About this tool Calculate the slenderness ratio (λ = Le/r) for columns and struts. Enter the actual length, select end conditions to determine the effective length, and choose a section type to calculate the radius of gyration.
Four section types are supported: circular solid, circular hollow, rectangular solid, and custom (enter radius of gyration directly). Four standard end conditions from fixed–fixed (k=0.5) to cantilever (k=2.0).
Results classify the column as short (λ ≤ 22, second-order effects negligible) or slender (λ > 22, second-order effects must be considered). Per BS EN 1992-1-1 (Eurocode 2) and BS EN 1993-1-1 (Eurocode 3).
How to use this tool 1. Enter the actual column length — clear height between restraints, in metres.
2. Select end conditions — this determines the effective length factor k.
3. Select section type and enter dimensions — or enter radius of gyration directly for non-standard sections.
Technical information λ = Le / r where Le = k × L
Effective length factors: Fixed–Fixed k=0.5, Fixed–Pinned k=0.7, Pinned–Pinned k=1.0, Cantilever k=2.0.
Radius of gyration: solid circle r=d/4, hollow circle r=√((OD²+ID²)/16), rectangle r=h/√12.
Limitations The λ ≤ 22 short column limit is a simplified approximation from EC2. The actual limit depends on end moments, axial load ratio, and creep — use the full EC2 method (5.8.3.1) for detailed design.
Effective length factors assume idealised end conditions. Real connections are rarely perfectly fixed or pinned — use engineering judgement or the EC2/EC3 nomograms for actual restraint conditions.
For steel columns to Eurocode 3, classification uses non-dimensional slenderness (λ̄) rather than λ directly. This tool gives the geometric slenderness as a first check.
Revision history 25 August 2026: Initial release
Disclaimer This tool is provided for educational and general information purposes only. It is not a substitute for professional engineering advice, design or verification.
Diggy and its contributors are not licensed engineering consultants and no results generated by this tool should be used directly for construction, design or safety-critical decisions.
All values and outputs are based on published empirical correlations and should be independently checked and confirmed by a qualified geotechnical engineer before use.
By using this tool, you accept full responsibility for how you interpret and apply the information provided.
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