Square Mile (mi²) - Unit Information & Conversion

Quick Answer

What is a Square Mile? A square mile (mi²) is the area of a square with sides exactly 1 mile (5,280 feet) long. It's the standard unit for measuring large areas in the US and some Commonwealth countries.

Quick Conversions:

• 1 mi² = 640 acres (exactly)
• 1 mi² = 27,878,400 square feet (ft²)
• 1 mi² = 3,097,600 square yards (yd²)
• 1 mi² = 2.59 square kilometers (km²)
• 1 mi² = 259 hectares (ha)

Who Uses It?

• US government (geographical statistics, census data)
• Geographers (measuring cities, states, countries)
• Urban planners (city area calculations)
• Land surveyors (US Public Land Survey System)

Quick Comparison Table

Square Mile Size References

Square Miles	Acres	Square Kilometers	Typical Example
0.5 mi²	320 acres	1.29 km²	Small town
1 mi²	640 acres	2.59 km²	Standard section (PLSS)
2 mi²	1,280 acres	5.18 km²	Medium town
10 mi²	6,400 acres	25.9 km²	Large town/small city
50 mi²	32,000 acres	129.5 km²	Mid-size city
100 mi²	64,000 acres	259 km²	Large city
300 mi²	192,000 acres	777 km²	Major metropolitan area
500 mi²	320,000 acres	1,295 km²	Large metropolitan region
1,000 mi²	640,000 acres	2,590 km²	Small US state equivalent
10,000 mi²	6.4 million acres	25,900 km²	Medium US state

US City Areas (for Reference)

City	Area (mi²)	Area (km²)	Population Density
New York City	302 mi²	783 km²	29,300/mi²
Los Angeles	503 mi²	1,302 km²	8,300/mi²
Chicago	234 mi²	606 km²	11,900/mi²
Houston	670 mi²	1,735 km²	3,600/mi²
Phoenix	518 mi²	1,342 km²	3,200/mi²
Philadelphia	142 mi²	368 km²	11,800/mi²
San Antonio	505 mi²	1,308 km²	3,200/mi²
San Diego	372 mi²	964 km²	4,400/mi²
San Francisco	47 mi²	122 km²	18,600/mi²
Washington DC	68 mi²	177 km²	11,200/mi²

Definition and Standards

Mathematical Definition

The square mile (symbol: mi², alternative: sq mi) is a unit of area in the Imperial and US Customary systems, defined as:

The area of a square whose sides each measure exactly one statute mile in length.

Formula: $$ 1 \text{ mi}^2 = 1 \text{ mile} \times 1 \text{ mile} $$

Fundamental Relationships

Within the Imperial/US System:

• 1 mile = 5,280 feet (ft) = 1,760 yards (yd)
• 1 mi² = (5,280 ft)² = 27,878,400 ft²
• 1 mi² = (1,760 yd)² = 3,097,600 yd²
• 1 mi² = 640 acres (fundamental definition)

The 640-Acre Relationship: This is not arbitrary. The US survey system was designed so that:

• 1 section = 1 square mile = 640 acres
• ½ section = 320 acres
• ¼ section = 160 acres (historically a "homestead" size)
• ⅛ section = 80 acres
• 1/16 section = 40 acres

Metric Conversions (Exact):

Based on the 1959 International Yard and Pound Agreement:

• 1 mile = 1.609344 kilometers (exactly)
• 1 mi² = (1.609344 km)² = 2.58998811033 6 km²

Practical Metric Conversions:

• 1 mi² ≈ 2.59 km² (rounded)
• 1 mi² = 258.999 hectares ≈ 259 ha
• 1 mi² = 2,589,988 square meters

Visual Representation

A perfect square mile:

• Each side: 5,280 feet = 1.609 km
• Perimeter: 4 miles = 21,120 feet = 6.44 km
• Diagonal: 1.414 miles = 7,470 feet = 2.28 km

How big is it?

• About 505 soccer fields (FIFA regulation)
• About 484 American football fields (including end zones)
• About 1,280 city blocks (assuming 200 ft × 200 ft blocks)
• A 10-minute walk from one side to the opposite side

History and Evolution

The Roman Mile (Ancient Origins)

The word "mile" comes from the Latin "mille passus" (thousand paces).

