By Zencalcy Editorial TeamLast reviewed About us
Euler's formula gives the theoretical axial load at which a long, slender, ideal column will buckle. Buckling is a instability mode that suddenly lateral‑deflects the column.
Critical load for column buckling.
P_cr = π² E I / (K L)²
P_cr is the critical load, E the Young's modulus, I the area moment of inertia of the cross‑section, K the effective length factor (pinned‑pinned K=1, fixed‑free K=2, etc.) and L the actual column length.
| Symbol | Meaning |
|---|---|
| P_cr | Critical buckling load. |
| E | Young's modulus. |
| I | Area moment of inertia. |
| K | Effective length factor. |
| L | Column length. |
P_cr = π² × 2×10¹¹ × 1×10⁻⁶ / (1×2)² ≈ 49.3 kN.
Continue with the Slenderness Ratio Calculator, Thin Cylinder Hoop Stress Calculator, or the Thin Cylinder Longitudinal Stress Calculator — or browse more materials and elasticity tools and all physics calculators.
The column will deflect laterally and may fail by crushing or fracture, depending on slenderness.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Content updated: September 2026