Enter the displacement of the spring and the spring constant into the calculator to determine the restoring force.

Restoring Force Formula

The following equation is used to calculate the Restoring Force.

Fr = k*d
  • Where Fr is the restoring force (N)
  • k is the spring constant (N/m)
  • d is the displacement (m)

To calculate a restoring force, multiply the spring constant by its displacement.

What is a Restoring Force?


A restoring force is a force that acts on an object to restore the object to its equilibrium position when it is displaced. In physics, “restoring force” can refer to any force that restores equilibrium to an object.

Restoring forces are a particular class of conservative forces. They are always directed toward the equilibrium point, and their magnitude increases as you move further away from the equilibrium position.

When you release a spring, which compresses or expands away from its rest length, it experiences a restoring force that pulls it back toward its rest length. In the case of an object moving on a frictionless surface in response to gravity, only weight constitutes the restoring force.

How to Calculate Restoring Force?

Example Problem:

The following example outlines the steps and information needed to calculate the Restoring Force.

First, determine the total displacement. In this example, the displacement of the spring is 2m.

Next, determine the spring constant. This spring constant is measured to be 325 N/m.

Finally, calculate the restoring force using the formula above:

Fr = k*d

Fr = 325*2

Fr = 650 N


What is a spring constant, and how is it determined?

The spring constant, denoted as ‘k’ in physics, measures a spring’s stiffness. It is determined experimentally by measuring the force required to cause a certain displacement in the spring. The unit of the spring constant is Newtons per meter (N/m).

Can the formula for restoring force be applied to all types of springs?

Yes, the formula Fr = k*d is a general formula that applies to all linear elastic springs, including compression springs, extension springs, and torsion springs. However, for non-linear springs or those that do not follow Hooke’s Law closely, this formula may not accurately predict the restoring force.

How does displacement affect the restoring force in a spring?

Displacement directly affects the restoring force in a spring. According to Hooke’s Law, the restoring force is directly proportional to the displacement from the equilibrium position. This means that the further the spring is stretched or compressed from its rest length, the greater the restoring force acting on it to return it to equilibrium.