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Slenderness Ratio Calculator

Radius of gyration, slenderness ratio λ = KL/r and Euler critical stress for a column.

INPUTS
m
×10⁶ mm⁴
mm²
GPa
RESULTS
Radius of gyration r = √(I/A)
82.5 mm
Slenderness ratio λ = KL/r
36.4
Euler critical stress σcr = π²E/λ²
1,492.9 MPa
Classification
Short column — material crushing governs, not buckling
50100150200250510025100025
Euler critical stress vs slendernessslenderness λσcr [MPa]
How it works

Slenderness λ = KL/r condenses column geometry into one number: effective length over radius of gyration. Below ~50 the material yields first; above ~120 elastic Euler buckling takes over; in between, real columns fail by inelastic buckling and codes interpolate with buckling curves. Since r = √(I/A), spreading area away from the axis (tubes, H-sections) is the direct way to cut slenderness.

Worked example

IPE 200 (I = 19.4×10⁶ mm⁴, A = 2850 mm²): r = √(19.4e6/2850) = 82.5 mm. Pinned 3 m column: λ = 3000/82.5 = 36.4 — a short column, so σcr = π²·200000/36.4² ≈ 1490 MPa far exceeds yield and crushing governs, not buckling.

Frequently asked questions

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