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Spring Constant Calculator

Find a spring's stiffness with Hooke's law F = k x — enter the force and the extension to get the spring constant k, or solve for force or displacement.

 

Formula

$$ F = k\,x \qquad k = \frac{F}{x} \qquad x = \frac{F}{k} $$

Worked example

A spring stretched 0.1 m by a 20 N force has \( k = F/x = 20/0.1 = 200\ \text{N/m} \). The elastic potential energy stored is \( \tfrac12 k x^2 = \tfrac12(200)(0.1)^2 = 1\ \text{J} \).

How it works

Hooke's law says the force a spring exerts is proportional to how far it is stretched or compressed: F = k x. The spring constant k measures stiffness — a higher k means a stiffer spring that needs more force for the same extension.

Enter any two of force, extension and k to find the third. The law holds within the spring's elastic limit; beyond that the spring deforms permanently and the relationship breaks down. The energy stored is ½kx².

Frequently asked questions

How do you calculate the spring constant?

Divide the applied force by the resulting extension: k = F / x. If 20 N stretches a spring 0.1 m, k = 200 N/m.

What are the units of the spring constant?

Newtons per metre (N/m) — the force needed per metre of extension. A stiffer spring has a larger value.

What is Hooke's law?

Hooke's law states that the restoring force of a spring is proportional to its displacement: F = kx, valid within the elastic limit.

How much energy is stored in a stretched spring?

The elastic potential energy is ½kx² — half the spring constant times the extension squared.

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