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Physics & engineering

Hooke’s law spring force and energy

Hooke’s law spring force and energy: Within the linear elastic range, restoring force = −k × displacement and stored energy = ½ × k × displacement².

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How it works

Within the linear elastic range, restoring force = −k × displacement and stored energy = ½ × k × displacement².

Input definitions

Spring constant (N/m)
Enter the value in the labeled unit.
Displacement from equilibrium (m)
Enter the value in the labeled unit.

A worked example

Spring constant (N/m)
200
Displacement from equilibrium (m)
0.1
-20

Assumptions & limits

Use consistent stated units. Ideal geometric or physical model; verify dimensions and applicability before real-world design.

Sources & review

Maintained by AnsRio. Methods and examples use automated checks; this does not imply independent professional certification.

Method updated 2026-10-17. Content checked against the stated method and examples. Our verification approach.

Common questions

Why can the spring force be negative?

The sign indicates that the restoring force opposes displacement. Stored elastic energy remains nonnegative.

How does Hooke’s law spring force and energy work?

Within the linear elastic range, restoring force = −k × displacement and stored energy = ½ × k × displacement².

What are the limits of Hooke’s law spring force and energy?

Use consistent stated units. Ideal geometric or physical model; verify dimensions and applicability before real-world design.

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