Hooke's Law Spring Calculator
Find the force and energy in a stretched spring.
Your numbers
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Force (N)
Force (N)
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Stored energy (J)
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Oscillation period (s)
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Frequency (Hz)
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Hooke's Law Spring Calculator by TheCalcTools
How the Hooke's Law Spring Calculator works
Enter the spring constant, how far the spring is stretched or compressed and an attached mass.
The restoring force is proportional to the extension.
Energy and oscillation period follow from k, x and m.
The formula
F = k xE = ½ k x²
Worked example
Using the default values shown in the calculator:
| Spring constant (N/m) | 200 |
|---|---|
| Extension (m) | 0.15 |
| Attached mass (kg) | 0.5 |
- F = 200 × 0.15 = 30 N.
- Energy = ½ × 200 × 0.15² = 2.250 J.
- With a 0.5 kg mass the period is 0.314 s.
Result:
| Force (N) | 30.000 |
|---|---|
| Stored energy (J) | 2.2500 |
| Oscillation period (s) | 0.3142 |
| Frequency (Hz) | 3.183 |
Frequently asked questions
Does Hooke's law always hold?
Only within the elastic limit. Past it the spring deforms permanently and force is no longer proportional to extension.
What does a larger k mean?
A stiffer spring. It needs more force for the same stretch and oscillates faster.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.