Three methods, routed by size
The wrong way to compute a patch is to scale the room-size math down. A 1 square foot hole does not need a sheet of drywall, a 4.5 gallon pail of joint compound, a 250 foot roll of paper tape, and a pound of screws. That is what a linear scale-down gives you, and it is the reason most drywall patch calculators on the web are worthless. The fix is to route by method.
Mesh patch kit. Under a fist (roughly 0.25 square feet, a 6 by 6 inch hole or smaller). The fix is a self-adhesive aluminum mesh square with premixed compound in the same kit. $6 to $12 at any hardware store. Three coats of mud, sand, paint. Done in an afternoon. No sheet, no tape, no pail.
California patch. Fist to dinner plate (0.25 to 4 square feet). Also called a butterfly patch. Cut a scrap drywall piece slightly larger than the hole, score and peel the gypsum off the back to leave a paper flap on all four sides, slide the gypsum plug into the hole, glue the paper flap to the wall surface with mud. It floats on the paper, no backer strips, no framing. A 1 quart compound tub, a 75 foot mini tape roll, and a handful of screws are the entire shopping list.
Cut to studs. Bigger than 4 square feet. Cut back to the nearest studs on both sides of the opening, screw 1 by 3 pine furring strips across the existing studs as backers for the new piece, cut a fresh piece from a sheet, land it on the backers, tape and mud the four seams. Sheet math applies here. Compound and tape constants are different from the full-room calculator because a patch is almost entirely perimeter, not field.