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The table the inspector checks, in three inputs.
Deck permits fail on footing size more than anything else, and the answer is a lookup, not a guess: tributary area per footing against soil bearing capacity in IRC Table R507.3.1. This calculator computes the tributary area (with the ledger-carries-half rule for attached decks) and interpolates the exact table — square or round, thickness included.
Deck builders use it at the permit counter: tributary area in, the exact IRC R507.3.1 footing size out — no more upsizing every pier to 24 inches out of habit. Homeowners use it to check a contractor's plan before the holes are dug, because undersized footings are invisible until the deck starts to lean.
Attached with 3 footings on the beam, each carries 192 ÷ 6 = 32 sq ft. On 1,500 psf soil that interpolates to a 14-inch square or 16-inch round footing, 6 inches thick; on 2,000 psf it drops to 12×12 or 14-inch round. Footings still go below the frost line regardless of size.
The share of deck surface one footing carries — measured to the midway point between that footing and the next bearing point on each side, including any cantilever. On a ledger-attached deck the house carries half the deck, so beam footings only split their half.
Tributary areas over 160 sq ft (extrapolation is not permitted), ground snow loads above 50 psf (the 60/70 psf rows govern instead), hot tubs and masonry kitchens (point loads need engineering), and soils below 1,500 psf bearing (a soils investigation is required).