Spring Calculator (Hooke's Law)
Find spring properties using Hooke's Law.
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Formulas
F = k × xHooke's Law: force proportional to displacement
E = ½kx²Elastic potential energy stored in spring
Hooke's Law
Valid within the elastic limit. Common spring constants: car suspension ~20-40 kN/m, pen click spring ~100-500 N/m, trampoline ~5-10 kN/m.
How Spring Force Works
An ideal spring follows Hooke's law: the force it exerts is directly proportional to how far it is stretched or compressed from its rest position:
F = k × xF is the spring force in newtons, k is the spring constant (stiffness) in N/m, and x is the displacement from the natural length in metres.
A higher spring constant means a stiffer spring that resists displacement more strongly. The relationship is linear only within the spring's elastic range; stretch it too far and it deforms permanently.
Worked Examples
A spring with k = 200 N/m compressed by 0.05 m:
F = 200 × 0.05 = 10 N
Energy stored in that compressed spring is E = ½kx² = 0.5 × 200 × 0.05² = 0.25 J, released when the spring returns to rest.
Springs in Series and Parallel
| Arrangement | Effective stiffness | Result |
|---|---|---|
| Parallel | k_total = k1 + k2 | Stiffer |
| Series | 1/k_total = 1/k1 + 1/k2 | Softer |
Parallel springs share the load and feel stiffer; series springs each carry the full force and the combination is softer than either alone.
Frequently Asked Questions
What is the spring constant?
It is the stiffness of the spring — the force required to stretch or compress it by one metre. It depends on the wire material, coil diameter, and number of coils.
When does Hooke's law stop applying?
Beyond the elastic limit, the spring deforms permanently and force is no longer proportional to displacement. The linear model only holds within the elastic range.
How is spring energy calculated?
The elastic potential energy is E = ½kx². It equals the area under the force-displacement line.