked Examples

Example 1: Wrench on Bolt

30 cm wrench, 50 N force perpendicular

Step 1:τ = 0.3 × 50 × sin(90°)
Step 2:= 0.3 × 50 × 1 = 15 N·m

Torque of 15 N·m.

Example 2: Angled Force

0.5 m lever, 100 N at 60°

Step 1:τ = 0.5 × 100 × sin(60°)
Step 2:= 50 × 0.866 = 43.3 N·m

Torque of 43.3 N·m — less than if force were perpendicular (50 N·m).

Example 3: Door Push

0.9 m from hinge, 20 N push perpendicular

Step 1:τ = 0.9 × 20 × sin(90°) = 18 N·m

18 N·m — easy to open.

Common Mistakes & Tips

  • !Using the full distance instead of the perpendicular distance (moment arm) when force is not at 90°.
  • !Confusing torque (N·m) with energy (J) — they have the same units but different physical meanings.
  • !Forgetting that torque is a vector with direction given by the right-hand rule.
  • !Not accounting for multiple torques when analyzing equilibrium problems.

Related Concepts

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Frequently Asked Questions

Why are longer wrenches easier to use?

Torque = force × lever arm. A longer wrench increases r, so the same torque requires less force. A 0.3 m wrench needing 50 N becomes only 25 N with a 0.6 m wrench.

Is torque the same as moment?

In physics and most engineering contexts, torque and moment are used interchangeably. Some disciplines distinguish them: torque for rotating shafts, moment for static loading. The mathematics is identical.

How do car engines produce torque?

Combustion pressure pushes pistons down, which turn the crankshaft via connecting rods. The force on the piston times the crankshaft offset creates torque. Modern engines produce 200-500 N·m, with peak torque at mid-range RPM.