How to use the Helical Spring Calculator
- 1. Enter the springWire diameter, coil diameter (mean, outer or inner) and active coils.
- 2. Add load and GAxial load, modulus of rigidity and the end type.
- 3. Get the designStress, deflection, stiffness, lengths and pitch, with steps.
Spring formulas
- Spring index C = D/d, where D is the mean coil diameter.
- Wahl factor K = (4C − 1)/(4C − 4) + 0.615/C. It covers both direct shear and coil curvature.
- Shear stress τ = K × 8WD / (πd³).
- Deflection δ = 8WD³n / (Gd⁴) and stiffness k = Gd⁴ / (8D³n).
- Strain energy U = Wδ/2.
Squared and ground ends add 2 inactive coils, and the solid length is (n + 2)d. Free length = solid length + maximum deflection + a clash allowance, often 15% of the deflection.
Worked example and exam tips
Wire d = 6 mm, mean diameter D = 48 mm, 10 active coils, load 200 N and G = 81.37 GPa. C = 8, K = 1.184, τ = 1.184 × 8 × 200 × 48 / (π × 216) = 134 MPa. δ = 8 × 200 × 48³ × 10 / (81 370 × 6⁴) = 16.78 mm and k = 11.9 N/mm.
- Keep the spring index between 4 and 12. Below 4 the spring is hard to coil; above 12 it buckles and tangles.
- Deflection rises with D³, so a small change in coil diameter makes a big change in stiffness.
- If the free length is more than about 4 times D, check for buckling or use a guide rod.
Frequently asked questions
What is the Wahl correction factor?
It increases the simple torsion stress to allow for direct shear and the extra stress on the inner side of the curved wire. The tool also shows the stress with only the direct-shear factor.
How many inactive coils should I take?
It depends on the ends: none for plain, 1 for plain and ground, and 2 for squared or squared and ground ends.
What is clash allowance?
A small gap left between the coils at maximum load so that they never touch. 15% of the maximum deflection is a common textbook value.
Is this calculator free?
Yes. You fill in a short form once to see your result, and the other Uncodemy tools then open without it. Every calculation runs in your browser and nothing you type is sent anywhere.