What is Euler's buckling formula?

Pcr = π²EI / (KL)², where E is modulus of elasticity, I is least moment of inertia, L is unsupported length, and K is the effective length factor determined by end conditions.

What does the effective length factor K mean?

K adjusts the real column length to account for how the ends are restrained: pinned-pinned K=1.0, fixed-fixed K=0.5, fixed-pinned K=0.7, fixed-free (cantilever) K=2.0. A smaller K gives a higher buckling load.

When is Euler's formula valid?

Euler's formula applies only to elastic (long) columns. A common rule of thumb: it is valid when KL/r > 100 for steel. For short or intermediate columns, inelastic formulas (e.g. Johnson parabola) should be used instead.

What moment of inertia value should I use?

Always use the LEAST (minimum) moment of inertia of the cross-section, because buckling occurs about the weakest axis.

Does this account for imperfections or eccentricity?

No. Euler's formula is the ideal theoretical limit. Real designs apply a safety factor (typically 2–4) and may use design codes (AISC, Eurocode) that include imperfection corrections.

Euler Buckling Load Calculator

Calculate the critical axial load at which a slender column buckles using Euler's formula.

Column Parameters

Modulus of Elasticity (E)

Steel ≈ 200 GPa | Aluminum ≈ 70 GPa | Wood ≈ 10 GPa

Least Moment of Inertia (I)

Unsupported Length (L)

Radius of Gyration (r) — optional, for KL/r

End Conditions

Pinned – Pinned K = 1.0

Fixed – Fixed K = 0.5

Fixed – Pinned K = 0.7

Fixed – Free (Cantilever) K = 2.0

Enter column parameters on the left and click Calculate.

Summary

Euler's buckling formula determines the maximum axial compressive load a slender column can carry before it suddenly deflects sideways. The critical load depends on the material stiffness (E), cross-section moment of inertia (I), unsupported length (L), and end-fixity conditions (K). This tool solves Pcr = π²EI / (KL)² and reports the result in both newtons and kilonewtons alongside the effective slenderness ratio.

How it works

Enter the modulus of elasticity (E) for the column material.
Enter the least moment of inertia (I) of the cross-section.
Enter the unsupported column length (L).
Select the end-fixity condition to set the effective length factor K.
The calculator applies Euler's formula Pcr = π²EI / (KL)² and displays the critical load.
The effective slenderness ratio KL/r is also shown as a check against elastic buckling assumptions.

Use cases

Size steel wide-flange columns in multi-story frames.
Check aluminum extrusions used as compression struts in space frames.
Evaluate timber posts for axial-load capacity in wood construction.
Assess slenderness of scaffold tubes and shoring legs.
Verify compression chord members in roof trusses.
Screen preliminary column designs before running full FEA.

Frequently Asked Questions

Last updated: 2026-06-05 · Reviewed by Nham Vu