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.
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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:
Where:
- τ (tau) = torque, measured in Newton-meters (N·m)
- F = applied force, measured in Newtons (N)
- r = lever arm distance from the pivot point, measured in meters (m)
- θ = angle between the force vector and the lever arm
When the force is applied perpendicular to the lever arm (θ = 90°), sin(90°) = 1 and the formula simplifies to:
How to Use This Calculator
- 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.
- 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.
- Click Calculate: The calculator solves for the unknown variable using the torque formula and shows a step-by-step solution.
- 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 crown | 0.001 N·m | Tiny precision torque |
| Opening a water bottle | 0.5 N·m | Grip and twist |
| Turning a doorknob | 2 N·m | Everyday rotation |
| Opening a stubborn jar | 10 N·m | Requires firm grip |
| Bicycle pedaling | 40–80 N·m | Moderate cycling effort |
| Car wheel lug nut | 100–140 N·m | Torque wrench required |
| Compact car engine | ~200 N·m | Peak engine torque |
| V8 muscle car engine | ~700 N·m | High-performance |
| Industrial motor | 1,000–10,000 N·m | Heavy machinery |
| Wind turbine rotor | 100,000+ N·m | Massive 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
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