Elastic Potential Energy: Definition, Formula & Examples

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  • 0:01 Elastic Potential Energy
  • 1:07 Hooke's Law
  • 2:12 Finding Elastic…
  • 4:20 Lesson Summary
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Lesson Transcript
Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

Expert Contributor
Amanda Robb

Amanda holds a Masters in Science from Tufts Medical School in Cellular and Molecular Physiology. She has taught high school Biology and Physics for 8 years.

Discover what elastic potential energy is and the types of objects that can have it. Then learn how we find the formula for elastic potential energy using a spring.

Elastic Potential Energy

Potential energy is the energy an object has stored in it due to its position. When we think of potential energy, often the first thing that comes to mind is an object high in the air and just starting to fall. It has potential energy stored in it due to its height, and that energy will be turned into kinetic energy as it falls. However, this is not the only situation in which an object has potential energy. It is a specific type of potential energy called gravitational potential energy.

Another common type of potential energy is elastic potential energy. This is the energy an object has in it due to being deformed. Any object that can be deformed and then return to its original shape can have elastic potential energy. Objects that this would apply to include things like rubber bands, sponges, and bungee cords, among many others. When you deform these objects, they move back to their original shape on their own. As a counter-example, an object that would not be affected by elastic potential energy would be something like a sheet of aluminum foil. If you crumple a sheet of it into a ball it won't change back into a sheet when you let go.

Rubber Band Deforming by Stretching
rubber band stretching

Hooke's Law

One of the most common objects to look at when discussing elastic potential energy is a spring. Springs can be deformed in two different ways in which they return to normal afterwards. They can be stretched, and they can be compressed.

In order to find the formula for elastic potential energy of a spring, we first need to look at something called Hooke's law. This law states that the force needed to stretch a spring is proportional to the displacement of the spring. The displacement of the spring is how far the spring has stretched or compressed from its original shape.

Diagram of Spring Displacement
diagram of spring displacement

Mathematically, Hooke's law can take the following forms.

  • F = - kx
  • F = kx

We often see the formula with the negative sign in order to represent that Hooke's law is a restoring force, but the positive version is a valid representation as well. Here x is the displacement of the spring, and k is something known as the spring constant. This constant is the measure of the stiffness of a spring, and it is unique to each spring. The spring constant depends on factors such as what material the spring is made of and the thickness of the coiled wire, among others.

Finding Elastic Potential Energy

So, why do we need to know all this to find the elastic potential energy? Well, that's because the potential energy is equal to the work done by the spring, and work is a force multiplied by a distance. So Hooke's law gives us our force. For the distance, we use the displacement of the spring. You might assume we would get the formula for elastic potential energy as follows:

PE = Work = force * distance


PE = (kx) * x

This then simplifies to:

PE = kx^2

However, this turns out to be wrong. To see the correct equation for elastic potential energy, we need to look at a force vs. displacement graph.

Force vs. Displacement Graph
force vs displacement graph

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Additional Activities

Calculating Elastic Potential Energy

In this experiment, students will be stretching a rubber band to different lengths and observing how far it flies across the room, and then calculating its elastic potential energy. Students should understand that increased stretch results in increased elastic potential energy and thus increased movement. To do this experiment, you'll need some normal rubber bands, a ruler, a meter stick and ample space. Prior to doing this experiment, warn students to aim rubber bands at a large empty area (preferably outside) and never towards another person.

Student Instructions

The great thing about elastic potential energy is that it applies to all strings and springs. Today, we're going to use a common form of a spring, a rubber band, to demonstrate the relationship between the displacement of the spring and the elastic potential energy. Typical rubber bands have a spring constant (k) of about 88N/m. To do the experiment, grab a few rubber bands and follow the instructions below, then answer the questions. To do this experiment you'll need a big open space.

Be careful when using rubber bands; never launch them at anyone, or yourself!

  1. Start by stretching one rubber band as far as you can without breaking it. Measure how far you stretched the rubber band with a ruler and record the length, in meters (m), as your displacement (x)
  2. Release the rubber band and record how far it travels in meters.
  3. Use the spring constant (88N/m) to calculate the elastic potential energy using the equation in the lesson.
  4. Stretch the rubber band to half as far as you did the previous time and repeat step 2-4.
  5. Stretch the rubber band 1/4 of the length as you did in step 1, then repeat steps 2-4.

TrialDisplacementDistance TraveledPotential Energy


  1. How did the displacement relate to the potential energy in the rubber band?
  2. How did the potential energy relate to the distance the rubber band was able to travel?
  3. If we repeated this experiment with a material with a larger spring constant, what results would you expect?

Expected Results

Students should notice a direct relationship between the displacement and the potential energy of the rubber band. They should also notice an increase in the distance the rubber band can travel with increased potential energy. If students do not observe this, there may be human error in the measurement, or a need for fresh rubber bands.

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