Normal Force Calculator

Enter the force due to friction on an object, and the coefficient of friction, or enter the total force (weight) and the angle at which that force is acting in order to calculate the normal force.

What is the normal force?

A normal force is known as the force acting against an object “normal to a surface” In other words, this means what force is acting against an object that is perpendicular to the surface the object is resting on. In most cases this force is equal to the weight of an object. Since an object at rest needs to have equal forces acting on all sides, and the only known force is the weight, (or force due to gravity), then the normal force must equal the weight.

Most often normal force is referenced when talking about physics problems involving friction. This is because the force due to friction acting on an object is directly proportional to the normal force.

Normal Force Formula

The following two formulas are used int he calculators above to determine the normal force:

Fn = Ff / Cf

  • Where Fn is the normal force
  • Ff is the force due to friction
  • Cf is the coefficient of friction

Fn= F * sin (theta)

  • Where Fn is the normal force
  • F is the total force
  • and theta is the angle at which the total force is acting

How to calculate a normal force?

The following examples is a step by step guide on how to calculate the normal force acting on an object given the friction force and coefficient of friction.

  1. The fist step is to determine the force of friction acting on the object. This is typically measure experimentally. We will assume the object is still at rest. In this case, the force acting on the object will be associated with the static coefficient of friction. We find this to be 20 Newtons.
  2. The next step is to determine the coefficient of static friction between the object and the surface it is contacting. This is also normally determined experimentally. We will assume we find the coefficient of friction to be .75. Recall that the coefficient is unit less.
  3. Finally, enter the information into the formula above to determine the normal force. Fn = 20 N * .75 = 15 N.
  4. Analyze the results and apply learning to future problems.
normal force calculator

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