Column Buckling (Euler)

A slender column does not crush — it suddenly bows sideways. See how end restraints and slenderness set the Euler critical load at which it buckles.

Column Buckling (Euler)Live

critical load & slenderness

Controls

Presets

Young's modulus E (GPa)

Moment of inertia I (10⁶ mm⁴)

Length L (m)

Cross-section area (mm²)

A slender column fails not by crushing but by buckling sideways at the Euler critical load Pcr = π²EI/(KL)². The effective-length factor K depends on the end restraints — fixing both ends quadruples the capacity versus pinned. Educational tool, not a substitute for code-based design.

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Data Inspector

Critical load Pcr2193 kN

Effective length3.00 m

Slenderness KL/r52

Critical stress731 MPa

Governing equation

P_{cr} = \frac{π ^{2} E I}{( K L ) ^{2}} = \frac{π ^{2} ( 200 GPa ) ( 10 \times 1 0 ^{6} mm ^{4} )}{( 1 \times 3 m ) ^{2}} = 2193 kN

Reading this result: Intermediate slenderness (KL/r = 52): buckling and yielding compete, so design codes blend the two rather than trusting Euler alone.

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How it works

Euler's formula gives the critical buckling load Pcr = π²EI/(KL)², where the effective-length factor K captures the end conditions. Fixing both ends quarters the effective length and quadruples capacity versus a pinned column. Slenderness KL/r decides whether buckling or material yielding governs. Educational tool, not a code-based design.

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Frequently asked questions

Is this Euler column buckling calculator tool really free?▾

Yes. Column Buckling (Euler) runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.

Do I need to install anything?▾

No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.

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How accurate are the results?▾

The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.