🔬 Hooke's Law Calculator

Hooke's Law, named after the English physicist Robert Hooke who published it in 1676, states that the force needed to extend or compress a spring is proportional to the distance it is stretched. The law is expressed as F = k × x, where F is the restoring force (N), k is the spring constant (N/m), and x is the displacement from equilibrium (m). When you stretch a rubber band, compress a car's shock absorber, or pluck a guitar string, you are seeing Hooke's Law in action.

This calculator is designed for physics students, mechanical engineers, product designers, and anyone working with springs, elastic materials, or suspension systems. Simply enter any two of the three values—force, spring constant, or displacement—and the calculator instantly solves for the third.

The calculator applies F = k × x in three modes: solve for F = k×x, solve for k = F/x, or solve for x = F/k. The spring constant k measures stiffness: a higher k means a stiffer spring that requires more force to stretch.

The elastic potential energy stored in a spring is U = ½kx². For the examples above, a spring with k=50 N/m stretched 0.10 m stores U = 0.25 J of energy.

1. Enter any two of the three values: Force (F), Spring Constant (k), or Displacement (x).
2. Leave the third field blank—that is what will be calculated.
3. Click the Calculate button.
4. Review the result for the unknown value.
5. Check that the units are consistent (N, N/m, and m).

What is the spring constant k?

The spring constant (k, in N/m) measures how stiff a spring is. A higher k means more force is needed to stretch the spring by the same amount. A typical lab spring might have k = 20 N/m, while a car suspension spring can be k = 10,000 N/m or more.

What is the elastic limit?

The elastic limit is the maximum displacement beyond which a spring will not return to its original length. Hooke's Law is valid only up to this limit. Stretching beyond it causes permanent deformation.

Does Hooke's Law work for compression too?

Yes. Hooke's Law applies to both extension and compression. When you compress a spring, the displacement x is negative, but the magnitude of the restoring force is still F = k|x|.

What is the negative sign in F = -kx?

The negative sign indicates that the restoring force always points opposite to the displacement. When you pull a spring to the right, the spring pulls back to the left. This calculator reports force magnitudes for convenience.

How is Hooke's Law related to simple harmonic motion?

A mass on a spring that obeys Hooke's Law oscillates with angular frequency ω = √(k/m) and period T = 2π√(m/k). The restoring force is what drives the oscillation.

Can I use this for rubber bands or bungee cords?

Only approximately. Rubber bands and bungee cords are non-linear: they do not obey F = kx exactly. Their effective spring constant changes with displacement, so Hooke's Law gives a rough estimate at best.

Always use SI units for consistent results: force in newtons (N), spring constant in N/m, displacement in metres (m). Hooke's Law applies only within the elastic limit—beyond a certain stretch, the spring deforms permanently and the linear relationship breaks down. The negative sign in F = -kx indicates the restoring force points opposite to displacement; this calculator reports magnitudes. For oscillating systems, the angular frequency is ω = √(k/m), where m is the attached mass.