Euler's Buckling Formula is a mathematical equation used to predict the critical load at which a slender column will buckle under compression. The formula is expressed as P_cr = \frac\pi^2 E I(K L)^2 , where P_cr is the critical load, E is the modulus of elasticity, I is the moment of inertia, K is the column effective length factor, and L is the actual length of the column. This formula is particularly important in engineering and construction, as it helps ensure that structures can withstand compressive forces without failing. Leonhard Euler, a Swiss mathematician, developed this formula in the 18th century, and it remains a fundamental principle in structural analysis today.