Work out slenderness ratio instantly with clear inputs, formula shown and shareable results.
Slenderness ratio is effective length divided by the radius of gyration about the axis considered, with effective length set by end restraint. It determines whether a compression member fails by yielding or by buckling: the Euler stress, pi² E / lambda², falls with the square of slenderness and is the elastic buckling limit.
Slenderness
lambda = K L / r
Euler stress
sigma cr = pi² E / lambda², E = 200,000 MPa for steel
Preliminary estimate only. Compression member design must be verified by a qualified structural engineer using the code buckling curves, not the Euler stress alone.
lambda = K L / r. Slenderness ratio is effective length divided by the radius of gyration about the axis considered, with effective length set by end restraint.
The smallest one available on the unbraced length being considered, because buckling occurs about the weakest axis. Bracing in one plane can change which axis governs.
This calculator takes 3 inputs: Unbraced length, Radius of gyration, End restraint. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.