What is the slenderness ratio formula?

The slenderness ratio is KL/r, where K is the effective length factor (determined by end conditions), L is the unbraced length of the column, and r is the minimum radius of gyration of the cross-section. A smaller r (weaker axis) governs design.

What is the AISC slenderness limit?

AISC 360 Section E2 recommends that KL/r should not exceed 200 for compression members. For tension members and braces, a preferred limit of 300 is used (not mandatory). Exceeding these limits does not mean automatic failure, but it signals that elastic buckling may control behavior.

What is the effective length factor K?

K adjusts the physical length for end conditions: 1.0 for pinned-pinned, 0.5 for fixed-fixed, 0.7 for fixed-pinned, and 2.0 for fixed-free (cantilever). In practice, theoretical K values are often increased to account for partial fixity and sway.

How do I find the radius of gyration r?

r = sqrt(I/A), where I is the moment of inertia about the weak axis and A is the cross-sectional area. For standard sections, r values are tabulated in the AISC Steel Construction Manual. Use the minimum r (weak-axis value) for the governing slenderness check.

What happens if KL/r exceeds 200?

The member is likely to buckle elastically before yielding. AISC recommends increasing the section size, reducing the unbraced length with intermediate bracing, or changing the end conditions to lower KL/r below 200.

Can I use this for timber or concrete columns?

The KL/r formula is general, but AISC limits apply only to steel. Timber design (NDS) uses Le/d or Le/r with different limits, and concrete columns use Le/r with ACI 318 criteria. The computed ratio from this tool can still be useful for comparison.

Slenderness Ratio Calculator

Enter column length, effective length factor K, and radius of gyration r to compute the slenderness ratio KL/r and check it against the AISC 300 limit.

Column Parameters

Units:

Unbraced Length L (m)

Distance between lateral support points.

End Condition

Min. Radius of Gyration r (mm)

Use the weak-axis r from section tables (governs buckling).

AISC Slenderness Limit

Enter column parameters and click Calculate.

Slenderness ratio and AISC check will appear here.

K Factor

—

dimensionless

Eff. Length KL

—

KL/r

—

slenderness ratio

Slenderness Gauge

0 Limit: 200 400

Calculation Breakdown

Unbraced length L —

Effective length factor K —

Effective length KL —

Radius of gyration r —

Slenderness ratio KL/r —

AISC limit applied —

Utilization ratio (KL/r) / limit —

Slenderness Classification Reference

KL/r Range	Classification	Behavior
< 60	Short / Stocky	Yielding governs — buckling unlikely
60 – 120	Intermediate	Inelastic buckling range
120 – 200	Long / Slender	Elastic (Euler) buckling governs
> 200	Exceeds Limit	Not recommended — redesign required

Summary

The slenderness ratio KL/r is the primary index used to classify structural columns as short, intermediate, or long (slender). It equals the effective unbraced length (K × L) divided by the minimum radius of gyration (r) of the cross-section. AISC 360 recommends limiting KL/r to 200 for compression members and 300 for tension or brace members. A higher ratio means more susceptibility to elastic buckling before the material reaches its yield strength.

How it works

Enter the unbraced column length L in meters or feet.
Select the end-condition to set the effective length factor K (or enter a custom K value).
Enter the minimum radius of gyration r of the cross-section in mm or inches.
The calculator computes the effective length KL and the slenderness ratio KL/r.
Results are checked against the AISC 360 recommended limit of 200 for compression members.
A color-coded status shows whether the member is within acceptable limits.

Use cases

Preliminary design check for steel columns under axial compression.
Verifying that bracing members meet AISC slenderness limits.
Comparing slenderness across different section sizes or lengths.
Structural engineering coursework and exam practice.
Quick screening before running a full buckling analysis.
Checking both SI and imperial unit systems side by side.

Frequently Asked Questions

Last updated: 2026-05-28 · Reviewed by Nham Vu