Spring Constant Calculator
Hooke's Law says a spring's extension is directly proportional to the force applied — this finds the stiffness constant k from a measured force and extension, plus the energy stored at that point.
Inputs
Result
625 N/m
Stored energy 2 J
How it works
k = F / x
How the spring constant calculator works
k = F ÷ x, where F is applied force and x is the resulting extension from the spring's natural length.
Stored elastic energy = ½ × k × x², the area under the force-extension line up to that point.
Worked example: 50 N force, 0.08 m extension
- k = 50 ÷ 0.08 = 625 N/m.
- Stored energy = 0.5 × 625 × 0.08² = 0.5 × 625 × 0.0064 = 2 J.
Common mistakes to avoid
Assuming k stays constant beyond the spring's elastic limit
Hooke's Law only holds within a spring's elastic range — stretch it too far and it deforms permanently, and the force-extension relationship stops being linear well before that point.
Using total spring length instead of extension from natural length
x specifically means how far the spring has stretched or compressed from its own rest length, not the spring's absolute length — using the wrong reference point gives a meaningless k.
Frequently asked questions
What does a higher spring constant actually mean physically?
A stiffer spring — more force is needed to achieve the same extension, or equivalently, the same force produces less extension than in a spring with lower k.
Why does stored energy use ½kx² instead of just kx²?
Because force increases linearly with extension (starting from zero), the average force over the stretch is half the final force — the ½ factor accounts for that averaging, matching the triangular area under a force-extension graph.
How do springs combine in series and parallel?
Springs in parallel add their k values directly (stiffer overall); springs in series combine like capacitors in series (1/k_total = 1/k1 + 1/k2), making the combination less stiff than either alone.
Can this be used for a compressed spring, not just a stretched one?
Yes — Hooke's Law applies symmetrically to compression and extension for an ideal spring, with x simply representing the displacement in either direction.
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