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Helical Compression Spring Design Calculator

Shigley's / DIN EN 13906

Design and verify helical compression springs evaluating spring rate, solid height, Wahl factor corrected stresses, buckling risks, and surge frequency.

Spring Rate (k)
16.20 N/mm
Solid Load (Fs)
421.2 N
Solid Height (Hs)
24.00 mm
Spring Index (C)
5.00 -

Geometries & Dynamics

Mean Diameter (D)10.000 mm
Inner Diameter (D_id)8.000 mm
Total Coils (N_t)12
Pitch (p)4.600 mm
Wahl Factor (K_W)1.310
Surge Frequency (f_n)723.0 Hz
Estimated Weight0.0093 kg
Slenderness (L_f/D)5.00

Safety & Limits

Solid Deflection (δ_s)26.00 mm
Solid Stress (τ_s)1757 MPa
Shear Modulus (G)81,000 MPa

Spring Schematic

Interactive Spring Layout
D: 10.0Lf: 50.0C: 5.0

Verification Calculation Log

  • 1Mean Diameter (D): D_od - d = 12 - 2 = 10.000 mm
    • •Spring Index (C): D / d = 10.000 / 2 = 5.00
    • •Wahl Factor (K_W): (4C - 1)/(4C - 4) + 0.615/C = 1.310
    • •Spring Rate (k): (G * d^4) / (8 * D^3 * N_a) = 16.20 N/mm
    • •Solid Force (F_s): k * (L_f - H_s) = 421.20 N
    • •Solid Stress (tau_s): K_W * (8 * F_s * D) / (pi * d^3) = 1757 MPa

Mathematical Models & Equations

Spring Index (C)
C = D / d
Wahl Factor (K_w)
K_W = (4C - 1)/(4C - 4) + 0.615/C
Spring Rate (k)
k = (G * d^4) / (8 * D^3 * N_a)
Solid Spring Force (F_s)
F_s = k * (L_f - L_s)
Torsional Shear Stress (tau)
\tau = K_W * (8 * F * D) / (\pi * d^3)
Surge Frequency (f_n)
f_n = (d / (2\pi * D^2 * N_a)) * \sqrt{G / (2 * \rho)}

Engineering Application Notes

Design limits typically cap the spring index C between 4 and 12 for coiling considerations. Ensure solid stress remains below material proportionality limits to prevent permanent set. Buckling typically occurs when Lf/D > 4. If buckling is a concern, guide rods or sleeves should be employed.

Standard Citations & References

  • Shigley's Mechanical Engineering Design, Chapter 10 - Springs
  • DIN EN 13906-1 Cylindrical helical springs made from round wire and bar
  • SMI (Spring Manufacturers Institute) Design Handbooks