One of the earliest mathematical explanation of the phenomenon of buckling was given by Euler (1759) who proposed the Euler's theory.
fE = Euler’s critical stress,
PE = Euler’s critical load,
A = Area of cross section,
I = Moment of inertia of the section,
Radius of gyration,
Slenderness ratio of the element, and
k = A coefficient which depends upon the end condition of the column.
Also various empirical formulae, e.g. Rankine’s, Johnson’s and Perry’s are available for estimating the buckling load of columns.