Hooke's Law Calculator

Hooke's law is one of the simplest and most widely applicable laws in physics: the force a spring exerts is directly proportional to how far it has been stretched or compressed from its natural length. Written as F = kx, the force F in newtons equals the spring constant k (in N/m) times the displacement x in metres. The spring constant k measures stiffness: a large k means a stiff spring that requires a large force for a small stretch, while a small k describes a soft spring that extends easily. The law applies not just to coiled metal springs but to any elastic material within its elastic limit, including rubber bands, suspension systems, elastic tendons, and even the bonds between atoms. This calculator solves Hooke's law in all three directions: find the force from k and x, find the spring constant from force and displacement, or find the displacement from force and spring constant. It also computes the elastic potential energy stored in the spring as PE = 0.5kx2. This quantity grows with the square of the displacement, so doubling the extension quadruples the stored energy, which is why over-stretched springs and bungee cords release so much energy on the return. The default example uses k = 200 N/m and x = 0.05 m, giving a restoring force of 10 N and a stored energy of 0.25 J. Results update as you type. Use this calculator for physics homework, for spring selection in engineering design, for understanding suspension systems, or to explore elastic potential energy in oscillating systems.

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N/m
m
10 N
spring force (restoring)
Elastic PE stored0.25 J
Displacement in cm5 cm
Force in kgf1.02 kgf

F = kx. Elastic PE = 0.5kx². Valid within the elastic limit. Results in SI units, rounded for display.

How it works

Hooke's law: F = kx. Spring constant: k = F/x. Displacement: x = F/k. Elastic potential energy: PE = 0.5kx². Because PE involves x squared, it is more sensitive to displacement than force is. The spring constant in N/m is the slope of the force-displacement graph and can be measured experimentally by dividing a known applied force by the resulting extension.

Worked example

A spring with constant k = 200 N/m is stretched x = 0.05 m (5 cm). Spring force = 200 times 0.05 = 10.00 N. Elastic PE = 0.5 times 200 times 0.05 squared = 0.5 times 200 times 0.0025 = 0.25 J. These match the default values pre-filled above.

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Frequently asked questions

What is Hooke's law?

Hooke's law states that the force exerted by a spring is proportional to its displacement from the natural length: F = kx. The spring constant k (in newtons per metre) measures stiffness. The law holds while the spring stays within its elastic limit and has not been permanently deformed.

How do you calculate elastic potential energy stored in a spring?

The elastic potential energy is PE = 0.5 times k times x squared, where k is the spring constant and x is the displacement. Because of the squared term, doubling the displacement quadruples the energy stored. This energy is fully released when the spring returns to its natural length.

How do you find the spring constant from measurements?

Rearrange Hooke's law: k = F / x. Apply a known force (such as a hanging mass times gravity) and measure the extension. For example, a force of 10 N extending a spring by 0.05 m gives k = 10 / 0.05 = 200 N/m.