By Zencalcy Editorial TeamLast reviewed About us
The slenderness ratio is a key parameter that separates buckling‑dominated behaviour (long columns) from crushing‑dominated behaviour (short columns). It is defined as λ = K L / r, where K is the effective length factor, L the column length and r the radius of gyration.
Non‑dimensional parameter for column stability.
λ = K L / r
r = √(I / A) is the radius of gyration, I the area moment of inertia and A the cross‑sectional area. λ² = π² E / σ_y separates long columns (Euler) from short columns (material yield).
| Symbol | Meaning |
|---|---|
| λ | Slenderness ratio. |
| K | Effective length factor. |
| L | Column length. |
| r | Radius of gyration. |
| I | Area moment of inertia. |
| A | Cross‑sectional area. |
r = √(1×10⁻⁶ / 1×10⁻⁴) = 0.1 m; λ = 1×2 / 0.1 = 20.
Continue with the Thin Cylinder Hoop Stress Calculator, Thin Cylinder Longitudinal Stress Calculator, or the Thin Spherical Pressure Vessel Stress Calculator — or browse more materials and elasticity tools and all physics calculators.
Values between 20 and 120 are common; > 120 are very slender and Euler buckling governs.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Content updated: September 2026