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Elastic Potential Energy Calculator

Energy stored in a stretched or compressed spring.

How it is calculated

The tool uses E = ½ × k × x². k is the spring constant in newtons per metre (N/m) and x is how far the spring is stretched or compressed from its natural (rest) length, in metres. The energy E comes out in joules (J), rounded to two decimals.

The spring constant must be greater than zero. The displacement can be positive (stretch) or negative (compression): it is squared, so the sign makes no difference to the energy. The formula assumes an ideal spring that obeys Hooke's law (force proportional to displacement) and stays within its elastic limit. It gives the energy stored, not the work lost to friction or heat.

Worked example

A spring with k = 200 N/m is stretched 0.15 m. Square the displacement: 0.15² = 0.0225. Multiply by k: 200 × 0.0225 = 4.5. Take half: 2.25 J. Stretching the same spring to 0.30 m, twice as far, stores 9.00 J, four times as much.

Try this example →

Common mistakes

  • Entering the displacement in centimetres or millimetres. It must be in metres, so 15 cm is 0.15; typing 15 gives a result 10,000 times too large.
  • Giving the spring constant in N/cm or N/mm. The value needs to be in N/m.
  • Using the total length of the spring as x. Only the change from the natural length counts.
  • Squaring after halving, or forgetting the square entirely. Energy grows with x², not x, so doubling the stretch quadruples the energy.
  • Assuming it works beyond the elastic limit. A spring stretched too far deforms permanently and the formula no longer holds.

About this calculator

This calculator uses Hooke's law energy formula, PE = ½kx², where k is the spring constant (stiffness, in N/m) and x is the displacement from the spring's natural resting length. Because the restoring force grows linearly with displacement, the stored energy grows with the square of it — stretching a spring twice as far stores four times the energy.

Mechanical engineers use it to size springs in suspensions, valves and mattresses so they store or release the right amount of energy, and physics students use it to verify energy conservation in problems like a mass launched by a compressed spring or a bungee cord's stretch at the bottom of a jump.

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