Column Buckling Calculator
Will a slender column buckle before it crushes? Euler critical load from the section, length and end conditions — with slenderness ratio, allowable load and a buckle-vs-crush verdict.
Why Slender Columns Fail Early
A short, stocky post fails by crushing when the stress reaches yield. A long, slender one does something more dangerous: it buckles sideways at a load far below the crushing load, often without warning. Euler buckling is the calculation that finds that critical load:
E is the modulus of elasticity, I the least moment of inertia (columns buckle about the weak axis), L the unbraced length and K the end-condition factor. Notice strength (yield) does not appear — for a slender column, stiffness and length decide everything.
End Conditions Change Everything
How the ends are held sets the effective length K L. The same column can carry sixteen times more load fixed-fixed than fixed-free:
| End conditions | K |
|---|---|
| Pinned – pinned | 1.0 |
| Fixed – fixed | 0.5 |
| Fixed – pinned | 0.7 |
| Fixed – free (cantilever) | 2.0 |
Is Euler Even Valid? Check Slenderness
Euler only applies above a critical slenderness ratio, the column constant Cc = √(2π²E / Fy). Above Cc the column is long and Euler governs. Below it the column is intermediate or short, yields or buckles inelastically first, and Euler overestimates the capacity — so the calculator flags it and caps the allowable at the squash (yield) load.
Frequently Asked Questions
What is the slenderness ratio?
The effective length divided by the radius of gyration, K L / r. It is the single number that tells you how buckling-prone a column is — higher means more slender.
Which moment of inertia do I use?
The smallest one. A column buckles about its weakest axis, so this tool uses the least I of the section automatically.
Why does my answer ignore the steel grade?
For a truly slender column the Euler load depends on stiffness (E) and geometry, not strength. Yield only matters once the column is stocky enough to crush first – which is exactly the case the verdict warns about.
Related calculators
- Moment of Inertia Calculator — the I that drives buckling.
- Section Modulus Calculator — the bending side of member sizing.
- Mechanical Stress Calculator — axial and bending stress checks.
- Factor of Safety Calculator — margin against the critical load.
- Beam Load Calculator — loads feeding into the column.