About

Land area measurements in the US customary system rely on two primary units: the acre and the square mile. The relationship is exact: 1 sq mi = 640 acres. This factor derives from the original definition where 1 acre = 1 chain × 1 furlong (66 ft × 660 ft = 43,560 ft²), and 1 sq mi = 5,280² = 27,878,400 ft². Dividing gives exactly 640. Errors in this conversion appear in property deeds, zoning applications, and agricultural subsidy filings. A misplaced decimal can misrepresent parcel size by orders of magnitude.

This converter applies the exact integer ratio with no intermediate rounding. It handles both directions: acres to square miles and square miles to acres. Note: this tool uses the international acre (4,046.8564224 m²). The US survey acre differs by approximately 2 parts per million, which matters only for parcels exceeding 100,000 acres.

Formulas

The conversion between acres and square miles uses an exact integer relationship derived from the Public Land Survey System (PLSS). One section of land is defined as 1 mi × 1 mi = 640 acres.

A_{sq mi} = A_acres640

For the reverse conversion:

A_acres = A_{sq mi} × 640

Where A_acres is the area in acres and A_{sq mi} is the area in square miles. The factor 640 is exact. In metric equivalents: 1 acre = 4,046.8564224 m² and 1 sq mi = 2,589,988.110336 m². The ratio 2,589,988.1103364,046.8564224 = 640 exactly, confirming the integer relationship.

Reference Data

Acres	Square Miles	Square Feet	Square Meters	Hectares	Typical Use
0.25	0.000390625	10,890	1,011.71	0.1012	Residential lot
0.5	0.00078125	21,780	2,023.43	0.2023	Large suburban lot
1	0.0015625	43,560	4,046.86	0.4047	Standard acre reference
5	0.0078125	217,800	20,234.28	2.0234	Small farm plot
10	0.015625	435,600	40,468.56	4.0469	Hobby farm
40	0.0625	1,742,400	161,874.26	16.1874	Quarter-quarter section
80	0.125	3,484,800	323,748.51	32.3749	Half-quarter section
160	0.25	6,969,600	647,497.03	64.7497	Quarter section (homestead)
320	0.5	13,939,200	1,294,994.05	129.4994	Half section
640	1	27,878,400	2,589,988.11	258.9988	Full section (1 sq mi)
1,000	1.5625	43,560,000	4,046,856.42	404.6856	Large ranch parcel
1,280	2	55,756,800	5,179,976.22	517.9976	Two sections
2,560	4	111,513,600	10,359,952.43	1,035.9952	Half township row
5,000	7.8125	217,800,000	20,234,282.11	2,023.4282	Large agricultural estate
10,000	15.625	435,600,000	40,468,564.22	4,046.8564	Major landholding
23,040	36	-	-	-	Full township (6×6 mi)
50,000	78.125	-	-	-	Small national forest unit
100,000	156.25	-	-	-	County-scale parcel

Frequently Asked Questions

The factor 640 is definitional, not empirical. The US Public Land Survey System defined 1 section as 1 mile × 1 mile. One mile contains 80 chains (1 chain = 66 ft). One acre is 1 chain × 10 chains = 10 square chains. A section is 80 × 80 = 6,400 square chains = 640 acres. There is zero rounding involved.

The international acre uses the international foot (exactly 0.3048 m), giving 1 acre = 4,046.8564224 m². The US survey acre uses the US survey foot (1200/3937 m), giving 1 acre ≈ 4,046.872609874252 m². The difference is about 2 parts per million - roughly 0.01 m² per acre. For parcels under 100,000 acres this difference is negligible. Note: the US survey foot was officially deprecated in 2023 by NIST.

In the PLSS, a township is a 6 × 6 mile grid containing 36 sections. Each section is 640 acres (1 sq mi). A quarter section is 160 acres - the standard homestead unit under the Homestead Act of 1862. A quarter-quarter section is 40 acres, the smallest standard subdivision in federal land records.

Yes. Since the divisor is 640 = 2⁷ × 5, any acre value that is not a multiple of 640 and contains prime factors other than 2 and 5 will produce a terminating decimal in square miles. However, if you input an irrational or very long decimal, floating-point representation may introduce noise beyond the 15th significant digit. This tool formats results to avoid displaying such artifacts.

Multiply acres by 0.40468564224. Equivalently, 1 hectare ≈ 2.471053814671653 acres. This tool focuses on the acres ↔ square miles conversion, but the reference table above includes hectare equivalents for common values.

For parcels under roughly 10,000 square miles, treating the Earth as flat introduces errors below 0.01%. The 640 acres/sq mi factor assumes a Euclidean plane. For state-level or national-level areas, geodetic calculations using ellipsoidal models (e.g., WGS 84) are required. This converter assumes planar geometry, which is appropriate for virtually all real estate and agricultural applications.