Euler & Johnson Buckling Calculator

Column buckling — automatically selects Euler (long column) or Johnson (intermediate column) based on slenderness ratio.

Elastic modulus E (GPa)Second moment of area I (mm⁴)Cross-section area A (mm²)Effective length L (mm)End-condition factor KYield strength Sy (MPa)Calculate

Equations

Euler: Pcr = π²EI/(KL)². Johnson: Pcr = A[Sy − Sy²(KL/r)²/(4π²E)], used when KL/r is below the critical slenderness ratio.

Assumptions

Ideal pin/fixed end conditions per K factor, initially straight column, elastic or Johnson-parabolic transition only.