Load ÷ soil = footing
The footing spreads your deck's weight over soil that can hold it. Spans in, required pier diameter out — with the soil doing the deciding.
Load basis: 50 psf (40 live + 10 dead), the standard deck design load. Heavy snow country and hot tubs run higher — check with your local building department. Verify soil class locally; a soil that fails a shovel test fails a footing too.
The other half is depth: the footing bottom goes below your frost line, on undisturbed soil, or the freeze lifts the whole works. Look up your state's line, then figure the concrete with the sonotube calculator once you know diameter and depth.
The load basis here is the standard 40 psf live + 10 psf dead. It covers people, furniture, and the deck itself — not hot tubs, not roofs, and not the snow belt's worst. Those cases go to your building department first, calculator second.
Enough bearing area that the soil under it doesn't give. Tributary area × 50 psf ÷ soil bearing value = required area; as a round pier that's typically 10–18″ diameter for backyard decks, with clay soils demanding the big end. The calculator above turns your spans into the number.
The patch of deck one footing actually carries: half the joist span (the ledger carries the other half) times the post spacing along the beam. A 12 ft joist span with posts 8 ft apart puts 48 square feet on each footing.
You mostly don't, without asking. The code's presumptive values — 1,500 psf for clays, 2,000 for sands, 3,000 for gravels — are the safe floor, and your building department knows the local soil. When unsure, pick the weakest class; a bigger footing is cheap insurance.
Hot tubs, roof loads, tall posts, heavy snow country, or soil that stays wet. If the calculator pushes past common form-tube sizes, that's the site telling you to make the call.