c.1300, "tool for measuring right angles," from Old French esquire "a square, squareness," from Vulgar Latin *exquadra, from *exquadrare "to square," from Latin ex- "out" (see ex-) + quadrare "make square, set in order, complete" (see quadrant).
Meaning "rectangular shape or area" is recorded by late 14c.; replaced Old English feower-scyte. Sense of "open space in a town or park" is from 1680s. The mathematical sense of "a number multiplied by itself" is first recorded 1550s.