Definition · Plain-language
Hooke’s law
Hooke’s law states that the force needed to stretch or compress a spring is directly proportional to the distance it is stretched or compressed, written F = kx.
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Force proportional to extension
Robert Hooke set out his law in 1678: the extension of a spring is proportional to the load applied to it. Written F = kx, the force F equals the spring constant k times the extension x — the distance the spring is stretched or compressed from its natural length. The spring constant measures stiffness: a large k means a stiff spring that needs a big force for a small stretch, while a small k means a soft, easily stretched spring. The relationship is linear, so a graph of force against extension is a straight line through the origin, and its gradient is the spring constant.
The elastic limit
Hooke’s law is not unlimited — it holds only while the material behaves elastically, meaning it springs back to its original shape when the force is removed. Stretch a spring too far and it passes its elastic limit (or limit of proportionality): the line of force against extension bends, the spring no longer returns to its starting length, and the simple proportionality fails. Beyond this point the material deforms plastically (permanently) and may eventually break. Knowing where this limit lies is essential in engineering, because structures are designed to stay safely within the elastic range.
Where it is used
Hooke’s law describes far more than coiled springs. It applies, within limits, to the stretching of wires, the bending of beams and the squashing of rubber, making it a foundation of materials science and structural engineering. It is the principle behind spring balances and kitchen scales, which read a weight from how far a spring extends, and behind car suspension, mattresses and the vibration of guitar strings. Because the force grows in step with the displacement, springs also store predictable amounts of elastic potential energy, which is why they are used to cushion, return and measure forces.
Key facts
At a glance
- Definition: force is proportional to the extension or compression of an elastic object
- Equation: F = kx (force = spring constant × extension)
- Spring constant k: measures stiffness, in newtons per metre
- Graph: force against extension is a straight line through the origin
- Validity: holds only up to the elastic limit
- Beyond limit: the material deforms permanently and the law fails
Common misconceptions
What people often get wrong
Often heard: Hooke’s law applies no matter how far you stretch a spring.
Actually: It applies only up to the elastic limit. Stretch beyond that and the spring deforms permanently, the proportionality breaks down, and it will not return to its original length.
Often heard: A higher spring constant means a softer, easier-to-stretch spring.
Actually: The opposite is true. A higher spring constant means a stiffer spring that needs more force for the same extension.
Often heard: Hooke’s law only applies to metal coil springs.
Actually: It applies, within limits, to many elastic materials and structures — wires, rubber, bending beams — wherever deformation stays proportional to the applied force.
Going deeper
