Spring Constant Calculator

The spring constant k measures how stiff a spring is. It is the proportionality factor in Hooke's law F = k x, where F is the restoring force and x is how far you have stretched or compressed the spring from its rest position. Units are newtons per meter (N/m).

Rearrange Hooke's law to k = F / x. If a 20 N force stretches a spring by 0.1 m, the spring constant is 20 / 0.1 = 200 N/m.

U = 0.5 k x squared, in joules when k is in N/m and x in meters. So a 100 N/m spring stretched 0.1 m stores U = 0.5 x 100 x 0.01 = 0.5 J.

For an ideal mass-spring oscillator, T = 2 pi sqrt(m / k). The period only depends on mass and stiffness, not amplitude. A 2 kg mass on a 200 N/m spring gives T about 0.628 s.

Springs in series get softer: 1 / k_total = sum of 1 / k_i. Springs in parallel get stiffer: k_total = sum of k_i. Two 100 N/m springs in series act like 50 N/m; in parallel they act like 200 N/m.