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Torque Calculator

Calculate the torque (moment of force) instantly using force, distance, and angle parameters.

Updated

What is the Torque Calculator?

Calculate torque magnitude from force, lever-arm distance, and angle, or solve for one of those values. The calculator also includes torque-unit conversion and a bolt-torque estimate based on a selected nut factor.

The result depends on the entered units and assumptions. Bolt-tightening estimates are approximate; use the fastener and equipment manufacturer's specifications for real applications.

How it works

This calculator estimates torque magnitude using the applied force, lever-arm distance, and the angle between them.

The underlying calculation utilizes the cross product of the lever arm vector and the force vector. The scalar magnitude of torque is calculated using the following mathematical formula:

τ=F⋅r⋅sin⁡(θ)\tau = F \cdot r \cdot \sin(\theta)

Where:

  • τ\tau (Torque): The resulting rotational force (e.g., Newton-meters or pound-feet).
  • FF (Force): The linear force applied to the object.
  • rr (Distance/Radius): The length of the lever arm from the axis of rotation to the point where the force is applied.
  • θ\theta (Angle): The angle between the force vector and the lever arm.

Step-by-Step Execution

  1. Enter the Force: Input the magnitude of the applied force.
  2. Enter the Distance: Specify the exact distance from the pivot point (the lever arm length).
  3. Specify the Angle: Input the angle at which the force is applied relative to the lever arm. (A 90° angle yields maximum torque, while a 0° angle yields zero torque).
  4. Read the result: The tool converts the selected inputs to base units, applies the formula, and displays the result in your chosen unit.

Bolt torque estimate

The bolt mode uses T=K⋅D⋅FT = K \cdot D \cdot F, where KK is an entered nut factor, DD is fastener diameter, and FF is preload. This is a simplified estimate; friction, lubrication, fastener condition, and manufacturer guidance affect actual tightening results.

Examples

Perpendicular Force Calculation

Calculating the torque when a 50 Newton force is applied at a 90-degree angle at a distance of 0.5 meters.

Force: 50 N, Distance: 0.5 m, Angle: 90 degrees
 
Torque: 25 N·m

Angled Force Applied

Determining the torque with a 100 pound-force applied at a 45-degree angle on a 2-foot lever.

Force: 100 lbf, Distance: 2 ft, Angle: 45 degrees
 
Torque: 141.42 lbf·ft

Frequently asked questions

What is torque?

Torque (also called the moment of force) describes how strongly a force tends to turn an object around a pivot or axis. Its effect depends on both the force and how far, and in what direction, it acts from that pivot.

What is the formula used in the Torque Calculator?

The calculator uses the standard physics equation for torque: τ=F⋅r⋅sin⁡(θ)\tau = F \cdot r \cdot \sin(\theta). In this equation, FF represents the applied force, rr represents the distance from the pivot point to the application of force, and θ\theta is the angle between the force and the lever arm.

How does the angle (θ\theta) affect the torque?

The angle of the applied force affects the torque magnitude. It is greatest when the force is perpendicular to the lever arm (θ=90∘\theta = 90^\circ). A force parallel to the lever arm (θ=0∘\theta = 0^\circ or 180∘180^\circ) contributes zero torque about that pivot; other forces or existing motion may still cause rotation.

What units should I use for torque calculations?

Common units include newton-metres (N·m), pound-feet (lbf·ft), and pound-inches (lbf·in). Choose force, distance, and output units separately; the calculator converts the inputs before computing torque.

Is my calculation data sent to a remote server?

Calculations are performed in the browser. The tool does not need to send the entered values to a calculation service.

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