Free · Physics models
Helical Compression Spring Stiffness
Relate wire size, mean coil diameter, active turns and shear modulus for a close-coiled helical spring.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
A 1-millimeter wire, 11-millimeter outer coil diameter, ten active turns and an 80-gigapascal shear modulus give stiffness of 1,000 newtons per meter, equivalent to 1 newton per millimeter.
Spring stiffness = G×wire diameter⁴/(8×mean coil diameter³×active turns), with mean diameter = outer diameter−wire diameter and active turns = total turns−inactive end turns.
Worked example
Enter these known values and leave the other values blank.
- Shear modulus (G)
- 80000000000 Pa
- Wire diameter
- 1 mm
- External diameter
- 11 mm
- Total coils
- 10
- Internal diameter
- 9 mm
- Active coils
- 10 coils
- Spring rate
- 1000 N/m
Assumptions and limitations
- Use a positive shear modulus, wire diameter and active-turn count. Outer coil diameter must exceed wire diameter.
- End choices subtract zero, two or four inactive turns from the total turn count. These are the captured idealized end conventions.
- The close-coiled, circular-wire formula models linear elastic axial stiffness. Stress limits, buckling, coil contact, fatigue, manufacturing tolerances and variable-pitch geometry are excluded.
- Clear the unknown numeric field before solving a supported inverse.
Common questions
What does this scenario assume?
Use a positive shear modulus, wire diameter and active-turn count. Outer coil diameter must exceed wire diameter.
What does the result leave out?
The close-coiled, circular-wire formula models linear elastic axial stiffness. Stress limits, buckling, coil contact, fatigue, manufacturing tolerances and variable-pitch geometry are excluded.
References
Model input requirements: Outer diameter must exceed wire diameter.