Volume = length × width × thickness. In feet and inches that is length (ft) × width (ft) × thickness (in) ÷ 12 cubic feet, and dividing by 27 gives cubic yards. The extra percentage is added on top because forms are never perfectly level and some mix is always lost. Ready-mix trucks sell by the cubic yard (or cubic metre); for small jobs, premixed bags are easier. An 80 lb bag makes about 0.6 cu ft, a 60 lb bag about 0.45 cu ft and a 40 lb bag about 0.3 cu ft.
Example: a 10 × 10 ft patio slab 4 in thick is 100 × 4 ÷ 12 = 33.3 cu ft, or 1.23 cubic yards. With 10% extra that is 36.7 cu ft, or 62 bags of 80 lb concrete.
Four inches (10 cm) is the usual thickness for patios, walkways and shed bases. Driveways and garage floors are typically 5 to 6 inches (12 to 15 cm).
About 45 bags of 80 lb, 60 bags of 60 lb or 90 bags of 40 lb make one cubic yard (27 cu ft).
Yes, 5 to 10% extra is standard, because running short mid-pour causes cold joints. Ready-mix companies often have a minimum order, so check before you decide between bags and a truck.
See also: paint calculator · volume converter · square footage calculator
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Related: volume calculator for cylinders and other shapes.