Math
Spring Constant Calculator
Apply Hooke's law F = k x to solve for force, spring constant, or displacement. Compute elastic potential energy, simple-harmonic period, and series or parallel combined stiffness.
Spring Constant Calculator
Solve F = k x. Fill in any two of force, spring constant, and displacement.
Stiffness in newtons per meter. Must be greater than zero.
Distance from equilibrium in meters. Must be greater than zero.
Force F
5 N
Force F
5 N
Spring constant k
100 N/m
Displacement x
0.05 m
Displacement x
5 cm
Frequently Asked Questions about the Spring Constant Calculator
What is the spring constant?
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).
How do I calculate the spring constant from force and displacement?
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.
What is the formula for elastic potential energy?
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.
How do I find the period of a mass on a spring?
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.
How do springs combine in series versus parallel?
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.