Column Buckling Capacity Calculator

Work out column buckling capacity instantly with clear inputs, formula shown and shareable results.

About Column Buckling Capacity Calculator

A compression member fails either by crushing at the squash load, area times yield strength, or by buckling at the Euler load, pi² E I / Le², whichever is lower. Real columns fail below both because of initial curvature and residual stress, so a safety factor of about 1.67 is applied to the governing value.

Formulas

Euler load

Pcr = pi² E I / Le², with I = A r²

Capacity

Design capacity = min(Pcr, A fy) / 1.67

Worked example

With the default values below, Column Buckling Capacity Calculator returns Design compression capacity of 449.1. Change any input above and every figure here is recalculated in your browser.

Inputs used

Cross-sectional areaminimum 1 mm²: 3,000 mm²
Radius of gyrationminimum 1 mm: 45 mm
Effective lengthminimum 0.1 m: 3.5 m
Yield strengthminimum 10 MPa: 250 MPa

Results

Design compression capacity: 449.1 kN
Euler buckling load: 978.9 kN
Squash load: 750.0 kN
Slenderness ratio: 77.78

Step by step

1Values used
2Euler load
3Capacity
4Design compression capacity= 449.1 kN
5Euler buckling load= 978.9 kN
6Squash load= 750.0 kN
7Slenderness ratio= 77.78

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
Preliminary estimate only. Compression member design must be verified by a qualified structural engineer using the code buckling curves and section classification.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Preliminary estimate only. Compression member design must be verified by a qualified structural engineer using the code buckling curves and section classification.

Frequently Asked Questions

How is the Column Buckling Capacity figure worked out?

Pcr = pi² E I / Le², with I = A r². A compression member fails either by crushing at the squash load, area times yield strength, or by buckling at the Euler load, pi² E I / Le², whichever is lower.

Why do real columns fail below the Euler load?

Initial out-of-straightness, residual rolling stresses and load eccentricity all start bending before the theoretical critical load, which is why codes use empirical buckling curves rather than the Euler formula alone.

What values do I need to enter?

This calculator takes 4 inputs: Cross-sectional area, Radius of gyration, Effective length, Yield strength. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.