Euler Buckling Load Calculator
Reviewed by Hamza Gujjar, Algorithm Architect & Software Developer
Last updated: July 27, 2026Euler Buckling Load Calculator
Slender columns can suddenly buckle sideways under compressive load well before the material actually yields - this calculator applies Euler's classic buckling formula to find that critical failure load.
Pcr = (π² × E × I) / (K × L)²
End Condition Factor (K)
| End Condition | K |
|---|---|
| Fixed-Fixed | 0.5 |
| Fixed-Pinned | 0.7 |
| Pinned-Pinned | 1.0 |
| Fixed-Free (flagpole) | 2.0 |
Example
A steel column (E = 200 GPa, I = 8├ù10Ôü╗ÔüÀ mÔü┤), 3m long, pinned-pinned (K=1.0):
Critical Buckling Load ≈ 175.46 kN
Why End Conditions Matter So Dramatically
A fixed-free column - like a flagpole fixed at the base and free at the top - buckles at just 1/16th the load of an equivalent fixed-fixed column with identical material and dimensions, purely due to the end condition factor's squared appearance in the denominator (K=2.0 gives K²=4, versus K=0.5 giving K²=0.25, a 16x difference).