Hooke's Law Calculator - F = kx Spring Force

How to use this tool

1. Select which variable to solve for (force, spring constant, or extension).
2. Enter the two known values.
3. View the result and the elastic potential energy stored in the spring.

Hooke's Law Formula

For the magnitude of the spring force, F = k × x, where k is the spring constant and x is the positive distance from equilibrium. This calculator solves for that magnitude from any two of force, spring constant, and extension. It converts force, spring-rate, and length inputs to SI units before calculating, so units such as lbf/in and mm can be mixed safely.

The signed restoring force is F_restore = −k × x. Its minus sign means the spring force points back toward equilibrium, opposite the displacement. The numeric solver reports force magnitude; its extension value is a distance magnitude and does not encode a direction. To apply the magnitude, select whether the spring is stretched or compressed when reasoning about the direction in a physical setup.

Spring constant references

The interactive reference table above the article includes approximate examples: a watch hairspring is about 10 N/m, a bungee cord about 100 N/m, a mattress spring about 500 N/m, keyboard switches about 500–1,500 N/m, and car suspension springs about 15,000–40,000 N/m. Choose an example to apply its k value; the calculator converts it to your current spring-rate unit and combines it with the entered extension. Actual springs vary by design, load, and how far they are displaced, so use manufacturer data for a specific component.

Elastic potential energy

A compressed or stretched spring stores energy. The elastic potential energy is:

PE = ½kx²

For example, a spring with k = 500 N/m compressed by 0.1 m stores PE = ½ × 500 × 0.01 = 2.5 joules. This energy is released when the spring returns to equilibrium - the basis of mechanical watches, spring-loaded toys, and retractable pens.

The energy result is shown in joules with the metric preset and foot-pounds force (ft·lbf) with the imperial preset. The per-field selectors may use mixed units; their values are normalized before solving, while the energy tile follows the selected preset.

Elastic limit

Hooke's Law only holds within the elastic region of a material. Beyond the elastic limit (the yield point), the material deforms plastically and will not return to its original shape when the force is removed. On a stress-strain curve, the elastic region is the initial linear portion; the yield point marks where the curve begins to bend.

Real-world applications

• Shock absorbers: springs and dampers absorb road impacts in vehicles
• Seismic isolators: large springs decouple buildings from ground motion
• Mechanical keyboard switches: spring force determines actuation feel
• Vehicle suspension: spring constant is tuned for ride comfort vs. handling
• Medical devices: surgical retractors and stents use calibrated spring forces