Column Buckling Calculator (Euler and Johnson)

Your details

Switches length and force units across all inputs and outputs.
How the column ends are restrained. This determines the effective-length factor K.
Actual unsupported length of the column.
mm
Second moment of area about the weak axis. For a 100x100 mm square: I = 100^4 / 12 = 8,333,333 mm^4.
mm⁴
Total cross-sectional area of the column. Used to compute radius of gyration and Johnson formula.
mm²
Select a preset material or choose Custom to enter your own E and yield stress.
The allowable load is the critical load divided by this factor. Typical structural design uses 2 to 4.
Critical buckling load (Pcr)Slender column - Euler governs
411.23

The axial load at which the column buckles (Euler or Johnson formula applied automatically).

Pcr unitkN
Allowable load (Pa)137.08
Slenderness ratio (S)219.1
Critical slenderness ratio (Sc)125.7
Radius of gyration (r)9.129
Effective length (Le)2,000
Formula usedEuler
Column classSlender (long column)
219.1
Very short strut<10Intermediate (Johnson)10-80Slender (Euler)80-160Very slender160+

Critical buckling load: 411.23 kN (Euler formula, Slender (long column)).

  • The Euler formula was applied because the slenderness ratio (219.1) is above the critical slenderness ratio (125.7).
  • At the critical load of 411.23 kN, the column will suddenly deflect sideways. Any load beyond this is unsafe regardless of material strength.
  • The allowable load (137.08 kN) already includes your safety factor of 3. Keep the applied load below this value.

Next stepTo increase the critical load, consider increasing I (wider or thicker section), reducing the unsupported length, or adding intermediate bracing to change the effective length.

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