Every joist, beam, post, and footing collects load from a defined slice of the structure around it, and that slice is its tributary area. For a deck post the recipe is concrete: the beam picks up half the joist span (the other half goes to the ledger or opposite support) plus the full cantilever hanging past it, and that tributary width multiplied by the post spacing gives the area one post carries. Joists spanning 12 ft with no cantilever and posts 6 ft apart put 12/2 × 6 = 36 square feet on each post.
Multiply the tributary area by the design pressure and the member load falls out — at the IRC deck basis of 40 psf live plus 10 psf dead, those 36 square feet become an 1800 lb post load. The footing is then sized by dividing that load by the allowable soil bearing pressure: 1800 lb over 1500 psf soil demands 1.2 sq ft of bearing, a 15 in round or 14 in square footing. The cantilever matters more than it looks — joists may overhang the beam by up to a quarter of their span, and that overhung strip is added to the tributary width, not shared with any other support.