For every force a structure must have an opposing strength, or it will fail. The structure must also stand up to all forces at all times, so it must hold up the weight of the structure, the contents of the structure and other elements such as wind. Because it's impossible to know exactly how much force will be exerted from those combined forces -- engineers calculated a range, then add a margin of error, so the strength will always exceed the force. Much of their engineering work is available in the form of matrices for specific applications.
Things You'll Need
Detailed blueprints of your structure
Beam matrix or framing matrix
Obtain the pounds per lineal feet of load from an engineer. This calculation must be done with engineering expertise, either as a custom calculation, or a standardized calculation which apply to some applications, such as residential, stick-framed door, window and post-and-beam opening construction.
Look at a beam matrix, if you have engineering calculations indicating how much strength you need for a specific header. Custom lumber and beam manufacturers will make these matrices available. Find the beam dimensions that meet or exceed the strength of the load you need to support.
Look at a framing matrix, if you're building a typical wood-framed structure. One matrix may combine this information. Generally, in residential, wood-framed construction, common header functions have standardized sizes for any load that might apply within the scope of a residential building. For standard header framing, if you have an opening -- or span -- of X number of feet, the matrix will tell you what size it must be to support that size of span.
Choose the dimension that best fits your design -- whether you're building from custom calculations or a standard framing matrix. For example a header that is 3 1/2 inches and very deep, might support an equivalent load as a header that is 5 1/2 inches wide, but not quite as deep as the 3 1/2 inch header. These headers can be structurally equivalent, so you can choose which one best suits your plan. If you're hiding a header within an interior wall, you want its width to match the wall; if it's an thicker, exterior wall, you want the width to match that wall.
Some suppliers can help you size your beams, while creating a material list based on your drawings.
It's possible to size beams yourself for typical projects. For less common jobs, it's best to have an engineer not only provide the calculations, but specify the structural members as well.