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Linear Spring Stored Energy

Calculate elastic energy in an ideal linear spring from its stiffness and signed displacement from equilibrium.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A spring with stiffness 200 N/m displaced by 0.1 m stores 1 J. Compressing it by −0.1 m stores the same energy in this ideal model.

Stored energy = ½kx²

Worked example

Enter these known values and leave the other values blank.

Spring stiffness
200 N/m
Displacement from equilibrium
0.1 m
Stored elastic energy
1 J

Assumptions and limitations

  • Stiffness must be positive and is entered in newtons per meter. The displacement selector converts the length into meters before applying the formula.
  • Displacement is measured from the unstressed equilibrium position and may be positive or negative. Energy is nonnegative and scales with the square of displacement.
  • The spring is ideal and linear over the entered displacement. Plastic deformation, hysteresis, damping and nonlinear stiffness are not modeled.
  • Solving displacement from energy returns its nonnegative square-root branch. Compression and extension of equal magnitude store equal energy.

Common questions

Does doubling displacement double stored energy?

It quadruples the energy because displacement is squared: ½k(2x)² = 4 × ½kx².

Is this the work done by the spring during extension?

It is the stored potential-energy increase from equilibrium. For an ideal spring, the work done by the spring during that extension has the opposite sign.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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