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Moment of Force Calculator

The Moment of Force Calculator in Physics

The Moment of Force Calculator is a digital tool designed to simplify the complex calculations involved in determining torque.

Understanding the term Torque:

The “Moment of Force,” also known as “torque,” is a concept in physics that describes the rotational effect or turning force applied to an object around an axis or pivot point. Just as force is responsible for linear motion, torque is responsible for rotational motion. It measures how effectively a force can cause an object to rotate.

Torque depends not only on the magnitude of the force applied but also on the distance from the axis of rotation where the force is applied and the angle at which the force is applied. The longer the lever arm (the distance from the axis to the point where the force is applied), the greater the torque produced for the same applied force. Similarly, the angle at which the force is applied relative to the lever arm affects the torque produced.

Formula for Calculating Moment of Force

Mathematically, torque (τ) is calculated using the formula:

τ = r⋅F⋅sin(θ)


  • τ represents the torque (moment of force) in Newton meters (Nm).
  • r is the length from the axis of rotation to where the force is applied, and it’s measured in meters (m).
  • F is the force applied, measured in newtons (N).
  • θ is the angle between the force vector and the direction from the axis of rotation to the point of application, measured in radians.


Let’s consider a simple example to calculate the moment of force when a wrench is used to tighten a bolt. Suppose a force of 50 newtons is applied at the end of a wrench, which is 0.25 meters long. The angle between the force and the lever arm is 30 degrees.


  • F=50N
  • r=0.25m
  • θ=30∘

First, we need to convert the angle from degrees to radians:

θ = 30/180×π = π/6 radians

Now put the values into the formula to calculate the torque (τ): 

 τ = 0.25⋅50⋅sin (⁡π/6) 

Using the sine of π/6, which is 0.5, the calculation becomes: 

 τ = 0.25m⋅50N⋅0.5 = 6.25Nm

So, the moment of force (torque) applied to the bolt is 6.25Nm.

Moment of Force Calculator


How to Operate the Moment of Force Calculator

Input values of Force, Lever Arm and Angle:

  • Force: This is the magnitude of the force applied to the object. Input this value in newtons (N).
  • Lever Arm: The lever arm is the distance between the axis of rotation and the point where the force is applied. Provide this distance in meters (m).
  • Angle: The angle represents the orientation of the force relative to the lever arm. Enter this angle in degrees.

Click the Calculate Button:

After entering the required values, click the “Calculate” button. The calculator will immediately process the inputs using the torque formula and unveil the calculated moment of force (torque) in newton-meters (Nm).

Reset for a new Calculation: 

If you wish to perform another calculation, click the “Reset” button. This action will clear all input fields and the calculated torque value, allowing you to start a new calculation.

At The End

The Moment of Force Calculator is a remarkable tool that simplifies the complex world of rotational dynamics. Its user-friendly interface and accurate calculations enable us to understand how forces cause objects to twist and turn around an axis.