Euler Buckling Load Calculator
Calculate the critical axial load at which a slender column buckles using Euler's formula.
Column Parameters
Steel ≈ 200 GPa | Aluminum ≈ 70 GPa | Wood ≈ 10 GPa
Enter column parameters on the left and click Calculate.
Critical Buckling Load (Pcr)
kN
= N
= lbf
Formula Breakdown
Pcr = π² × E × I / (K × L)²
E
I
L
K
KL (effective length)
KL/r (slenderness)
Note: KL/r < 100 — the column may be in the intermediate or short range where Euler's formula overestimates capacity. Consider an inelastic column formula (e.g. AISC or Johnson parabola) for final design.
This is the theoretical ideal load. Apply a safety factor of 2–4 for design. Euler's formula assumes a perfectly straight, centrally loaded column with no residual stresses.
Summary
Calculate the critical axial load at which a slender column buckles using Euler's formula.
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: 2026-06-10 ·
Reviewed by Nham Vu