 Spring force constant (k)
N/m
Spring stretch length (Δx)
ft
Spring potential energy (U)
J

# Elastic Potential Energy Calculator

By Bogna Haponiuk

This elastic potential energy calculator makes it easy to determine the potential energy of a spring when stretched or compressed. Read on to get a better understanding of this concept, including an elastic potential energy definition and an example of calculations. Make sure to check out our gravitational potential energy calculator, too!

## Elastic potential energy definition

Imagine a simple helical spring. You can compress or stretch it (to some extent, of course). To do it, though, you need to perform some work - or, in other words, to provide it with some energy. This energy is then stored in the spring and released when it comes back to its equilibrium state (the initial shape and length). Remember that the elastic potential energy is always positive.

Why exactly is this called 'potential energy'? You can think of it like this: the spring doesn't spend the energy at once (in contrary to kinetic energy), but has the potential to do so.

Don't forget that you cannot compress or stretch a spring to infinity and expect it to return to its original shape. After you reach its elasticity limit, it will get deformed permanently.

## Spring potential energy equation

Our elastic potential energy calculator uses the following formula:

`U = ½kΔx2`

where:

• `k` is the spring constant. It is a proportionality constant that describes the relationship between the strain (deformation) in the spring and the force that causes it. Its value is always real and positive. The units are Newtons per meter;
• `Δx` is the deformation (stretch or compression) of the spring, expressed in meters; and
• `U` is the elastic potential energy in Joules.

Try the Hooke's law calculator if you want to calculate the force in the spring as well.

## How to calculate the potential energy of a spring

Follow these steps to find its value in no time!

1. Determine the spring constant `k`. We can assume a spring of `k = 80 N/m`.
2. Decide how far you want to stretch or compress your spring. Let's say that we compress it by `x= 0.15 m`. Note that the initial length of the spring is not essential here.
3. Substitute these values to the spring potential energy formula: `U = ½kΔx2`.
4. Calculate the energy. In our example it will be equal to `U = 0.5 * 80 * 0.15² = 0.9 J`.
5. You can also type the values directly into the elastic potential energy calculator and save yourself some time :)
Bogna Haponiuk