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 moment of inertia (length^4)
  • L is the length

To calculate the critical load, multiply pi squared by the modulus of elasticity and the moment of inertia, then divide by the length squared.

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