Eulers Buckling Load Calculator

Eulers critical load (P_cr):

Youngs Modulus (E):

Second Moment of Area (I):

Length (L):

Column effective length factor (K):

How This Is Calculated

$$ P_{cr} = \frac{{\pi}^{2}EI}{(KL)^{2}}$$ where:

P_cr = Eulers critical load (N)

E = Youngs Modulus (N/m² or Pa)

I = Second moment of area of the columns cross section (mm⁴ or m⁴)

L = Length (m or cm)

K = Column effective length factor

Assumptions

The material behaves according to Hookes law, i.e. it is linearly elastic.
The column is perfectly straight with no initial imperfections.
The deflections of the column are small compared to its length when under load.
The column has a uniform cross-sectional area along its length.
The ends of the column are perfectly pinned.
The length is significantly greater than the columns cross-sectional area.
The load applied is purely axial and does not include bending moments or lateral forces.

Related Calculators

Engineer's Bening Moment Equation

Bending Stress

Uniformly Distributed Load