Compute Euler buckling load from material inputs fast. Select realistic end restraints and dimensions easily. Export clean reports for reviews, calculations, and documentation teams.
This tool uses the Euler critical buckling load for a slender, straight, elastic column:
Pcr = (π² · E · I) / (K · L)²
Real columns may buckle earlier due to imperfections or eccentricity.
| Case | E | L | End condition | Section inputs | Approx. Pcr |
|---|---|---|---|---|---|
| 1 | 200 GPa | 2 m | Fixed–Pinned (K=0.699) | Rectangle b=50 mm, h=100 mm, weak axis | ≈ 1052.07 kN |
| 2 | 70 GPa | 1.5 m | Pinned–Pinned (K=1.0) | Solid circle d=30 mm | ≈ 12.21 kN |
| 3 | 210 GPa | 3 m | Fixed–Fixed (K=0.5) | Tube Do=60 mm, Di=50 mm | ≈ 303.41 kN |
Values are rounded and assume ideal Euler behavior.
Column buckling is a geometric instability that can occur even when stresses are well below yield. For slender members, a small lateral disturbance can grow rapidly, causing a sudden loss of load-carrying capacity. The computed critical load helps you screen designs early and compare alternatives objectively.
This calculator uses Euler’s elastic buckling model for straight, prismatic columns. The method assumes linear elasticity, small deflections up to buckling, and an initially perfect member loaded concentrically. Because real columns have imperfections and eccentricity, practical design typically applies reduction factors or code-based curves.
End conditions strongly affect the effective length factor K. Common engineering values include pinned–pinned K=1.0, fixed–free (cantilever) K=2.0, fixed–pinned K≈0.699, and fixed–fixed K=0.5. A lower K shortens the effective length and increases the critical load.
The elastic modulus E sets how strongly the member resists bending during buckling. Typical values are about 200 GPa for structural steels, 69–70 GPa for aluminum alloys, and roughly 25–35 GPa for normal-weight concrete. Higher E increases buckling capacity linearly.
The second moment of area I controls stiffness about the axis that bows. For rectangles, buckling about the “weak” axis can reduce I sharply because I scales with the third power of the smaller dimension. For tubes, increasing outer diameter is effective because I scales approximately with diameter to the fourth power.
If you provide area A, the calculator reports radius of gyration r=√(I/A) and slenderness K·L/r. Larger slenderness indicates greater buckling sensitivity. Euler stress σcr=Pcr/A supports quick screening, but inelastic or local buckling can govern for stocky sections.
Euler load scales as Pcr ∝ E·I/(K·L)². Doubling the length reduces Pcr by a factor of four, while doubling I doubles Pcr. This strong 1/L² dependence makes bracing, intermediate supports, and end-fixity improvements powerful levers for increasing capacity.
Use the reported Pcr as an ideal elastic benchmark. For design decisions, consider crookedness, load eccentricity, connection flexibility, and code requirements. When results look marginal, improving end restraint, shortening unbraced length, or selecting a section with higher I about the governing axis is usually more effective than changing strength alone.
Euler theory is most reliable for slender columns that remain elastic up to buckling. If the member is stocky, inelastic buckling or crushing may control and code-based column curves are more appropriate.
K converts the actual length into an effective length that matches the end restraints. More restraint means a smaller K, a shorter effective length, and a higher critical load.
Elastic buckling is governed by stiffness, not yield strength. A high-strength material with the same E and geometry will buckle at nearly the same Euler load as a lower-strength material.
Use the axis about which the column is most likely to bend. If lateral support is similar in both directions, the weak axis usually governs because it has the smaller second moment of area.
No. A is optional, but it enables Euler stress and slenderness outputs. Those extra values help compare designs and check whether the member is in a slender regime.
Very sensitive. Because Pcr varies with 1/L², a 10% increase in unbraced length reduces critical load by about 19%. Shortening or bracing a column is highly effective.
Initial crookedness, eccentric loading, connection flexibility, residual stress, and local plate buckling can reduce capacity. Use the result as a baseline and apply appropriate safety or code reduction factors.
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.