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Hooke’s Law Calculator

Apply Hooke’s law to relate spring force, stiffness and displacement.

About Hooke’s Law Calculator

Hooke’s law is a linear approximation that holds only while deformation is elastic. Beyond the elastic limit the material yields and the relationship breaks down entirely. Designing a spring close to its elastic limit risks permanent set, where it never returns to its original free length.

Formula

Hooke’s Law

F = k x, valid only below the elastic limit

elastic limit
Displacement beyond which deformation becomes permanent

Worked example

With the default values below, Hooke’s Law Calculator returns Spring Force of 40.000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Spring constantminimum 0 N/m
800 N/m
Displacement from restminimum 0 m
0.05 m
Elastic limit displacementminimum 0.001 m
0.12 m

Results

Spring Force
40.000 N
Energy Stored
1.0000 J
Displacement Against the Elastic Limit
41.7%
Force at the Elastic Limit
96.00 N
Status
Within the elastic region

Step by step

  1. 1Values used
  2. 2Hooke’s Law
  3. 3Spring Force= 40.000 N
  4. 4Energy Stored= 1.0000 J
  5. 5Displacement Against the Elastic Limit= 41.7
  6. 6Force at the Elastic Limit= 96.00 N
  7. 7Status= Within the elastic region

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Hooke’s Law calculated?

F = k x, valid only below the elastic limit Hooke’s law is a linear approximation that holds only while deformation is elastic. Beyond the elastic limit the material yields and the relationship breaks down entirely.

Why does Hooke’s Law matter?

Designing a spring close to its elastic limit risks permanent set, where it never returns to its original free length.

What values do I need to enter?

This calculator takes 3 inputs: Spring constant, Displacement from rest, Elastic limit displacement. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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