Spring Energy Calculator: E = 1/2 kx^2

The energy stored in a stretched or compressed spring.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • E_s = \tfrac12\,k\,x^2
  • x = \sqrt{\frac{2E_s}{k}}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the elastic potential energy: elastic potential energy = 1/2 x spring constant x extension or compression^2
  2. Put the values in (every value in its SI unit): elastic potential energy = 1/2 x 200 x 0.05^2
  3. The answer: elastic potential energy: 0.25 J
  4. The same answer in other units: 250 mJ; 0.00025 kJ; 0.184391 ft lbf

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is the formula for the energy in a spring?

Half times the spring constant times the extension squared. A 200 N/m spring stretched 0.05 m stores 0.25 J.

Why is there a half in the formula?

The force grows from zero to kx as the spring is stretched, so the average force is half of the final force.

Where does the energy go when the spring is released?

It turns into kinetic energy of whatever the spring pushes.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any school physics text (elastic potential energy).

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