Classical Mechanics
Hooke's Law Calculator
Solve F = kx for spring force, spring constant or extension. Also calculates spring potential energy.
Result
F = kx
Spring PE (½kx²)
—
J
Step-by-Step Solution
What is Hooke's Law?
Hooke's Law states that the force exerted by a spring is directly proportional to its extension (or compression) from its natural length, provided the elastic limit is not exceeded. Beyond the elastic limit, the spring deforms permanently and Hooke's Law no longer applies.
F = kx
F = force (N) | k = spring constant (N/m) | x = extension or compression (m)
💡 The spring stores elastic potential energy = ½kx². This equals the work done in stretching the spring and is released when the spring returns to its natural length.
Real-World Applications
Mechanical Engineering
Springs in car suspension, shock absorbers and mechanical watches all rely on Hooke's Law.
Spring Scales
Traditional weighing scales use spring deformation to measure force (and hence weight).
Seismic Isolation
Buildings in earthquake zones use spring-like isolators to absorb ground vibrations.
Musical Instruments
Guitar strings, drum skins and piano strings all follow Hooke's Law within their operating range.
Frequently Asked Questions
What is the spring constant k?
The spring constant (N/m) measures a spring's stiffness. A high k means the spring is stiff (needs more force per metre of extension). A low k means it is compliant (soft). k depends on the material, wire diameter and number of coils.
What is the elastic limit?
Beyond the elastic limit, the spring undergoes plastic (permanent) deformation and no longer obeys Hooke's Law. The material loses its spring-back property. Always ensure your applied force stays below this limit.
How does the spring PE relate to kinetic energy?
In a spring-mass system (SHM), energy converts back and forth: PE_spring = ½kx² ↔ KE = ½mv². At maximum extension, all energy is PE. At the rest position, all energy is KE.