Elastic Potential Energy Calculator
Calculate the energy stored in a compressed or stretched spring using Hooke’s law (PE = ½kx²).
How it works
- 1Enter the spring constant k in N/m — a measure of stiffness (a stiffer spring has a higher k).
- 2Enter the displacement x (how far the spring is compressed or stretched from its natural length) in centimetres or inches.
- 3The calculator converts x to metres then evaluates PE = ½·k·x², returning the stored energy in joules.
Use cases
- Physics students verifying Hooke’s law experiments and spring-energy calculations.
- Mechanical engineers sizing springs for energy storage such as actuators and shock absorbers.
- Toy and product designers estimating the launch energy stored in a compressed spring.
Frequently asked questions
What formula does this calculator use?
It uses PE = ½·k·x², where k is the spring constant in N/m and x is the displacement in metres. The ½ comes from integrating Hooke’s law (F = kx) over the displacement. For example, k = 200 N/m compressed 0.05 m stores ½ × 200 × 0.05² = 0.25 J.
Why does the energy increase so rapidly with displacement?
Because x is squared, doubling the displacement quadruples the stored energy. Going from 5 cm to 10 cm multiplies the energy by 4, not 2 — so small extra compressions store disproportionately more energy.
Does it matter whether the spring is compressed or stretched?
No — the formula uses x², so the sign of the displacement cancels out. A spring compressed 3 cm stores the same energy as one stretched 3 cm, provided k is the same and the spring obeys Hooke’s law over that range.
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