Spring Design Calculator

The spring rate (stiffness) is calculated with the standard formula k = Gd⁴ / (8D³Na), where G is the shear modulus of the material in MPa, d is the wire diameter in mm, D is the mean coil diameter in mm, and Na is the number of active coils. The result is in N/mm (Newtons per millimeter). This formula is derived from Hooke's law applied to the torsional deflection of a circular cross-section wire.

The Wahl correction factor (Kw) accounts for two stress-raising effects in helical springs: the curvature of the coil and the direct shear stress component. Without this correction, shear stress calculations would underestimate the true stress at the inner coil surface where stress concentration is highest. Kw = (4C−1)/(4C−4) + 0.615/C, where C = D/d is the spring index. For a spring index of 6, Kw ≈ 1.25, meaning stress is 25% higher than simple calculations would suggest.

Spring index C = D/d is the ratio of mean coil diameter to wire diameter. A spring index between 4 and 12 is considered optimal for most applications. Index below 4 produces very tight coils that are difficult to manufacture and have high stress concentrations. Index above 12 creates springs that are prone to buckling and tangling. Index values between 6 and 9 represent the most common manufacturing-friendly range.

Solid length Ls is the compressed height of the spring when all coils are touching. For squared-and-ground ends (the most common configuration for precision springs), total coil count Nt = Na + 2 (two inactive coils at each end are added to the active coil count), and Ls = Nt × d. Maximum deflection is Lf − Ls, which is the maximum working travel before the spring goes solid.

The 45% of ultimate tensile strength (Sut) is the industry-standard static allowable shear stress for spring wire. It incorporates a safety factor against yielding while accounting for the fact that shear strength is typically about 0.67 × Sut for steel. Using 45% of Sut provides a conservative but practical baseline. For fatigue loading (cyclic compression), lower stress limits based on endurance data should be used.

Active coils (Na) are the coils that deflect and carry load — they are free to move. Inactive or dead coils are the coils at each end that are in contact with the end plates and do not deflect. For squared-and-ground ends, there are approximately 1 inactive coil at each end, so total coils Nt = Na + 2. The solid length depends on total coils, but spring rate depends only on active coils.

Music Wire (ASTM A228) offers the highest strength (Sut 2170 MPa) and is the most common choice for static or low-cycle applications at room temperature. Chrome Silicon (ASTM A401) is preferred for high-temperature or high-cycle fatigue applications. Stainless Steel 302 provides corrosion resistance. Phosphor Bronze and Beryllium Copper are used where electrical conductivity or non-magnetic properties are required, but they have significantly lower strength.

This calculator is specifically designed for helical compression springs with squared-and-ground ends. Extension springs have initial tension, different end configurations, and different solid height calculations. The spring rate formula k = Gd⁴/(8D³Na) is the same, but the stress analysis (including initial tension stress) and end-type corrections differ. For extension spring design, additional parameters including initial tension and hook geometry must be considered.