Formulas which are used to calculate compression spring design parameters are spring index formula, Wahl factor formula, spring rate formula, shear stress at spring body formula, spring outer diameter at solid height formula, spring stability condition and Hooke's law. All these compression spring formulas and conditions are given in the following chart.

Note: For further information on compression spring design formulas, check Shigley's Mechanical Engineering Design.

Parameter Symbol Formula
Spring outer diameter  OD Spring outer diameter
Spring inner diameter ID Spring inner diameter
Spring index C Spring Index
Wahl factor Kw Wahl factor
Shear stress at spring body (corrected with Wahl factor)- used for unprestressed springs τs Shear stress in spring (wahl factor included)
Shear stress at spring body  (uncorrected )- used for prestressed springs τs Shear stress in spring (wahl factor not included)
Spring rate k Spring rate
OD at solid height ODat solid Outer diameter at solid height of spring
Spring stability condition --- Compression spring stability condition against buckling
Hooke's Law --- Hooke's Law in Mechanical Springs

Parameter Open or plain (Not ground) Open or plain (Ground) Squared or closed (Not ground) Squared or closed (Ground
Total coils [Nt] Na Na+1 Na+2 Na+2
Free height [Lf] pNa+d p(Na+1) pNa+3d pNa+2d
Solid height [Ls] d(Nt+1) dNt d(Nt+1) dNt
Pitch [p] (Lf - d) / Na Lf / (Na+1) (Lf -3d) / Na (Lf -2d) / Na
Guidelines for Dimensional Characteristics of Compression Springs
Source : From Design Handbook [Ref 1] page 32

List of Parameters
Symbol Definition
OD Spring outer diameter
ID Spring inner diameter
D Spring mean diameter
d Wire diameter
p Pitch
Lf Spring free length
Ls Spring solid height
F Axial force
Fs Force at solid length
ΔF Force difference (Ex: F2-F1
Δx Deflection (Ex: L2-L1)