Hooke's Law Calculator
Hooke's law relates the restoring force of an ideal spring to how far it is stretched or compressed.
N
N/m
m
- 1
Spring constant k
100 N/m - 2
Displacement x
0.05 m - 3
Force F = k × x
100 × 0.05 = 5
How does this calculator work?
Hooke's law says spring force equals stiffness times displacement: F = k × x. Enter any two of force F (N), spring constant k (N/m), and displacement x (m), and this calculator solves the third, using k = F / x or x = F / k as needed, and also reports the stored elastic energy ½ k x².
Formula
How this is calculated
Hooke's law states that the force F (in newtons) needed to extend or compress a spring is proportional to the displacement x (in metres) from its rest position, with the spring constant k (in newtons per metre) as the proportionality factor: F = k × x.
Enter any two of the three quantities and leave the third blank to solve for it. Given k and x the calculator returns F = k × x; given F and x it returns k = F / x; given F and k it returns x = F / k. It also reports the elastic potential energy stored in the spring, U = ½ k x², in joules.
The model assumes an ideal linear spring within its elastic limit; real springs deviate once stretched too far or permanently deformed. The restoring force acts opposite to the displacement, so a positive F here represents the magnitude of that force. Division-by-zero cases (solving for k with x = 0, or for x with k = 0) return no result.
Frequently asked questions
The spring constant k measures stiffness in newtons per metre: it is the force required to stretch or compress the spring by one metre. A larger k means a stiffer spring.
Only within the elastic (linear) region. Beyond the proportional limit the force is no longer linear in displacement, and past the elastic limit the spring deforms permanently.
The elastic potential energy is U = ½ k x², the area under the force-displacement line. This calculator reports it alongside the force.
Also known as
TG we-Calculate Editorial Team. (2026). Hooke's Law Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/hookes-law-calculator
TG we-Calculate Editorial Team. "Hooke's Law Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/hookes-law-calculator.
TG we-Calculate Editorial Team, "Hooke's Law Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/hookes-law-calculator
@misc{wecalculate_hookes_law_calculator, title = {Hooke's Law Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/hookes-law-calculator}}, year = {2026}, note = {TG we-Calculate} }
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