Use Hooke’s law, F = kx, to find the force in a spring, its spring constant or how far it stretches. This free calculator also gives the elastic potential energy stored, and in the second mode the period of a mass bouncing on the spring.
Spring formulas
Worked example
A spring with k = 200 N/m is stretched 5 cm (0.05 m). The force is 200 × 0.05 = 10 N and it stores ½ × 200 × 0.05² = 0.25 J. Hang a 0.5 kg mass on it and it bounces with a period of 2π√(0.5/200) = 0.31 s.
Hooke’s law only holds up to the limit of proportionality. Beyond the elastic limit the spring deforms permanently and the graph of force against extension curves.
Frequently asked questions
What is Hooke’s law?
The force needed to stretch or compress a spring is proportional to the distance: F = kx, where k is the spring constant.
How do I find the spring constant?
Hang a known weight, measure the extension and divide: k = F/x. For 5 N giving 2.5 cm, k = 5 ÷ 0.025 = 200 N/m.
How much energy does a spring store?
E = ½kx², the area under the force–extension graph. Stretching 200 N/m by 5 cm stores 0.25 J.
What happens with springs in series or parallel?
In series the combination is softer (two identical springs give k/2); in parallel it is stiffer (2k).
Related tools
Free educational tool by HawkInc. Results are calculated in your browser and rounded for display; check critical work by hand or with a second method.