Helical Compression Spring Rate

k = G d^4 / (8 D^3 Na), G the wire shear modulus by material, d the wire diameter, D the mean coil diameter (OD - d), Na the active coils. A 0.080 in hard-drawn wire, 0.75 in mean coil, 8 active coils is 17.4 lb/in (spring index 9.4). Get Na from total coils by end condition (squared-and-ground Nt - 2). A good index D/d is 4-12. Rate only, not stress or solid height; Machinery's Handbook / Shigley, the spring maker governs.

k = G d^4 / (8 D^3 Na); spring index = D / d. G by material: music wire 11.85e6, hard-drawn 11.5e6, chrome-silicon 11.2e6, stainless 302 10.0e6, phosphor bronze 6.0e6 psi.

Standard helical-spring rate per Machinery's Handbook and Shigley's Mechanical Engineering Design, by name; shear modulus G values from the ASTM spring-wire standards (A228 music wire, A227 hard-drawn, A401 chrome-silicon, A313 stainless, B159 phosphor bronze).

The rate formula is a public machine-design result; the per-material shear modulus is a published material constant.

Estimate. AHJ and licensed professional govern.

Field names used by the API: wire_diameter_in, mean_coil_diameter_in, active_coils, material, spring_rate_lb_in, spring_index

• Rate formula k = G d^4 / (8 D^3 Na), round wire, active coils NaMachinery's Handbook / Shigley
• Shear modulus G by material (music wire 11.85e6 psi ... phosphor bronze 6.0e6 psi)ASTM spring-wire standards
• Spring index D/d of 4-12 recommended for manufacturabilityspring-design practice