Assess buckling risk using K-factor, length, and gyration radius. Compare axes, estimate Euler stress, and export clear reports. Built for contractors and site engineers.
| Case | Length | K | Section | r used (mm) | λ |
|---|---|---|---|---|---|
| 1 | 3.0 m | 1.0 | 300×300 mm rectangle | 86.603 | 34.641 |
| 2 | 4.0 m | 1.0 | Solid circle d=200 mm | 50.000 | 80.000 |
| 3 | 6.0 m | 2.0 | Hollow circle D=273, d=219 mm | 86.031 | 139.463 |
λ = (K · L) / r
Fe = π²E / λ² estimates Euler elastic buckling stress.
Pcr = π²EI / (K·L)² estimates Euler critical load when I is known.
Slenderness ratio helps you judge whether a compression member is likely to fail by buckling before its material strength is reached. On construction sites, temporary bracing and imperfect alignment can raise effective length, increasing risk.
The factor K converts your physical length into an effective length that reflects end conditions. A well-restrained frame can approach K=0.5, while cantilevered conditions may approach K=2.0. Field bracing quality often decides where you land.
Radius of gyration r summarizes how the section’s area is distributed about an axis. A larger r means the section resists buckling better for the same length. Sections with thin walls can have good area but low stiffness if material is far from the governing axis.
Most columns buckle about the weaker (smaller r) axis. That is why this calculator can use the minimum radius automatically. If you have Ix and Iy, you can check either axis to match your detailing and bracing direction.
Many practical building columns fall between λ≈30 and λ≈120, depending on height, bracing bays, and section type\. Lower values generally behave more “stocky,” while higher values become more buckling\-sensitive and demand tighter alignment control\. For steel columns, increasing r by selecting a shape with thicker flanges can reduce λ noticeably; for concrete members, adding lateral ties and reducing spacing improves effective restraint during placement and curing\.
Euler stress Fe = π²E/λ² is an ideal elastic buckling estimate. It is not a complete design check because real members have imperfections, residual stresses, and inelastic behavior. Still, Fe is valuable for comparing alternatives and seeing the effect of length or section changes.
To reduce λ, you can shorten the unbraced length with intermediate ties, increase stiffness using a section with larger r, or improve end restraints to reduce K. Even small bracing changes can make a measurable difference to buckling margins.
Codes and design standards apply additional reduction factors, resistance equations, and capacity checks that depend on material, connection behavior, and load combinations. Use this tool to organize inputs and run fast comparisons, then complete the formal check using your governing standard.
It compares effective length to a section’s radius of gyration. Higher values generally mean higher buckling sensitivity and greater need for bracing and alignment control.
Use the smaller radius for conservative buckling checks. If your bracing prevents buckling in one direction, you may check the relevant axis explicitly.
K depends on end restraint and frame behavior. As a quick guide, pinned-pinned often uses 1.0, fixed-fixed about 0.5, fixed-pinned about 0.7, and cantilever about 2.0.
Pcr needs the second moment of area I about the governing axis. If you only provide r directly, I may be unknown, so the calculator provides stress Fe and λ instead.
No. It provides slenderness and Euler reference values. Final design should follow your project code, including strength reduction, load combinations, and detailing requirements.
Yes. Choose meters, millimeters, centimeters, inches, or feet for length. Internally the tool converts everything to millimeters for consistent calculations.
Unsupported length and the radius of gyration have the strongest influence. Improving bracing to reduce L or selecting a stiffer section to increase r usually lowers λ effectively.
Use results responsibly; confirm codes with your engineer always.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.