How this instrument works
An acre began as a day's work rather than a shape: as much ground as one ploughman with a yoke of oxen could turn between dawn and dusk. Dimensions came later, from Edmund Gunter's surveying chain of 1620 — 66 feet, 100 links, 22 yards. Ten square chains make an acre, or 43,560 square feet, and that odd-looking total is simply 66 × 660: one chain wide by one furlong long, furlong meaning how far teams ploughed before turning.
A statute mile runs 80 chains. Multiply it by itself and you have 6,400 square chains; at ten square chains to an acre, each square mile contains 640 acres. No measurement enters into it — only arithmetic on definitions, since both units now descend from a foot fixed at 0.3048 m by treaty in 1959. Invert that count and every acre is 1⁄640 of one square mile, which decimal notation writes out cleanly as 0.0015625 because 640 factors into seven twos and one five.
That 640 is stamped across half a continent. Under America's Land Ordinance of 1785, surveyors cut public land into townships six miles square, each divided into 36 numbered sections of one square mile. Homestead quarter sections ran 160 acres, and farm talk's 'back forty' is one quarter of that quarter. Deeds, auction catalogues and wildfire bulletins still speak in acres; atlases, county gazetteers and population-density tables want square miles. Traffic between those two vocabularies is what this page handles.
- Type your parcel size into Acres (ac). It opens at 640 — one full survey section.
- Read Square miles (mi2) below, recalculated on every keystroke and shown to six decimals.
- Holding hectares, roods or chains? Convert to acres first — 1 ha is 2.471054 ac, and 4 roods make 1 ac — then enter that figure.
- Going back up from map figures, multiply square miles by 640 and type your result into Acres (ac) to confirm it round-trips.
Worked example — one full survey section
A county assessor lists 640 acres of Kansas cropland: one whole section, boxed in by gravel roads on all four sides. Type 640 into Acres (ac) and Square miles (mi2) returns 1.0 — not 0.999998, not a rounded 1. Nothing had to be approximated, because sections were platted at one square mile in 1785 and 640 acres is what that unit has always held.
Scaling works in both directions with equal cleanliness. That quarter section of 160 acres gives 0.25 mi², the back forty gives 0.0625 mi², and a 100,000-acre wildfire — big enough for national bulletins — comes out at 156.25 mi², an area you could sketch on any road map. Every one of those decimals stops rather than trailing off.
Questions
Is 640 acres per square mile exact or rounded?
Exact. Both units trace back to a single definition of the foot, so 27,878,400 square feet per square mile divided by 43,560 per acre leaves 640 with no remainder. Its reciprocal, 0.0015625, terminates for tidy reasons: 640 is 2⁷ × 5, and decimal notation absorbs factors of two and five without repeating. Converters displaying 0.001563 have merely truncated their screen value; nothing about 1⁄640 is uncertain.
Does the US survey acre change this answer?
No. The survey foot, retired by NIST at the end of 2022, ran about two parts per million longer than its international counterpart, putting a survey acre at roughly 4046.873 m² against 4046.8564224 m² for the international version. Survey square miles stretched by exactly that same proportion, though, so 640 survives untouched in either system. That two-ppm gap only bites where you cross into metric — never between acres and square miles.
Why is an acre 43,560 square feet?
Because it is one chain by one furlong. Gunter's chain, standardised around 1620, measures 66 feet; furlongs run ten chains, or 660 feet. Multiply and 43,560 square feet appears. Surveyors adopted that awkward-looking 66 precisely because it makes land arithmetic painless: ten square chains equal an acre, so fields noted in chains convert to acreage by shifting one decimal point instead of grinding through long division.
Does an acre have any fixed shape?
No, and this catches people out. An acre states a quantity of area, not a plot with fixed sides — one narrow riverside strip and one blocky upland paddock can both be exactly one acre. Forced into a square, it measures about 208.71 feet along each side. For that same reason 'square acres' means nothing: an acre is already an area, so writing ac² would multiply your parcel by itself and inflate it wildly.
What does one square mile come to in metric?
Exactly 2.589988110336 km², since a mile is exactly 1609.344 m. One acre is exactly 4046.8564224 m², slightly over 0.4 ha. So 640 ac, 1 mi², 259 ha and 2.59 km² all describe one piece of ground; which label appears on the deed usually reveals more about national paperwork than about any difference in land.
Are acres still legal for land in Britain?
For land registration, yes. Britain withdrew acres from general trade use in 1995, but HM Land Registry and farming practice kept them, and estate agents still advertise fields in acres alongside hectares. Watch old Irish paperwork: plantation acres covered 7,840 square yards against England's 4,840, so nineteenth-century deeds read as though they used statute measure understate that holding by roughly 38 percent.