Euler Column Buckling Calculator
Critical buckling load of a column from length, end conditions (pinned, fixed, cantilever), cross-section and material — Euler load, slenderness ratio, whether Euler or yielding governs (Johnson parabola) and the safe load with a factor of safety.
How it works
Pcr = π² E I ÷ (K L)² for Le/r ≥ Cc = √(2π²E/fy); otherwise Johnson: Pcr = A fy [1 − fy (Le/r)² ÷ (4π²E)]; r = √(I/A)
A slender column fails not by crushing but by bowing sideways once the load reaches Euler’s critical value, which depends on stiffness (E × I) and the square of the effective length — so doubling the length quarters the capacity, and end fixity that halves the effective length quadruples it. The formula assumes a perfectly straight, centrally loaded, elastic column; for stockier members the material yields before Euler’s load is reached, and the Johnson parabola bridges the two regimes below the transition slenderness. Practical end fixity is never perfect, which is why the recommended K values are a little larger than the theoretical ones, and design codes apply further reductions for imperfections. Thin-walled tubes must also be checked for local buckling of the wall itself.
Worked example
A 60 × 3 mm steel tube 2.5 m long, pinned both ends: I = 21.8 cm⁴, r = 20.2 mm, slenderness 124 (above Cc = 120, so Euler applies) — critical load 69.1 kN, safe load about 27.6 kN with a factor of 2.5.
Frequently asked questions
Which axis buckles?
The one with the smaller I (weak axis), unless bracing prevents it. For rectangles the calculator uses the smaller dimension cubed automatically.
How do I choose the factor of safety?
Because buckling is sensitive to imperfections, 2–3 is typical for machine parts and scaffolding; structural codes use their own partial factors and buckling curves instead.
Related calculators
Engineering estimate for education and preliminary design. Use manufacturer data, applicable standards and appropriate safety factors, and have critical designs checked by a qualified engineer.