One acre is exactly 43,560 square feet. The number looks arbitrary but is not: it is 66 feet multiplied by 660 feet, the chain by the furlong, and every part of it comes from medieval English ploughing practice.
About the units
The acre and the square foot sit at opposite ends of the same system. The square foot is the working unit for buildings; the acre is the working unit for land. The connection between them runs through the surveyor's chain, invented by Edmund Gunter in 1620 and 66 feet long, and the furlong, 660 feet or ten chains, which was the standard length of a ploughed furrow. One chain by one furlong is one acre, and ten square chains is the same thing. That 66-foot chain also explains why 80 chains make a mile and why 640 acres make a square mile.
The exact factor
The derivation is 66 × 660 = 43,560, exactly. Equivalently, 10 square chains, since a square chain is 4,356 ft². Useful related exact values: 640 acres to the square mile, 4,840 square yards to the acre, and 43,560 ÷ 9 = 4,840 confirming the two agree. For estimation, an acre is a bit over 43,000 ft², and a square acre is about 209 feet on a side.
Where you meet this conversion
American real estate and construction, where a listing gives lot size in acres and building size in square feet on the same page. Development density calculations — dwelling units per acre against floor area in square feet — require the conversion at every step. Agricultural equipment specifications quote coverage rates in acres per hour while working widths are in feet, so the arithmetic runs through this factor. Roofing, paving and landscaping quotes are priced per square foot against sites measured in acres.