Slenderness Ratio Calculator

Work out slenderness ratio instantly with clear inputs, formula shown and shareable results.

About Slenderness Ratio Calculator

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.

Formulas

Slenderness

lambda = K L / r

K: 1.0 pinned, 0.65 fixed, 2.0 cantilever

Euler stress

sigma cr = pi² E / lambda², E = 200,000 MPa for steel

Worked example

With the default values below, Slenderness Ratio Calculator returns Slenderness ratio of 77.78. Change any input above and every figure here is recalculated in your browser.

Inputs used

Unbraced lengthminimum 0.1 m: 3.5 m
Radius of gyrationminimum 1 mm: 45 mm
End restraintone of Pinned both ends — K = 1.0, Fixed both ends — K = 0.65, Cantilever — K = 2.0: Pinned both ends — K = 1.0

Results

Slenderness ratio: 77.78
Effective length: 3,500 mm
Euler buckling stress: 326.30 MPa
Column classification: Intermediate column — inelastic buckling governs

Step by step

1Values used
2Slenderness
3Euler stress
4Slenderness ratio= 77.78
5Effective length= 3,500 mm
6Euler buckling stress= 326.30 MPa
7Column classification= Intermediate column — inelastic buckling governs

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
Preliminary estimate only. Compression member design must be verified by a qualified structural engineer using the code buckling curves, not the Euler stress alone.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Preliminary estimate only. Compression member design must be verified by a qualified structural engineer using the code buckling curves, not the Euler stress alone.

Frequently Asked Questions

How is the Slenderness Ratio figure worked out?

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.

Which radius of gyration should I use?

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.

What values do I need to enter?

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.