Spring Calculator — 3D Printed Spring Dimensions

Spring Calculations

• Helical spring rate = (G x b x h³) / (5.6 x n x D³) — the RoyMech rectangular-wire rate, where 1/5.6 ≈ 0.18 is the shape factor for a square section
• Shear modulus G = E / (2(1+ν)) ≈ 0.35 x E for FDM polymers (Poisson's ratio ν ≈ 0.4)
• Leaf spring rate = (E x b x h³) / (4 x L³) — the cantilever end-load rate 3EI/L³ (fixed at one end, load at the free tip)
• Max deflection = lesser of the strain limit (π x n x D² x γ / h) and the solid-height limit (free length − coils x h)
• Max force = Spring rate x Max deflection

Where G = shear modulus, E = Young's modulus, b = wire width, h = wire height, n = active coils, D = mean diameter, γ = allowable wire shear strain, L = span length. 3D printed springs use rectangular wire because square/rectangular cross-sections print far better on FDM than round ones. The max-deflection figure is capped at the solid height (where the coils touch), so it never exceeds what the spring can physically travel.