Helical Compression Spring Calculator: Rate, Deflection and Stress
The spring rate, deflection under a force and the shear stress in a helical compression spring.
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How this calculator works
A helical spring is a twisted wire. The spring rate is k = G d⁴ / (8 D³ n), where d is the wire diameter, D the mean coil diameter, n the number of active coils and G the shear modulus of the wire. Fewer coils, thicker wire or a smaller coil make a stiffer spring.
The shear stress is raised by the curvature of the wire, so the calculator applies the Wahl correction factor. Springs under repeated loading must also be checked for fatigue.
Formulas used
- k = \frac{G d^4}{8 D^3 n}
- \tau = K_W\frac{8 F D}{\pi d^3}
- K_W = \frac{4C - 1}{4C - 4} + \frac{0.615}{C}
Worked example
With the default numbers in the calculator above:
- Spring rate: 6.4 N/mm
- Deflection: 7.81 mm
- Spring index and Wahl factor: C = 8.33, Kw = 1.18
- Maximum shear stress: 139 MPa
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. Closed and ground end coils do not count, so subtract about one to two coils from the total.
What is the Wahl factor?
A correction for the extra stress on the inside of the coil because the wire is curved.
Is fatigue checked?
No. Springs that cycle need a fatigue check against the wire strength and surface condition.
Related calculators
Further reading: Shigley, Mechanical Engineering Design (mechanical springs).
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