Enter the modulus of elasticity, the moment of inertia, and the length of the column into the calculator to determine the critical force/load.

Critical Force Formula

The following equation is used to calculate the Critical Force.

CL = (pi^2 * E * I) / L^2

  • Where CL is the critical load (force)
  • E is the modulus of elasticity (force/length^2)
  • I is the momentum of inertia (length^4)
  • L is the length

What is a Critical Force?


A critical force is a measure of the force required to buckle a column with a given modulus of elasticity, moment of inertia, and length.

How to Calculate Critical Force?

Example Problem:

The following example outlines the steps and information needed to calculate Critical Force.

First, determine the modulus of elasticity . In this example, the modulus of elasticity is found to be 500 lbf/in^2.

Next, determine the momentum of inertia. For this problem, the momentum of inertia is found to be 20 in^4.

Next, determine the length. In this case, the length is measured to be 5 in.

Finally, calculate the Critical Force using the formula above:

CL = (pi^2 * E * I) / L^2

CL = (3.14159^2 * 500 * 20) / 5^2

CL = 3947.83 lbf