Mechanics of Materials · Spring design

Spring Rate Calculator

Size compression, extension, and torsion coil rates from wire geometry — with optional solid-height and shear stress checks that update as you type.

Spring type
Choose compression, extension, or torsion — formulas and units follow the mode.

High-carbon steel; common for small compression and extension springs.

d
D
n

Optional — load & stress

L₀
δ

Result

Spring rate

k = Gd⁴/(8D³n)

k
—

Enter wire diameter d and mean coil diameter D — the coil schematic below results highlights each dimension.

About spring rate

Helical spring stiffness, solid height, and coil shear stress from wire geometry.

Spring rate k is the load per unit deflection. For compression and extension coils, k is usually expressed in N/mm. For torsion springs, k is often given in N·mm per degree of winding rotation. Rate depends on wire diameter d, mean coil diameter D, active coils n, and material stiffness (G for helical coils, E for torsion legs).

  • Compression / extensionk = G·d⁴ / (8·D³·n)
  • Torsion springk = E·d⁴ / (3667·D·n)
  • Solid height (compression)L_s ≈ d·(n + 2)
  • LoadF = k·δ
  • Coil shear stressτ = 8·F·D / (π·d³)
  • Spring indexC = D / d

Variables: d and D in consistent length units; G in Pa (or GPa × 10⁹); n = active coils only. This tool does not apply the Wahl stress correction factor in v1.

Music wire compression spring: d = 2 mm, D = 20 mm, n = 10, G = 81.7 GPa.

k ≈ 2.04 N/mm

At δ = 10 mm, F = k·δ ≈ 20.4 N. Coil shear stress τ = 8FD/(πd³) ≈ 130 MPa (below a typical 690 MPa allowable for music wire in static service). Solid height L_s = 2×(10+2) = 24 mm.

Are compression and extension rates the same?
Yes for ideal helical coils with the same d, D, n, and G — end fittings and initial tension differ in real extension springs.
What are active coils?
Coils that deflect under load, excluding dead or inactive end coils. Solid-height estimate assumes squared-ground ends (n + 2).
Why is my spring index flagged?
C = D/d between about 4 and 12 is typical for cold-formed wire. Very low C is hard to coil; very high C may buckle when L₀/D is large.
Should I add a Wahl factor?
Curved-wire stress concentration can raise peak τ by ~10–15%. Use supplier data or FEA for critical springs; this calculator uses the basic τ formula.
  • Ideal helical geometry — no shot peening, preset, or nested springs.
  • Torsion constant 3667 is a handbook form — confirm with your supplier drawing.
  • No fatigue life, buckling, or resonance analysis on this page.
  • Not for safety-critical certification — verify with testing and applicable codes.