Boards are used as shelf decking. Each end rests on beams that have a 7/8" lip. We use 2x8", 2x10", and 2x12" pine boards of approximately 40" in length. I have not been able to locate a formula for pine laid flat. If anyone can point me in the right direction that would be helpful. Diagram below.
I recommend checking out the Sagulator.
You can use it to determine approximate load bearing capacity of almost any wood type for any span and weight. The Sagulator will report the expected deflection under a given load amount and type and will report whether it's considered acceptable or not. Of course, final judgement is up to you.
Do bear in mind that wood is a natural product and that no two boards will be exactly the same. I'd imagine that these are somewhat conservative numbers, but I haven't read all the fine print at their site to be sure of that.
You indicate 2" x 10" (or 12"). When plugging your numbers into the Sagulator, be sure to specify 1.5" by 9.5" or 11.25" if you're using standard dimensional framing lumber since that's sold as a "nominal" 2x10 or 2x12. You'll want the calculations to be based on actual lumber sizes.