Euler Critical Load Calculator

Transparent calculator for the Euler critical buckling load of a slender column, showing the equation, variables, substitution and result.

Buckling & Stability4 min read

bucklingcalculatoreulercritical loadcolumn

Equation

P_cr = pi^2 * E * I / L_e^2

where:
  P_cr = Euler critical load (N)
  E    = Young's modulus (Pa)
  I    = second moment of area about buckling axis (m^4)
  L_e  = effective length = K * L (m)
  K    = effective length factor
  L    = actual column length (m)

Variables

E — Young's modulus of the column material (Pa)
I — second moment of area about the governing (minimum) principal axis (m^4)
K — effective length factor depending on end conditions
L — unbraced column length (m)

Units

E in Pa (or N/m^2)
I in m^4
L and L_e in m
P_cr in N

Substitution example

For a steel column (E = 200 GPa) with I = 1.257 x 10^-8 m^4, L = 1.2 m, K = 1.0: L_e = 1.0 * 1.2 = 1.2 m P_cr = pi^2 * 200 x 10^9 * 1.257 x 10^-8 / (1.2)^2 = 17,231 N ≈ 17.2 kN

Result

The calculator outputs the Euler critical load P_cr in N and kN.

Assumptions

Perfectly straight column with no imperfections
Linear-elastic material behaviour
Centric loading (no eccentricity)
Small deformations (bifurcation)
Column is slender (slenderness ratio > transition slenderness)

Limitations

The Euler load is an upper bound — real columns buckle below this due to imperfections and residual stress
Not applicable to columns below the transition slenderness (use inelastic buckling method)
Not applicable to columns with local buckling of thin-walled sections
Does not account for load eccentricity or end flexibility
The effective length factor K must be chosen conservatively