Spring Calculator

A spring calculator is a software tool that uses standard spring engineering formulas to compute key design parameters — such as spring rate, deflection, force, stress, and solid height — based on the spring's physical dimensions and material properties. It saves engineers from manual calculations and helps verify designs before manufacturing.

Spring rate is calculated using the formula k = (G × d⁴) / (8 × D³ × Na), where G is the shear modulus of the material, d is the wire diameter, D is the mean coil diameter, and Na is the number of active coils. A higher spring rate means a stiffer spring that requires more force to deflect a given distance.

Compression springs are open-coil helical springs that resist compressive loads — they shorten under force. Extension springs have closed coils (often with hooks at each end) and resist tensile loads, stretching when a pulling force is applied. The spring rate formula is the same for both types, but solid height and hook geometry differ.

Spring index (C) is the ratio of the mean coil diameter to the wire diameter (C = D/d). It indicates the coil's curvature. A spring index between 4 and 12 is generally considered ideal — a very low index (below 4) indicates tight coiling that's hard to manufacture, while a very high index (above 12) produces fragile springs prone to tangling.

Solid height is the length of a compression spring when all coils are fully compressed together, calculated as the total number of coils multiplied by the wire diameter. It's a critical design constraint — the spring's working deflection must never allow the spring to reach solid height, as this causes coil clash and can damage the spring or the assembly.

Deflection (δ) equals the applied force (F) divided by the spring rate (k): δ = F / k. For example, if your spring rate is 5 N/mm and you apply a 20 N load, the spring deflects 4 mm. The loaded length is then the free length minus the deflection (for compression springs).

Common values are: Music Wire / Hard Drawn Steel ≈ 79,300 MPa, Stainless Steel 302/304 ≈ 68,900 MPa, Phosphor Bronze ≈ 41,400 MPa, and Beryllium Copper ≈ 44,800 MPa. Using the correct shear modulus for your material is essential for accurate spring rate and stress calculations.

The maximum safe load is the greatest force a spring can handle before the shear stress in the wire exceeds the material's yield strength, or before the spring reaches solid height. This calculator estimates maximum safe travel as the free length minus the solid height, and the corresponding force as the spring rate multiplied by that maximum travel.