Elastic critical buckling load and slenderness ratio for a column, for any standard end-support condition. Gives the theoretical elastic buckling load — not a code-compliant allowable load, which also needs safety/resistance factors and a short-column check.
Standard method — stated scope limits apply
Column
Enter column and section properties.
About This Calculation
Euler’s column buckling formula (1757) predicts the load at which a slender column fails by sudden lateral buckling rather than by the material simply crushing — a fundamentally different failure mode from a short, stocky column’s. The critical load depends on the column’s stiffness (EI), its length, and critically, how its ends are restrained: a column fixed at both ends can carry four times the load of the same column pinned at both ends, purely from the end conditions changing its effective buckling length.
Frequently Asked Questions
Why does the end-condition factor K matter so much?
K converts the column’s actual length into an "effective length" — the length an equivalent pinned-pinned column would need to buckle at the same load. A fixed-fixed column (K=0.5) is four times stiffer against buckling than the same column pinned-pinned (K=1), since critical load scales with 1/(KL)².
How do I know if my column is "short" or "slender"?
Slenderness ratio (effective length ÷ radius of gyration) is the standard indicator — a low slenderness ratio (commonly cited as roughly below 30) usually means the column will crush before it buckles elastically, meaning Euler’s formula alone overstates its real capacity; a real design still needs the appropriate short/intermediate-column code provisions for that range.
Does the Euler load include a safety factor?
No — this is the theoretical elastic critical load assuming a perfectly straight, centrally-loaded, perfectly elastic column. Real design codes apply safety/resistance factors and account for initial crookedness and eccentric loading on top of this, which is why a real allowable load is always well below the calculated Euler load.
What is radius of gyration, and why is it computed from I and area?
Radius of gyration (r = √(I/A)) is a measure of how the cross-section’s material is distributed relative to its centroid — a section with material spread further from center (like a tube vs. a solid rod of the same area) has a larger r and resists buckling better for the same cross-sectional area.