How is the spring rate calculated?

The spring rate k for a helical compression spring is k = Gd⁴/(8D³n), where G is the shear modulus, d is wire diameter, D is mean coil diameter, and n is the number of active coils. This formula assumes round wire and negligible pitch angle.

What is the Wahl correction factor?

The Wahl factor Kw accounts for curvature and direct shear effects in helical springs. Kw = (4C-1)/(4C-4) + 0.615/C, where C = D/d is the spring index. It increases the calculated shear stress, especially for small spring indices (tight coils).

What spring index C should I target?

A spring index C = D/d between 4 and 12 is typical. C 12 can lead to tangling and buckling. C = 6–10 is optimal for most applications.

What is solid height and why does it matter?

Solid height is the length of the spring when fully compressed so all coils touch. It equals (total coils) × wire diameter. The spring must never be compressed to solid height in service, or permanent set (plastic deformation) will occur.

Which shear modulus G should I use?

Common values: Music wire (ASTM A228) G ≈ 79.3 GPa, Stainless 302 G ≈ 69 GPa, Chrome-vanadium G ≈ 77.2 GPa, Phosphor bronze G ≈ 41.4 GPa. G varies slightly with temperature and wire diameter.

Free Engineering Tool #064

Helical Compression Spring Design Calculator

Design helical compression springs. Enter wire diameter, coil diameter, free length, active coils, and shear modulus to calculate spring rate, max load, shear stress, and solid height.

Spring Rate k Wahl Factor Auto-Calc

Wire Diameter d (mm)

Mean Coil Diameter D (mm)

Free Length L₀ (mm)

Active Coils n

Material (Shear Modulus G)

End Type

Quick presets

Results

Spring Rate k

—

Max Load at Solid (F_solid)

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Max Shear Stress τ (with Kw)

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Solid Height

—

Spring Index C

—

Wahl Factor K_w

—

Spring Profile

Spring Rate

Shear Stress with Wahl Correction

Wahl Factor

where C = D/d is the spring index.

Solid Height

Material	G (GPa)	Typical Use
Music Wire (A228)	79.3	General purpose, high fatigue life
Chrome-Vanadium	77.2	High-stress, shock loads
Stainless 302	69.0	Corrosion resistance
Phosphor Bronze	41.4	Electrical, non-magnetic
Beryllium Copper	44.8	Non-sparking, conductive

Example — Music Wire Spring

Given: d = 4 mm, D = 30 mm, L₀ = 80 mm, n = 10, G = 79300 MPa

C = 30/4 = 7.5

k = 79300 × 4⁴ / (8 × 30³ × 10) = 79300 × 256 / 2,160,000 = 9.39 N/mm

Solid height = (10+2) × 4 = 48 mm → Travel = 80 − 48 = 32 mm

F_solid = 9.39 × 32 = 300.5 N

⚠️ Note: Never compress a spring to solid height in service. Design working travel to ≤80% of available deflection. Check for buckling if free length/mean diameter > 4.