The span of a beam is the distance over which the beam bears its load. Beam span depends on the size of the beam, the weight of the load and the species of tree from which the beam was cut. These factors are related according to a simple formula, which is valid as long as the load is distributed fairly uniformly along the length of the beam.
Look up the "fibre strength in bending" rating of the species of wood you will use for your beam. Call this F. These values are available in construction books and in various lumber industry publications. If you cannot find your F value, you can use F = 1000 as an estimate.
Determine the total load in pounds that will be supported by the beam. For example, if the beam runs along the middle of the house to support the second-story floor system, the beam needs to carry one-third of the total floor load. If the beam is supporting one side of a shed roof, say for a porch, the beam's load is one half of the total roof load.
Choose values for the breadth and depth of the beam in inches. Call these B and d. You can perform the calculation multiple times with different values for breadth and depth to determine how changes in the beam size affect the span.
Calculate the maximum span of the beam in feet according to the following formula: Span = (F * B * d^2)/(9 * Load).