The math
Area is length × width. A square mile has sides of 5,280 ft, so its area is 5,280 × 5,280 = 27,878,400 sq ft. Divide by 43,560 (the number of sq ft in an acre) and you get exactly 640 acres — which is why U.S. land surveys divide townships into 36 one‑square‑mile sections of 640 acres each.