Spring Calculator

Formula

• Spring rate k = G × d⁴ ÷ (8 × D³ × Na)
• Wahl factor Kw = (4C − 1)/(4C − 4) + 0.615/C where C = D/d
• Shear stress τ = 8 × F × D × Kw ÷ (π × d³)

About this calculator

Part of our Mechanical Calculators collection. Beams, bolts, springs, gears, bearings, and core ME calculations.

How it works

Spring index C equals mean coil diameter divided by wire diameter. Spring rate k uses the Wahl correction factor and material shear modulus. Deflection equals load divided by spring rate. Check shear stress against the material yield guideline before finalizing wire size.

Enter your values in the inputs above and click CALCULATE. Results appear on the right without a page reload. No login and no server upload.

Worked example

Music wire spring: d = 2 mm, D = 16 mm, 10 active coils, 100 N load.

1. C = 16 ÷ 2 = 8
2. k ≈ 3.16 N/mm (G = 81,000 MPa for music wire)
3. Deflection = 100 ÷ 3.16 ≈ 31.6 mm

Result: Spring rate about 3.16 N/mm; check shear stress against material limit before finalizing.

When to use

• Initial wire size and coil count selection
• Checking deflection at a working load
• Screening spring index and buckling ratio

Limitations

• Compression springs, cylindrical coils only
• Closed-end solid height simplified as d × Na
• No fatigue life or surging frequency analysis

FAQ

What spring index should I target?

C between 4 and 12 is typical. Below 4 is hard to manufacture; above 12 may buckle without a guide.

What is buckling ratio?

Free length divided by mean coil diameter. Values above 4 may need a guide rod to prevent buckling.

What does stress / 45% yield mean?

Many spring designers limit operating stress to about 45% of material ultimate shear for static service.