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

Spring Force Formula

The following equation is used to calculate the Spring Force.

Fs = k*x
  • Where Fs is the spring force (N)
  • k is the spring constant (N/m)
  • x is the displacement of the spring (m)
    • The displacement is the distance of compression or tension

To calculate the spring force, simply multiply the spring constant by the displacement

What is a Spring Force?

Definition:

A spring force is a restoring force provided by a physical spring, a helical spring, or a torsion spring. The restoring force provided by the spring is proportional to the displacement of the elastic element. It always acts in the direction that tends to restore the equilibrium position of the body.

In other words, this means that when you apply a force to compress or stretch a spring, it pushes back against that external force with a restoring force (the amount of which depends on how much the spring has been compressed or stretched).

How to Calculate Spring Force?

Example Problem:

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

First, determine the spring constant. In this example, the spring constant is provided as 400 N/m.

Next, determine the amount of displacement. For this problem, the spring is compressed by .25 m.

Finally, calculate the spring force using the formula above:

Fs = k*x

Fs = 400*.25

Fs = 100 N

FAQ

What factors can affect the spring constant in a physical spring?

The spring constant, denoted as ‘k’, can be affected by several factors including the material of the spring, the diameter of the coil, the number of coils, and the overall design of the spring (such as helical, torsion, or conical). Different materials and designs can significantly alter the stiffness of the spring, thereby affecting its spring constant.

How does temperature affect spring force?

Temperature can have a significant impact on spring force, primarily through its effect on the material properties of the spring. As temperature increases, most materials tend to become softer, which can decrease the spring constant (‘k’) and thus reduce the spring force. Conversely, at lower temperatures, materials become harder and the spring force may increase. The exact effect depends on the material’s thermal properties and the range of operating temperatures.

Can spring force be negative?

In the context of the formula Fs = k*x, spring force itself is not negative; however, the displacement (x) can be negative if the spring is compressed (as opposed to being stretched). The negative sign in this context indicates the direction of the force. The spring force (Fs) is always directed in such a way as to restore the spring to its equilibrium position, opposing the displacement. So, while the numerical value for force is always positive, the direction can be considered negative if it opposes the initial displacement.