Spring energy tool

Elastic Potential Energy Calculator

Solve elastic potential energy, spring constant, or extension using E = ½kx².

Enter two known values

Solve an elastic energy problem

Free tool
J

This is the value being calculated.

N/m

Positive stiffness of the spring.

m

Positive extension or compression from equilibrium.

Use joules for energy, newtons per meter for spring constant, and meters for extension.

Try an example:

Your elastic energy result will appear here

Choose the missing variable and enter the other two known values.

Calculator guide

How this calculator works

Elastic Potential Energy Calculator determines the energy stored in stretched or compressed elastic materials such as springs. It helps physics students, engineers, and laboratory users analyze stored mechanical energy, spring systems, and elastic behavior using spring constant and displacement measurements.

Formula explanation

Elastic potential energy is stored when an elastic object is stretched or compressed and is calculated using spring properties.

Formula

Elastic Potential Energy = ½ × Spring Constant × Displacement²

Worked example

Example: Compressing a spring stores energy that can later be released as motion.

Assumptions

  • The elastic material follows ideal Hooke's law behavior.
  • The deformation remains within the elastic limit.
  • Spring constant remains constant during calculation.
  • Input values use compatible scientific units.

Examples

  • Example: Calculate stored spring energy when spring constant and displacement are known.
  • Example: Engineers analyze energy storage systems using elastic components and spring mechanisms.

Common mistakes

  • Using incorrect spring constant values.
  • Confusing force with energy.
  • Ignoring deformation distance.

Variables

  • Spring constant
  • Extension or compression distance
  • Elastic potential energy
  • Displacement from equilibrium
  • Material stiffness
  • Measurement units

Limitations

  • Results assume ideal elastic behavior.
  • Materials with permanent deformation require advanced material analysis.

Scientific references

  • OpenStax University Physics: Elasticity and Energy
  • NIST SI Energy Measurement References
  • Classical mechanics principles

Content review

Reviewed by: ScienceCalcHub Physics Review Team | Last reviewed: 2026-08-30

Applications

  • Physics education
  • Mechanical engineering design
  • Spring mechanism analysis
  • Material elasticity studies
  • Laboratory elasticity experiments
  • Energy storage system analysis

Frequently asked questions

How is elastic potential energy calculated?

Elastic potential energy is calculated using E = ½kx², where k is the spring constant and x is the displacement from the equilibrium position.

What factors affect elastic potential energy?

Elastic potential energy depends on the stiffness of the material and the amount of stretching or compression.

What is the SI unit of elastic potential energy?

The SI unit of elastic potential energy is the joule (J), which represents stored mechanical energy.

Where is elastic potential energy used?

Elastic potential energy is used in springs, mechanical systems, shock absorbers, and energy storage applications.

Accuracy and transparency

Created and maintained by our editorial team

This physics calculator is maintained by the ScienceCalcHub Editorial Team. Its calculation logic is tested with representative inputs, while the supporting guidance is checked for formula clarity, units, assumptions, and common mistakes.

Written by
ScienceCalcHub Editorial Team
Reviewed by
ScienceCalcHub Scientific Review Team
Review standard
Formula accuracy, units, examples, and educational clarity

Learn more about our formula-review and correction process, explore our calculation methodology, or view our scientific references.

  • Calculation logic tested
  • Variables and units explained
  • Assumptions stated clearly
  • Corrections handled transparently

Energy stored in a spring

What is elastic potential energy?

Elastic potential energy is stored when an elastic object, such as a spring, is stretched or compressed from its equilibrium position.

Formula

Elastic potential energy formula

Elastic EnergyE = ½kx²

  • E is elastic potential energy in joules.
  • k is the spring constant in newtons per meter.
  • x is extension or compression in meters.

Worked example

A 200 N/m spring extends 0.5 m

  1. Write the formula: E = ½kx².
  2. Substitute the values: E = ½ × 200 × 0.5².
  3. Calculate the energy: E = 25 J.

Rearranged equations

Solve for spring constant or extension

Spring Constant

k = 2E ÷ x²

Multiply energy by two, then divide by the square of extension.

Extension

x = √(2E ÷ k)

Divide twice the energy by the spring constant, then take the square root.

Units

Standard SI units

Use newtons per meter for spring constant and meters for extension.

Spring constantk in N/m

Hooke's law region

When does this formula apply?

The formula assumes the spring behaves elastically and remains within the region where its spring constant is effectively constant.

Calculation limits

Important assumptions

  • Spring constant must be greater than zero.
  • Extension magnitude must be greater than zero.
  • Elastic energy must be greater than zero when solving for another variable.
  • The spring is assumed to remain in its elastic range.
  • The calculator does not automatically convert units.

Related tools

Use the Gravitational Potential Energy Calculator to calculate energy due to height.

Use the Kinetic Energy Calculator for motion energy, or use the Work Calculator for force and displacement.

Questions and answers

Calculator FAQ

How is elastic potential energy calculated?

Elastic potential energy is calculated using E = ½kx², where k is the spring constant and x is the displacement from the equilibrium position.

What factors affect elastic potential energy?

Elastic potential energy depends on the stiffness of the material and the amount of stretching or compression.

What is the SI unit of elastic potential energy?

The SI unit of elastic potential energy is the joule (J), which represents stored mechanical energy.

Where is elastic potential energy used?

Elastic potential energy is used in springs, mechanical systems, shock absorbers, and energy storage applications.