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Spring Potential Energy Calculator

Work out spring potential energy instantly with clear inputs, formula shown and shareable results.

About Spring Potential Energy Calculator

Hooke's law makes force proportional to extension, so the work done stretching a spring is the area under a triangle: E = kx^2/2. A 250 N/m spring pulled 0.12 m stores 1.8 J while pulling back with 30 N. Because energy goes as extension squared, doubling the stretch takes four times the energy - three times more again from where you are.

Formulas

Stored energy

E = 0.5 k x^2

Hooke's law

F = k x

Worked example

With the default values below, Spring Potential Energy Calculator returns Energy Stored In The Spring of 1.8000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Spring constant kminimum 0 N/m
250 N/m
Extension or compression
0.12 m

Results

Energy Stored In The Spring
1.8000 J
Force At Full Extension
30.000 N
Extra Work To Double The Extension
5.4000 J
Average Force During Stretching
15.000 N

Step by step

  1. 1Values used
  2. 2Stored energy
  3. 3Hooke's law
  4. 4Energy Stored In The Spring= 1.8000 J
  5. 5Force At Full Extension= 30.000 N
  6. 6Extra Work To Double The Extension= 5.4000 J
  7. 7Average Force During Stretching= 15.000 N

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why the factor of one half?

Because the force builds from zero to kx as you stretch. The average force is half the final one, and work is average force times distance.

Does this hold for large extensions?

Only within the elastic limit. Beyond it the spring yields, Hooke's law fails and some energy does not come back.

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