JML is correct that span tables are the way you figure the maximum span for a particular application. But you need to know the particular species of wood.
If you just want to compare the stiffness of two pieces of lumber with different cross-sections, you can do that by calculating and comparing the moments of inertia of their respective cross sections. (Assuming that the wood species is the same.) That's quite easy to do for most lumber. This Wikipedia article explains the theory; about halfway down you'll find the formulas for different cross sections.
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Today's Featured Article - New Life for an Old Allis - by Tyler Woods. My friend Jon, has an old '39 Allis Chalmers B. He thought it a marginal tractor that had long since served its time. She smoked terribly and never had much power but he couldn't afford another so he was limping along with what he had. Jon's Allis has a small front loader and though it doesn't carry much, it serves his needs. It was the hard starting and low power that made him think it was time to replace the old girl. Jon called me to help him discover why his tractor wouldn't start
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