Euler Buckling Calculator
A free, browser-based calculator. Runs entirely in your browser — no sign up, nothing stored.
Enter Values
How to use this calculator
- Enter the material's Young's modulus E (GPa) and the column's second moment of area I (cm⁴) — use the smaller, weak-axis I.
- Enter the column length L and the effective length factor K for the end conditions.
- Read the critical (Euler) buckling load.
How it works
The Euler Buckling Calculator finds the load at which a slender column becomes unstable: Pcr = π²EI / (KL)².
K accounts for how the ends are held — pinned–pinned 1.0, fixed–fixed 0.5, fixed–free 2.0, fixed–pinned 0.7. A higher K means a longer effective length and a lower buckling load.
Worked example
Steel column, I = 500 cm⁴, 3 m, pinned ends. Pcr = π² × 200×10⁹ × 500×10⁻⁸ / (1×3)² ≈ 1097 kN. Halving the length quadruples the buckling load.
Tips
- Reducing the effective length (bracing, fixing the ends) is the most powerful way to raise buckling capacity.
- Buckling is independent of material strength — only stiffness (E·I) and length matter.
Frequently asked questions
Does the column always buckle at this load?
No — Euler's formula assumes a perfectly straight, slender, elastic column. Short or stocky columns yield or buckle inelastically at lower loads, and real columns have imperfections, so design codes reduce the capacity. Treat Pcr as an upper bound.
Which I should I use?
The smallest second moment of area (the weak axis), because the column buckles about whichever axis is least stiff unless it's braced.
Can I use these results for final design?
No. These calculators are for first-pass sizing, checking and learning. They assume ideal supports, static loads and elastic behaviour, and they don't apply load factors, member capacity, buckling or connection checks. Always verify against the relevant design code (e.g. AS 4100, AS 1170, Eurocode) and have a qualified engineer sign off structural work.
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Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.