Compression Spring Solid Height and Buckling Calculator
Solid height, deflection to solid and a buckling check for a helical compression spring.
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How this calculator works
The solid height is the length of the spring with all its coils touching. It depends on the end type: squared and ground ends add two coils and the solid height is the total coils times the wire diameter. The free length minus the solid height is the most the spring can be compressed.
A spring that is long compared with its coil diameter can bow sideways (buckle) when compressed. It is absolutely stable if the free length is less than 2.63 D / α, where α depends on how the ends are held. Leave a clash allowance of about 10 to 15 percent of the working deflection, so the coils never touch in service.
Formulas used
- L_s = N_t d\ \text{(squared and ground)}
- k = \frac{G d^4}{8 D^3 N_a}
- L_f < \frac{2.63\,D}{\alpha}\ \text{(stable)}
Worked example
With the default numbers in the calculator above:
- Total coils: 10
- Solid height: 30 mm
- Spring rate: 6.399 N/mm
- Deflection from free length to solid: 30 mm
- Force at solid height: 192 N
- Deflection at the working force: 15.63 mm
- Length at the working force: 44.37 mm
- Buckling check: free length against the limit: stable (no buckling)
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
What are active coils?
The coils that flex. End coils that are closed or ground do not count as active.
How do I stop a spring buckling?
Guide it on a rod or in a tube, use a shorter free length or a larger coil diameter.
What is coil clash?
The coils touching before the spring reaches its working length. It causes noise and a sudden rise in stress.
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Further reading: Shigley, Mechanical Engineering Design (mechanical springs).
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