Column Buckling Load Calculator

Reviewed by the CalculatorHub team, edited by James Graham. Uses Euler's formula per AISC 360. Last verified 14 June 2026.

The Euler critical buckling load (Pcr) is the maximum axial compressive load a slender column can carry before it buckles laterally. This calculator uses Euler's column formula: Pcr = (pi squared times E times I) divided by Le squared. Enter the material modulus, cross-section moment of inertia, column length, and end condition to compute the theoretical critical load. Always apply an appropriate safety factor per your design code (AISC, Eurocode 3, or AS 4100) before using this value in a structural design.

Modulus of Elasticity, E (GPa) Steel: 200 GPa, Aluminium: 69 GPa, Timber: 10-14 GPa

Second Moment of Area, I (cm⁴) From section tables (e.g. W200x52 has I = 52,900 cm^4 about strong axis)

Column Length, L (m) Actual unsupported length of the column

End Condition, K Effective length factor per AISC Table C-A-7.1

Custom K value

Effective Length Le (m)

4.00 m

Critical Buckling Load Pcr (kN)

1,026.25 kN

Euler buckling formula

Pcr = (pi² × E × I) / Le²
Le = K × L

Where: E = modulus of elasticity (Pa), I = second moment of area (m⁴), Le = effective length (m), K = effective length factor, L = actual column length (m).

The result Pcr is the theoretical load at which an ideal elastic column becomes unstable. In practice, apply phi_c = 0.90 (LRFD) or divide by 1.67 (ASD) per AISC 360-22 Chapter E.

Effective length factors (K values)

K = 0.5: Both ends fully fixed against rotation and translation (ideal fixed-fixed).
K = 0.7: One end fixed, other end pinned (rotation restrained at one end).
K = 1.0: Both ends pinned (standard simply supported column).
K = 2.0: One end fixed, other end free (flagpole or cantilever column).
AISC recommends using K = 1.0 for most practical braced frame columns unless analysis supports a lower value.

Column buckling calculator: frequently asked questions

What is the Euler buckling load formula?

The Euler critical load is Pcr = (pi^2 * E * I) / Le^2, where E is the modulus of elasticity (Pa), I is the second moment of area (m^4), and Le is the effective length of the column (m). This formula applies to slender columns that buckle elastically before yielding.

What is the effective length of a column?

The effective length Le = K * L, where L is the actual column length and K is the effective length factor depending on the end conditions. K = 0.5 for fixed-fixed, K = 0.7 for fixed-pinned, K = 1.0 for pinned-pinned, and K = 2.0 for fixed-free (cantilever).

When does Euler buckling apply?

Euler buckling applies when the slenderness ratio Le/r exceeds a threshold where elastic buckling governs over material yielding. For steel, this is typically above a slenderness ratio of around 120. Below that threshold, inelastic buckling methods such as AISC column curves should be used.

What units should I use?

The calculator works in SI units. Enter the modulus of elasticity in GPa (converted to Pa internally), the moment of inertia in cm^4 (converted to m^4), and the column length in metres. The result is in kilonewtons (kN).

What is the safety factor for column buckling?

AISC LRFD uses a resistance factor phi_c = 0.90 for compression members. ASD uses a safety factor of 1.67. The calculator outputs the theoretical Euler load; divide by your chosen safety factor for a design value.

Official sources

AISC 360-22 Specification for Structural Steel Buildings, Chapter E (Compression Members): AISC 360-22.
NIST Engineering Laboratory: nist.gov/el.

Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.