# Beam Calculator

Beam bending formula, shear, moment, deflection plots for cantilevered beams and simply supported beams.

Select a Beam

Enter Dimensions and Calculate

Review Results
###### Shear ()
Extremes
Max Displacement @ @ @

This calculator is based on Euler-Bernoulli beam theory. The Euler-Bernoulli equation describes a relationship between beam deflection and applied external forces. The simplest form of this equation is as follows:

EI((d^4w)/dx^4)=q(x)

The Shear Force and Moment can be expressed, respectively, as:

Q=-EI((d^3w)/dx^3), M=-EI((d^2w)/dx^2)

The nice thing about this theory is that we can use these equations along with the boundary conditions and loads for our beams to derive closed-form solutions to the beam configurations shown on this page. The bending moment, shear force, slope and defelction diagrams are all calculated using the above equations.

Need more power?

Of course, it is not always possible (or practical) to derive a closed-form solution for some beam configurations. If you have a beam with complex boundary conditions and loads you're better off solving the problem numerically with the finite element method like this: Shear & Moment Calculator.