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Physical Sciences
Classical Mechanics
1678
Beginner

Hooke's Law

F=−kxF = -kx

Spring force is proportional to displacement and opposes the direction of stretch or compression.

By Robert Hooke

Physical Sciences
Hooke's Law
1678 · Robert Hooke
Human Reviewed
84%

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Story PortalWho discovered this?Discover how Robert Hooke and others shaped this equation.Visual PortalWhat does it look like?See the equation come alive in the Visual Studio.Machine PortalWhere is it used?Explore machines powered by this equation — springs.Math PortalWhat does it derive from?Trace the mathematical lineage from newtons second law.Future PortalWhere is it going?Soft robotics
Why it matters: Foundation of elasticity theory, oscillations, and materials science.

Discoverers: Robert Hooke (1678)

What does it mean?

Spring force is proportional to displacement and opposes the direction of stretch or compression.

Why should I care?

Foundation of elasticity theory, oscillations, and materials science.

Equation Compass

North — Prerequisites

West — History

East — Applications

South — Derivations

Variables & Units

SymbolNameUnitMeaning
FFForceNRestoring force
kkSpring constantN/mStiffness
xxDisplacementmFrom equilibrium

Worked Example

k = 200 N/m, x = 0.05 m → F = -10 N.

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Sources & further reading

Search WikipediaSearch Wolfram MathWorldOpen in Wolfram|AlphaWatch explainers on YouTube

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Hooke's Law

F=−kxF = -kx

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Spring force is proportional to displacement and opposes the direction of stretch or compression.

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