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Elastic Potential Energy Calculator

Use this elastic potential energy calculator to calculate the energy stored in a spring with PE = 1/2kx². It also works as a spring potential energy calculator, spring energy calculator, elastic energy calculator, and EPE calculator.

Spring Potential Energy Calculator

Solve for elastic potential energy, spring constant, or displacement for a stretched or compressed spring.

Calculator Inputs

Use “.” as the decimal separator.

Results

PE = 1/2 kx²
Spring Constant [k]
—
Displacement [x]
—
Potential Energy [PE]
—
SI check
—
Meaning of the result

Enter values and click Calculate to solve the spring energy equation.

Spring Displacement Diagram

The stored energy increases with the square of displacement. Doubling the displacement increases elastic potential energy by four times.

Displacement x Spring

Elastic Potential Energy Formula

PE = 1/2 kx²
  • PE = elastic potential energy
  • k = spring constant
  • x = displacement from equilibrium

This is the standard spring energy equation often written as 1/2 kx² or PE = 1/2 kx².

How to Use the Calculator

  1. Select whether to solve for potential energy, spring constant, or displacement.
  2. Enter the two known values.
  3. Select the correct units.
  4. Click Calculate.
  5. Read the result in the chosen unit.

Examples

Example 1: Calculate elastic potential energy

A spring has a spring constant of 200 N/m and is stretched by 0.3 m.

PE = 1/2 × 200 × (0.3)² = 9 J

Example 2: Calculate spring constant

A spring stores 12 J when stretched by 0.4 m.

k = 2PE / x² = 2 × 12 / (0.4)² = 150 N/m

Elastic Energy in Springs

Elastic potential energy is the energy stored in a spring when it is stretched or compressed. That is why this page is also useful as a spring potential energy calculator, spring energy calculator, and elastic energy calculator.

FAQ

What is elastic potential energy?

Elastic potential energy is the energy stored in a spring or elastic object when it is stretched or compressed.

What is the formula for spring potential energy?

The formula is PE = 1/2 kx².

What does k mean in 1/2 kx²?

k is the spring constant, which measures spring stiffness.

What is the SI unit of elastic potential energy?

The SI unit is the joule (J).

Related Physics Calculators

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References

  • Giancoli, Douglas C. Physics: Principles with Applications. Pearson.
  • The current page and code-behind use the same spring energy relationship and solving modes for PE, k, and x.