Spring Constant Calculator — Hooke's Law k = F/x
Calculate spring constant, force, or extension using Hooke's Law F = kx. Covers series and parallel springs, energy storage, and practical engineering examples.
Hooke's Law is one of the oldest quantitative laws in physics — and one of the most practically useful. It says that the force a spring exerts is proportional to how far it's stretched or compressed. The proportionality constant k tells you how stiff the spring is. Know k and displacement, and you instantly know force. Simple, powerful, and widely applicable beyond just springs.
The CalcHub spring constant calculator solves for spring constant, force, or extension from the other two values.
The Formula
F = k × x- F = restoring force (Newtons, N)
- k = spring constant, or spring stiffness (N/m)
- x = displacement from natural length (m)
Combining Springs
| Configuration | Effective k |
|---|---|
| Springs in parallel | k_eff = k₁ + k₂ + k₃ + ... |
| Springs in series | 1/k_eff = 1/k₁ + 1/k₂ + 1/k₃ + ... |
Measuring Spring Constant Experimentally
The simplest method: hang known masses from the spring, measure extension.
k = F/x = mg/x
Hang 0.5 kg (F = 4.9 N), measure 3 cm extension:
k = 4.9 / 0.03 = 163 N/m
Reference Spring Constants
| Spring | k (N/m) |
|---|---|
| Soft rubber band | ~100 |
| Pen click spring | ~150–300 |
| Slinky | ~0.5–1 |
| Muscle (bicep) | ~600–1000 |
| Car suspension | 15,000–30,000 |
Worked Example
A spring extends 8 cm when a 2 kg mass hangs from it. Find k.
F = mg = 2 × 9.81 = 19.62 N
k = F/x = 19.62 / 0.08 = 245.25 N/m
Now, if that spring is stretched 15 cm, what force does it exert?
F = kx = 245.25 × 0.15 = 36.79 N
When does Hooke's Law stop working?
Beyond the elastic limit. Stretch a spring too far and it deforms permanently — the coils don't return to their original spacing. The spring constant is no longer constant. The stress-strain curve becomes nonlinear beyond the elastic limit, and plastic deformation begins.
How does spring stiffness relate to natural frequency?
For a mass-spring system: ω = √(k/m), f = (1/2π)√(k/m). Stiffer spring → higher frequency. This is used in vibration isolation, engine valve timing, and suspension design. Car engineers carefully tune spring-damper combinations for ride quality vs. handling.
Is Hooke's Law only for springs?
Not at all. It applies to any elastic material within its linear range: rubber bands, metal beams, molecular bonds, even the force between atoms in a solid at equilibrium. The spring constant becomes an elastic modulus when describing bulk materials: F/A = E × ΔL/L (Young's modulus for tension/compression).