# Euler Buckling Formula

## Theorem

$F = \dfrac {\pi^2 E I} {\left({K L}\right)^2}$

where:

$F$ = maximum or critical force (vertical load on column)
$E$ = modulus of elasticity
$I$ = area moment of inertia of the cross section of the rod
$L$ = unsupported length of column
$K$ = column effective length factor, whose value depends on the conditions of end support of the column, as follows:
For both ends pinned (hinged, free to rotate), $K = 1.0$
For both ends fixed, $K = 0.50$
For one end fixed and the other end pinned, $K \approx 0.699$
For one end fixed and the other end free to move laterally, $K = 2.0$
$K L$ is the effective length of the column

## Also known as

The Euler buckling formula is also known as the Euler column formula.

## Source of Name

This entry was named for Leonhard Paul Euler.