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Torque Calculator

Calculate torque from force and lever arm distance using τ = F × r × sin(θ). Solve for any unknown variable with detailed step-by-step solutions, unit conversions, and real-world torque comparisons.

Torque Calculator
r F τ Pivot
τ Torque F Force r Lever Arm θ Angle
ℹ Enter 2 of 3 values (torque, force, distance) to solve. Angle is optional (defaults to 90°).
Quick Examples
🔧 Wrench on Bolt 🚪 Opening a Door ⚙ Lug Nut Spec 🚲 Pedal at 45°
τ
Torque
F
Force
r
Lever Arm Distance
θ
Angle (optional)
deg
Leave blank for perpendicular force (θ = 90°)

Embed Torque Calculator Widget

About Torque Calculator

The Torque Calculator computes torque (moment of force) from force and lever arm distance using the formula τ = F × r × sin(θ). Enter any two main values to solve for the third, or provide all three to find the required angle. It includes step-by-step solutions, an interactive lever arm diagram, unit conversions, and real-world torque comparisons.

The Torque Formula

Torque measures how effectively a force causes rotation around a pivot point (fulcrum). The general formula is:

General Torque Formula
$$\tau = F \times r \times \sin(\theta)$$

Where:

When the force is applied perpendicular to the lever arm (θ = 90°), sin(90°) = 1 and the formula simplifies to:

Perpendicular Force (Simplified)
$$\tau = F \times r$$

How to Use This Calculator

  1. Choose your known values: Determine which quantities you know — torque, force, and/or lever arm distance. You need at least 2 of the 3 main values.
  2. Enter values with units: Input your known values and select the appropriate units from the dropdowns. Optionally enter the angle if the force is not perpendicular.
  3. Click Calculate: The calculator solves for the unknown variable using the torque formula and shows a step-by-step solution.
  4. Review results: Examine the lever arm visualization, unit conversion table, and real-world comparison to understand the torque magnitude.

Understanding the Variables

Variable Symbol SI Unit Description
Torque τ N·m Rotational force about a pivot point
Force F N Applied force magnitude
Lever Arm r m Distance from pivot to point of force application
Angle θ degrees Angle between force vector and lever arm (90° = perpendicular)

Real-World Torque Examples

Application Typical Torque Notes
Wristwatch crown0.001 N·mTiny precision torque
Opening a water bottle0.5 N·mGrip and twist
Turning a doorknob2 N·mEveryday rotation
Opening a stubborn jar10 N·mRequires firm grip
Bicycle pedaling40–80 N·mModerate cycling effort
Car wheel lug nut100–140 N·mTorque wrench required
Compact car engine~200 N·mPeak engine torque
V8 muscle car engine~700 N·mHigh-performance
Industrial motor1,000–10,000 N·mHeavy machinery
Wind turbine rotor100,000+ N·mMassive scale

Torque vs. Related Concepts

Torque vs. Force

Force (F = ma) causes linear acceleration, while torque causes rotational acceleration. A small force applied far from the pivot produces the same torque as a large force applied close — this is the lever principle described by Archimedes.

Torque vs. Work

Both torque and work share the same SI unit (N·m), but they measure different things. Work is energy transferred along a straight line (W = F × d), while torque is the rotational tendency about a point. To distinguish them, work is sometimes expressed in joules (J).

Torque and Angular Acceleration

Just as F = ma relates force to linear acceleration, the rotational equivalent is τ = Iα, where I is the moment of inertia and α is the angular acceleration. A larger moment of inertia requires more torque to achieve the same angular acceleration.

Frequently Asked Questions

What is torque?

Torque (also called moment of force) is a measure of the rotational force applied to an object. It is the product of the force magnitude, the distance from the pivot point (lever arm), and the sine of the angle between them. The SI unit of torque is the Newton-meter (N·m).

How is torque calculated?

Torque is calculated using the formula τ = F × r × sin(θ), where F is the applied force in Newtons, r is the lever arm distance in meters, and θ is the angle between the force vector and the lever arm. When the force is perpendicular to the lever arm (θ = 90°), the formula simplifies to τ = F × r.

What is the difference between torque and force?

Force causes linear acceleration of an object (F = ma), while torque causes rotational acceleration around a pivot point. Torque depends not only on the force magnitude but also on the distance from the pivot point and the angle of application. A small force applied far from the pivot can produce the same torque as a large force applied close to the pivot.

Why does the angle matter in torque calculations?

The angle between the force and lever arm determines how effectively the force produces rotation. Maximum torque occurs when the force is perpendicular (90°) to the lever arm, because sin(90°) = 1. At 0° or 180°, the force is parallel to the lever arm and produces zero torque, because the force pushes directly toward or away from the pivot point.

What are common units for torque?

The SI unit of torque is the Newton-meter (N·m). Other common units include foot-pound force (ft·lbf) used in the US/UK, kilogram-force meter (kgf·m), inch-pound force (in·lbf) for smaller measurements, and kilogram-force centimeter (kgf·cm). This calculator supports conversion between all these units.

Additional Resources

Reference this content, page, or tool as:

"Torque Calculator" at https://MiniWebtool.com/torque-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Mar 15, 2026

Developer API available: Run this tool from your app, automation, or agent with one JSON HTTP request. View API docs

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