Helical compression spring rate calculator
Use it to design a new spring or estimate the stiffness of one you can measure. The default shear modulus suits steel spring wire.
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How to use it
- Enter wire diameter, mean coil diameter, active coils and shear modulus.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
k = G d⁴ ÷ (8 D³ n), where d is the wire diameter, D the mean coil diameter and n the number of active coils. Spring index C = D ÷ d.
Example
Inputs: Wire diameter = 2 mm, Mean coil diameter = 20 mm, Active coils = 10, Shear modulus = 79.3 GPa. Result: Spring rate: 1.9825 N/mm; Spring rate in N/m: 1,982.5 N/m; Spring index: 10.
Limits and caveats
- Theoretical formula that ignores wire curvature and end effects; accuracy drops for very small spring index.
- Does not check shear stress, buckling or solid length.
Questions about this tool
What shear modulus do spring materials have?
Steel spring wire is about 79 to 82 GPa; 302 stainless steel is about 69 GPa.
How do I count active coils?
For a spring with closed and ground ends, active coils are usually the total count minus 2.
How do I measure the mean diameter?
Subtract the wire diameter from the outside diameter, or add it to the inside diameter.