Free Online Calculators

Spring Potential Energy Calculator

Calculate spring potential energy, spring constant, or displacement.

PEe = ½ · k · x²

Calculated Potential Energy

2.0000

Elastic Potential Energy

This is the energy stored in an object (like a spring, rubber band, or bow) when it is compressed or stretched from its natural shape.

The Equation

Derived from Hooke's Law ($F=kx$) by integrating force over distance.

PEe = ½ · k · x²
  • k (Stiffness): Spring Constant (N/m)
  • x (Distance): Stretch/Compression (m)

Key Insight

Because the displacement ($x$) is squared, doubling the stretch distance quadruples the stored energy!

This is why drawing a bow back those last few inches is much harder but adds significantly more power to the arrow.

spring potential energy formulas and interpretation

An ideal spring stores elastic energy when compressed or extended.

The calculator preserves direct solutions and supported spring-constant and distance units.

How to use the spring potential energy calculator

  1. Choose a model: Select the relationship matching the problem.
  2. Choose the unknown: Select the quantity to calculate.
  3. Enter values: Enter all known values with matching units and signs.
  4. Calculate: Review the result, formula, units, and direction.

Formula and variables

Elastic potential energy equals one-half the spring constant times displacement squared.

PEs = ½kx²
PEs — Spring energy
Stored elastic energy (J)
k — Spring constant
Spring stiffness (N/m)
x — Displacement
Compression or extension (m)

Compressed spring example

A 200 N/m spring is compressed by 0.1 m.

Spring constant
200 N/m
Displacement
0.1 m
  1. PEs = ½ × 200 × 0.1²
  2. PEs = 1 J

Result: The spring stores 1 joule.

Equal compression and extension magnitudes store equal energy.

Understanding your results

Interpreting the result

Energy grows with displacement squared while the spring remains in its elastic range.

Assumptions

  • The selected equation represents the physical system.
  • Inputs use a consistent reference direction.
  • Values are converted through coherent SI units.

Limitations

  • Vector components must be resolved along a common axis.
  • External forces or energy losses are not added automatically.
  • Results depend on the accuracy of entered measurements.

Common mistakes

  • Mixing incompatible units.
  • Dropping negative signs that represent direction.
  • Using weight where mass is required.
  • Entering a zero divisor.

Practical use cases

Physics problems

Check classroom, laboratory, and mechanics calculations.

Practical estimates

Estimate motion, forces, and energy for real systems.

Frequently asked questions

Can a result be negative?

Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.

Should I use SI units?

The interface can convert supported units, while the formulas are evaluated through coherent SI units.

Sources and review

Reviewed 2026-07-11.

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