Free · Physics models
Ideal Helical Compression and Torsion Spring
Connect wire geometry, elastic moduli, active coils and ideal spring force or torque.
- 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-mm wire, 10-mm mean coil diameter, ten active coils and 80-GPa shear modulus give ideal compression stiffness 1,000 N/m.
Compression stiffness follows wire-torsion compliance; helical torsion stiffness follows wire-bending compliance.
Worked example
Enter these known values and leave the other values blank.
- Wire diameter (d)
- 1 mm
- Mean diameter (D)
- 1 cm
- Number of active coils (Na)
- 10
- Modulus of rigidity (G)
- 80 GPa
- Spring index (C)
- 10
- Outer diameter (OD)
- 11 mm
- Spring constant (k)
- 1000 N/m
Assumptions and limitations
- The wire is circular, the coils are close wound and deformation is small and elastic. Compression/traction and torsion retain separate material modulus controls.
- Compression force is a signed restoring force. Torsion active coils include the captured approximate straight-leg compliance correction with rounded 3.1416. End styles change only the captured free-length relation.
- Stress concentrations, coil contact, fatigue, yield, manufacturing tolerances and preload are omitted.
- Clear the unknown numerical field before using a supported inverse; selection controls retain their captured branches.
Common questions
What assumptions matter for this model?
The wire is circular, the coils are close wound and deformation is small and elastic. Compression/traction and torsion retain separate material modulus controls.
What does this model leave out?
Stress concentrations, coil contact, fatigue, yield, manufacturing tolerances and preload are omitted.
References
- Gurudatta Springs: torsion-spring engineering equation
- NASA: torsion spring behavior
- Calculation definition and unit reference
Model requirements: Active compression coils must be positive. Wire diameter must be positive. Mean coil diameter must exceed wire diameter.