Euler's formula for buckling?

P_cr = π²EI / (K L)² (K = effective length factor)

When to use Rankine vs Euler?

Euler: long slender columns. Rankine: intermediate columns.

Calculate critical buckling load using Euler's formula and Rankine-Gordon empirical formula. Supports all end conditions and slenderness ratios.

Critical Load

485 kN

Pinned-pinned, L=4m, I=5000 cm⁴

Featured: Euler • Rankine • End Conditions • Slenderness Ratio

End Conditions

Column Length L (m)

Young's Modulus E (GPa)

Min Moment of Inertia I (cm⁴)

Cross-Section Area A (cm²)

Yield Strength σ_y (MPa)

Applied Axial Load P (kN)

Euler (long) vs Rankine (intermediate)

P_cr = π² E I / (K L)²

1/P_cr = 1/P_c + 1/P_e
P_c = σ_y × A (crushing)

Enter column parameters to see results

Pinned-Pinned: K=1.0

Fixed-Fixed: K=0.5

Fixed-Pinned: K≈0.7

Fixed-Free: K=2.0

Short: λ < 80 → crushing

Intermediate: 80–120 → Rankine

Long: λ > 120 → Euler