Enter the mass of the object and the angle of the incline into the calculator to determine the reaction force acting on the object.

Reaction Force Formula

The following formula is used to calculate a reaction force acting on an object on an incline.

F = m*g*cos(x) 
  • Where F is the force
  • m is the mass
  • g is the acceleration due to gravity (9.81 m/s^2)
  • x is the angle between the ground and the incline surface

To calculate a reaction force, multiply the mass by the acceleration due to gravity, then multiply by the cosine of the angle of incline.

Reaction Force Definition

A reaction force is defined as the force opposite force that occurs in response to an active force. This is states in Newton’s third law of motion that states that every force has an equal and opposite reaction force.

Example Problem

How to calculate a reaction force of an inclined plane?

  1. First, determine the mass of the object.

    Measure the mass of an object using an accurate scale, or calculate it through volume and density. For this example, the mass is found to be 50 kg.

  2. Next, determine the angle of the inclined plane.

    It’s important to note that in this example problem the reaction force is the normal force acting on the object and note the friction force. (assumed frictionless). The angle is found to be 50 degrees.

  3. Finally, calculate the reaction force.

    Calculate the reaction force using the formula F = m*g*cos(x) = 50*9.81*cos(50) = 315.287 N.


What is an example of a reaction force?

While there is technically an infinite number of reaction forces, the most common reaction force considered is the normal force. This is the force of the ground pushing against every object due to the force of gravity.

What is an action-reaction force?

An action-reaction force is the combination of two equal but opposite forces acting on two different objects. That is, one object exerts a force on another, such as a person pushing a wall, and the wall reacts by exerting the same force on the person.