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Elastic Potential Energy Calculator

Calculate the energy stored in a stretched or compressed spring.

About Elastic Potential Energy Calculator

The force in a spring rises linearly with displacement, so the energy — the area under that line — rises with the square. Doubling the stretch therefore stores four times the energy. Spring energy scaling with x² is why the last centimetre of compression stores far more than the first, and why over-compression fails components suddenly.

Formula

Elastic Potential Energy

E = ½ k x²

k
Spring stiffness in newtons per metre
x
Displacement from the rest position

Worked example

With the default values below, Elastic Potential Energy Calculator returns Elastic Potential Energy of 2.8125. Change any input above and every figure here is recalculated in your browser.

Inputs used

Spring constantminimum 0 N/m
250 N/m
Displacement from restminimum 0 m
0.15 m

Results

Elastic Potential Energy
2.8125 J
Force at That Displacement
37.500 N
Energy at Double Displacement
11.2500 J
Average Force Over the Stretch
18.750 N
Equivalent Drop Height for a 1 kg Mass
0.2867 m

Step by step

  1. 1Values used
  2. 2Elastic Potential Energy
  3. 3Elastic Potential Energy= 2.8125 J
  4. 4Force at That Displacement= 37.500 N
  5. 5Energy at Double Displacement= 11.2500 J
  6. 6Average Force Over the Stretch= 18.750 N
  7. 7Equivalent Drop Height for a 1 kg Mass= 0.2867 m

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

How is Elastic Potential Energy calculated?

E = ½ k x² The force in a spring rises linearly with displacement, so the energy — the area under that line — rises with the square. Doubling the stretch therefore stores four times the energy.

Why does Elastic Potential Energy matter?

Spring energy scaling with x² is why the last centimetre of compression stores far more than the first, and why over-compression fails components suddenly.

What values do I need to enter?

This calculator takes 2 inputs: Spring constant, Displacement from rest. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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