Slenderness Ratio Calculator — Column Buckling (KL/r)

Formula

How this is calculated

The slenderness ratio λ = KL/r compares a column's effective length KL to its least radius of gyration r. A larger λ means the column is more slender and therefore more susceptible to buckling at a lower load. The effective length KL accounts for the end conditions: a fixed-fixed column (K = 0.5) is much stiffer than a cantilever (K = 2.0) of the same physical length. The radius of gyration r = √(I/A) is computed from the section's second moment of area I and cross-sectional area A about its weak axis.

The AISC Steel Construction Manual (latest edition) sets a recommended maximum slenderness ratio of 200 for compression members. Below λ ≈ 50, a column is considered short and fails primarily by material yielding or crushing; between 50 and ~120 the failure mode is inelastic buckling (Johnson parabola range); above ~120 the column is long enough that elastic Euler buckling dominates, and critical stress drops with λ². This calculator computes λ only — critical buckling stress additionally depends on material yield strength (F_y), Young's modulus (E) and the applicable code equation.

Note: all dimensions are entered in millimetres and all results are in consistent SI units. The effective length factor K values listed follow AISC theoretical and recommended design values; actual K may differ if the assumption of perfectly rigid or perfectly pinned connections is not met in practice.