Spring Calculator — Hooke's Law, Energy & Oscillation
Enter the spring constant and displacement to find the restoring force and stored elastic energy. Add an attached mass to also get the oscillation period, frequency and angular frequency for simple harmonic motion.
N/m
m
kg
Restoring force — the spring pulls/pushes back with this force (F = k × x)
- 1
Displacement magnitude |x|
|0.05| = 0.05 - 2
Restoring force F = k × |x|
200 × 0.05 = 10
How does this calculator work?
Enter spring constant k (N/m) and displacement x (m) to get restoring force F = kx and elastic potential energy E = ½kx². Add mass m to compute oscillation period T = 2π√(m/k), frequency f = 1/T and angular frequency ω = √(k/m). All formulas assume an ideal massless spring with no damping.
Formula
How this is calculated
Hooke's Law states that the restoring force of an ideal spring is proportional to its displacement from the natural length: F = k × x, where k is the spring constant in N/m (stiffness) and x is the displacement in metres. The negative sign in the full form (F = −kx) signals that the force always acts back toward equilibrium; the calculator shows the magnitude of that force.
The elastic potential energy stored in a compressed or stretched spring is E = ½ k x². This energy converts entirely to kinetic energy at the equilibrium point and back to potential energy at maximum displacement during oscillation — there is no energy loss in an ideal spring.
If a mass m (kg) is attached to the spring in a frictionless system, the mass oscillates with period T = 2π √(m/k), frequency f = 1/T, and angular frequency ω = √(k/m). Notice that the period depends on mass and spring constant but NOT on displacement amplitude — this is the hallmark of simple harmonic motion (SHM). The model assumes an ideal, massless spring with no damping, air resistance or friction.
Frequently asked questions
The spring constant k (in N/m) measures how stiff a spring is — higher k means more force is needed for the same displacement. A soft slinky might have k ≈ 1 N/m; a car suspension spring ≈ 15,000–30,000 N/m; a stiff industrial spring can exceed 1,000,000 N/m.
In simple harmonic motion, the restoring force is proportional to displacement. A larger displacement produces a proportionally larger force that accelerates the mass faster by exactly the right amount, keeping the period constant. This isochronous property is why springs (and pendulums in the small-angle limit) are used as timekeeping mechanisms.
Hooke's Law is only valid within the elastic limit of the spring material. If the spring is stretched or compressed beyond this limit (its elastic or yield limit), it deforms permanently and no longer returns to its original length. The proportional relationship between force and displacement breaks down before this point for many real springs.
Also known as
TG we-Calculate Editorial Team. (2026). Spring Calculator — Hooke's Law, Energy & Oscillation [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/spring-calculator
TG we-Calculate Editorial Team. "Spring Calculator — Hooke's Law, Energy & Oscillation." TG we-Calculate. 2026. https://we-calculate.com/calculator/spring-calculator.
TG we-Calculate Editorial Team, "Spring Calculator — Hooke's Law, Energy & Oscillation," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/spring-calculator
@misc{wecalculate_spring_calculator, title = {Spring Calculator — Hooke's Law, Energy & Oscillation}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/spring-calculator}}, year = {2026}, note = {TG we-Calculate} }
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