Potential Energy Of A Spring Formula

In the usual position(i.e., when not stretched), there is no energy in the spring. But, when the position is altered from its usual position, the spring is able to store energy by the virtue of its position. This stored energy is known as potential energy. The potential energy of the spring is the potential energy stored as a result of the deformation of a particular elastic object, or a spring. It describes the work done to stretch the spring and depends on the spring constant k and the distance stretched.

Formula of Potential Energy of A Spring

The potential energy of a spring is given by,

P.E = ½ k x2


  • k is the spring constant
  • x is the spring displacement

Solved Examples

Example 1: Determine the potential energy of a spring whose spring constant is 200 N/m and the displacement is 0.8 m.


Given parameters are

k = 200 N/m

x = 0.8 m

The potential energy of a string formula is given by

P.E = 1/2 kx2

P.E = ½ (200 x (0.8)2)

P.E = 64 J

Example 2: The spring constant and displacement of a stretched string is 100 N/m and 0.5 m respectively. Determine the potential energy stored in the stretched string.


Given parameters are

k = 100 N/m

x = 0.5 m

Potential energy of a string formula is given by,

P.E = 1/2 kx2

P.E = 1/2 x (100 x (0.5)2)

P.E = 12.5 J

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