🌀 Spring Force Calculator

F = k × x — Hooke's Law solver for force, spring constant, or displacement.

Solve for

Spring Constant k (N/m)

Displacement x (m)

Spring Force (N)

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Result

How to Use This Calculator

Select whether you want to find the spring force F, the spring constant k, or the displacement x. Enter the two known values and click Calculate. When you solve for force, the calculator also shows the elastic potential energy stored in the spring at that displacement.

Choose what to solve for: Spring Force (N), Spring Constant k (N/m), or Displacement (m).

Enter the spring constant k in N/m if you know it. A typical lab spring might be 50 N/m; a car suspension spring is around 15,000-30,000 N/m.

Enter displacement x in metres. Positive values are extensions; negative values are compressions. Use negative if the spring is compressed.

Read the result. If solving for force, you also get the elastic PE = ½kx² stored in the spring at that point.

Hooke's Law Formula

F = k × x k = F / x (spring constant, N/m) x = F / k (displacement, m) PE = ½ × k × x² (elastic potential energy, J) F = restoring force (N), k = spring constant (N/m), x = displacement (m)

The restoring force always acts opposite to the displacement: stretch the spring and the force pulls back toward equilibrium; compress it and the force pushes back. The law holds only within the elastic limit. Beyond that point, the spring deforms permanently and k is no longer constant.

Worked Examples

k = 200 N/m, x = 0.05 m (compressed 5 cm)F = 10 N, PE = 0.25 J

Hanging mass stretches spring 0.1 m, F = 15 Nk = 150 N/m

Car spring k = 20,000 N/m, load = 2,500 Nx = 0.125 m (12.5 cm compression)

Bungee cord k = 40 N/m, stretched 5 mF = 200 N, PE = 500 J stored

Where This Comes Up in Real Life

Car suspensions are essentially springs. A loaded suspension spring with k = 25,000 N/m compressed by a wheel load of 3,750 N compresses by x = 3750 / 25000 = 0.15 m (15 cm). Engineers choose spring rates so the car rides at a comfortable height and the wheel can travel enough distance to absorb bumps without bottoming out. Stiffer springs handle heavier loads but transmit more road vibration.

Spring scales use Hooke's Law directly: stretch a spring a known distance, read the force. Many weighing scales in kitchens and labs work this way. A spring with k = 500 N/m stretched 3 cm (0.03 m) by a mass shows F = 15 N, corresponding to a mass of 15 / 9.81 = 1.53 kg. Structural engineers also apply the same principle when calculating how much a beam deflects under load, since beam deflection under a central point load follows a similar linear relationship with stiffness.

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 equilibrium: F = k × x, where k is the spring constant (N/m) and x is displacement (m).

What is the spring constant k?

The spring constant (stiffness) k measures how resistant a spring is to compression or extension. A higher k means a stiffer spring. Units: N/m.

What is elastic potential energy?

Energy stored in a compressed or stretched spring: PE = ½kx². When released, this converts to kinetic energy.

Does Hooke's Law always apply?

Hooke's Law holds only within the elastic limit of the spring. Beyond that, the spring deforms permanently and the relationship becomes nonlinear.

What are typical spring constant values?

Rubber band: ~1 N/m. Mattress spring: ~15,000 N/m. Car suspension: ~15,000–30,000 N/m. Watch spring: up to 10⁶ N/m.