I ran the span calculator again and found the following: At 20lbs psf live load and 10lbs psf dead load, which is considered an "attic" or ceiling joist spec, a #2 Doug Fir 2 x 10 spaced 16" OC will span 19' 7" which just makes it. That said, 2 x 10 x 20s run about $25 each at the local lumberyard, whereas 2 x 12 x 20s are about $28 each. Now that I'm only doing a loft over half of the barn (12' x 20' will be plenty of space), I only need 10 joists, so going with 2 x 10s over 2 x 12s will only save me $30. I get what you're saying though. The plan for the loft right now is just the crap that is clogging up the basement and closets-out of season clothes, seasonal decorations, baby stuff and toys that kid number one has outgrown that we'll need for kids two through ??? The really heavy stuff (tools and equipment) will stay on the ground floor.
attic or ceiling joist is not rated for storage. 10 lb psf is way to low, for a storage load 2x12 syp is only about 17 foot. better run those numbers again.
back to my suggestion above^^^^^^, have a qualified person run the loads and supply you with stamped drawings. You will save a lot of money in the long run and the building will stay standing.