Elastic Potential Energy Calculator
Find the energy stored in a stretched or compressed spring.
Results update as you type.
How it works
When you stretch or compress a spring, you store energy in it that can later be released, and this calculator finds that elastic potential energy. You enter the spring constant, which measures stiffness, and the displacement from the spring's natural length, and it returns the stored energy in joules. The energy equals half the spring constant times the displacement squared, which is the work you did against the spring's restoring force to deform it. The squared displacement means the energy climbs steeply: stretching a spring twice as far stores four times the energy, and three times as far stores nine times as much. This stored energy is what powers wind-up toys, launches projectiles from spring guns and pinball plungers, absorbs shocks in vehicle suspensions, and drives the oscillation of any spring-mass system. It is also the model physicists use for the potential energy in vibrating molecular bonds. Because energy is conserved, the elastic potential energy converts entirely into kinetic energy as the spring snaps back, which is how spring-powered mechanisms accelerate objects. The calculation assumes the spring obeys Hooke's law and is within its elastic limit. Enter the spring constant and displacement to find the stored energy.
PE = ½ · k · x²
The elastic potential energy stored in a spring equals one half the spring constant times the square of the displacement from its natural length. This is the work done to stretch or compress the spring, calculated as the area under the force-displacement line of Hooke's law. Because displacement is squared, doubling the stretch quadruples the stored energy, which is fully released when the spring returns to its rest position.
Source:Classical mechanics (elastic potential energy)
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Worked example
How to use this calculator
- 1
Enter your values
Enter spring constant (k) and displacement (x).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Elastic potential energy updates instantly as you type — no button to press.
Frequently asked questions
What is elastic potential energy?
Elastic potential energy is the energy stored in an elastic object, such as a spring, when it is stretched or compressed away from its natural shape. It equals half the spring constant times the square of the displacement. This stored energy is released when the object returns to its resting shape, converting into motion or other forms of energy.
Why is the displacement squared?
The displacement is squared because the restoring force itself grows linearly with displacement under Hooke's law, so the work done to stretch the spring, which is the area under the force-displacement line, is a triangle whose area involves the displacement squared. The practical effect is that stretching a spring twice as far stores four times the energy, not twice.
How does it relate to Hooke's law?
Hooke's law gives the force a spring exerts as the spring constant times displacement. Elastic potential energy is the work done against that force to stretch the spring, obtained by integrating the force over the displacement. The result, half the spring constant times displacement squared, is the energy stored, so the two concepts are directly linked through the same spring constant.
What happens to the stored energy?
When the spring is released, the stored elastic potential energy converts into kinetic energy as the spring accelerates back toward its natural length, setting attached objects in motion. In an ideal frictionless system all the energy transfers; in reality some is lost to heat and sound. This conversion is what powers spring launchers, clocks, and oscillating systems.
Does this work for compression too?
Yes. Elastic potential energy is stored whether a spring is stretched or compressed, and the formula is identical because the displacement is squared, making the sign irrelevant. Whether you pull a spring outward or push it inward by the same distance, it stores the same amount of energy, which it releases when returning to its natural length.