Spring Potential Energy Calculator
Estimate the elastic potential energy stored by an ideal linear spring displaced from its equilibrium position, along with the corresponding restoring force.
How to use this calculator
- Enter spring constant in N/m and signed displacement in metres. Displacement sign controls the restoring-force sign; energy remains non-negative.
- Check the labels and units before applying the result to a real task.
- Change one input at a time when comparing scenarios.
Formula and method
U = ½kx²; F = −kx
- U = ½kx²; F = −kx
- The calculation assumes Hooke’s law applies within the spring’s elastic range and ignores damping, friction and permanent deformation.
Worked examples
Worked example
A spring has stiffness 100 N/m and displacement 0.1 m.
Stored energy is 0.5×100×0.1² = 0.5 J; restoring-force magnitude is 10 N.
Stored energy is 0.5×100×0.1² = 0.5 J; restoring-force magnitude is 10 N.
Understanding the result
Estimate the elastic potential energy stored by an ideal linear spring displaced from its equilibrium position, along with the corresponding restoring force.
The calculation assumes Hooke’s law applies within the spring’s elastic range and ignores damping, friction and permanent deformation.
Important notes
The calculation assumes Hooke’s law applies within the spring’s elastic range and ignores damping, friction and permanent deformation.
Displayed values are rounded for readability; retain appropriate precision when continuing a calculation.
Frequently asked questions
Why is the energy not negative?
The stored elastic energy depends on displacement squared, so it is non-negative for a non-negative spring constant.
What does the minus sign in F = −kx mean?
It indicates the spring force points toward equilibrium, opposite to the displacement direction.
Can this model represent a spring that has permanently deformed?
No. The ideal linear relationship is not valid once the spring leaves its elastic range or behaves nonlinearly.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.