Euler Buckling Calculator

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Calculate the critical load at which a slender column will buckle.

Input Parameters

Modulus of Elasticity (E)

GPa

Moment of Inertia (I)

mm⁴

Column Length (L)

End Condition (K)

Calculation Results

Enter column parameters to calculate

About this calculator

Quick Reference

EModulus of Elasticity

IMoment of Inertia

LActual Length

KEffective Length Factor

Overview

Euler's buckling formula predicts the maximum axial load that a long, slender, ideal column can carry before it suddenly collapses due to instability.

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Pro Tips

The formula is only valid for long 'slender' columns.
K depends on how the ends are supported. A column fixed at both ends is much stronger than one free at one end.
The Moment of Inertia (I) is the smallest I for the cross-section, as buckling occurs in the weakest direction.

Fun Facts

"Euler's formula was published by Leonhard Euler in 1757."
"Buckling is a 'catastrophic' failure because it happens suddenly with little warning."
"Slenderness ratio (L/r) is another key metric: columns with L/r > 120 are usually considered 'long'."

Formula: P_cr = (π² * E * I) / (K * L)²