Spring constant calculator (Hooke’s law)
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Result
Find the spring constant k in three ways: from a force and the extension it causes (Hooke’s law), from several springs connected in series or in parallel, or from a mass and the period of its oscillation. With Hooke’s law the calculator also gives the elastic energy stored in the spring.
Step-by-step solution
Hooke’s law
Elastic energy
Key formulas
- Mass on a spring
- T = 2π·√(m/k)
- Angular frequency
- ω = √(k/m) = 2π/T
- Energy
- E = ½·k·A²
How to calculate a spring constant
- Hooke’s law: k = F/x, with the extension x in metres for k in N/m.
- Springs in parallel share the load: k = k₁ + k₂ + ….
- Springs in series carry the same force: 1/k = 1/k₁ + 1/k₂ + ….
- From an oscillation: T = 2π√(m/k), so k = 4π²m/T².
- Stored energy: E = ½·k·x² = ½·F·x.
Questions and answers
Why do springs in series give a smaller k?
Each spring carries the full force and stretches by its own amount, so the total extension is larger for the same force. Two equal springs in series have half the stiffness of one.
Is the energy F·x or ½·F·x?
½·F·x. The force grows from zero to F while the spring stretches, so the work done is the area under a straight line: half of F times x.
Does Hooke’s law always hold?
Only within the elastic limit. Beyond it the spring deforms permanently and the force is no longer proportional to the extension.
Does gravity change the period of a mass on a spring?
No. Gravity only shifts the equilibrium position; the period T = 2π√(m/k) is the same for a vertical and a horizontal spring.
Practise it yourself
Practise Springs & pendulums
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