Roman Definition:

• 1 pace (passus) = 2 steps = 5 Roman feet (pes)
• 1,000 paces = 5,000 Roman feet = 1 Roman mile
• 1 Roman mile ≈ 4,850 modern feet (about 1,480 meters)

Roman Land Measurement:

• Romans used the jugerum (about 2/3 acre) for agricultural land
• Centuriation: land divided into square grids for colonial settlements
• This grid system influenced later European land survey methods

Medieval England: Mile Chaos (500-1500 AD)

Multiple "Miles" Existed Simultaneously:

• Old London Mile: 5,000 feet
• Irish Mile: 6,720 feet (2.048 km)
• Scottish Mile: 5,952 feet (1.814 km)
• Various local miles: ranged from 4,800 to 7,000 feet

Why the confusion?

• Different regions had different "feet" lengths
• Local lords defined their own measurement standards
• Trade and legal disputes were common

The Statute Mile (1593)

Queen Elizabeth I's Parliament (1593):

• Standardized the statute mile at exactly 5,280 feet
• Made it the official measurement for England
• Named "statute" because it was defined by statute (law)

Why 5,280 feet?

• 1 mile = 8 furlongs (furlong = 660 feet, used in agriculture)
• 1 furlong = 10 chains (chain = 66 feet, standard surveyor's chain)
• This made conversions between agricultural measures convenient

Square Mile Standardization:

• As the statute mile was defined, the square mile naturally followed
• 1 mi² = 640 acres (this relationship was crucial for land sales)

British Empire and Colonial Land Surveys (1600s-1800s)

Square Mile in Colonial Administration:

• Used throughout British Empire for measuring:
  • Colonial territories
  • Land grants to settlers
  • Administrative districts
  • Natural resources (forests, mining claims)

Challenges:

• Early surveys often inaccurate (limited technology)
• Terrain (mountains, rivers) made perfect square miles impossible
• Native land claims conflicted with colonial grid systems

US Public Land Survey System (1785)

The Land Ordinance of 1785:

Perhaps the most important application of the square mile in history.

Problem: The newly independent United States owned vast unsurveyed western territories (Northwest Territory: modern Ohio, Indiana, Illinois, Michigan, Wisconsin, and part of Minnesota).

Solution: Congress passed the Land Ordinance of 1785, creating a systematic survey grid.

The System:

Township: 6 miles × 6 miles = 36 square miles

• Divided into 36 sections
• Each section numbered 1-36 (specific numbering pattern)

Section: 1 mile × 1 mile = 1 square mile = 640 acres

• The fundamental unit of sale
• Could be subdivided: half-section (320 ac), quarter-section (160 ac), etc.

Quarter-Section: ½ mile × ½ mile = 160 acres

• Became the standard homestead size (Homestead Act of 1862)
• Considered sufficient for a family farm

Impact:

• Surveyed over 1.5 billion acres (2.3 million square miles)
• Used in 30 US states (primarily west of the Ohio River)
• Created the rectangular field patterns visible from aircraft today
• Property descriptions still use this system: "SW¼ of Section 12, Township 3N, Range 4W"

States Using PLSS: Alabama, Alaska, Arizona, Arkansas, California, Colorado, Florida, Idaho, Illinois, Indiana, Iowa, Kansas, Louisiana, Michigan, Minnesota, Mississippi, Missouri, Montana, Nebraska, Nevada, New Mexico, North Dakota, Ohio, Oklahoma, Oregon, South Dakota, Utah, Washington, Wisconsin, Wyoming

States NOT Using PLSS (Original 13 colonies plus Texas, Hawaii, Kentucky, Tennessee, Vermont, West Virginia): These states used metes and bounds surveying (descriptive: "from the oak tree to the creek to the stone wall...").

International Yard Agreement (1959)

Standardization of the Yard/Foot/Mile:

• US, UK, Canada, Australia, New Zealand, South Africa agreed
• 1 yard = 0.9144 meters (exactly)
• 1 foot = 0.3048 meters (exactly)
• 1 mile = 1.609344 kilometers (exactly)
• 1 square mile = 2.589988110336 km² (exactly)

Why This Mattered:

• International scientific cooperation required consistent units
• Engineering projects crossing borders needed standards
• Eliminated minor differences between US and UK definitions

US Survey Foot Exception:

• US kept the "US survey foot" (1 ft = 1200/3937 m) for existing land records
• Difference: 2 parts per million (0.0002%)
• Matters for large-scale surveys spanning many miles
• Most states switched to international foot by 2023

Modern Era: Metrication and Persistence (1960-Present)

Global Metrication:

• 1965: UK began metrication (Ordnance Survey switched to km²)
• 1970: Canada officially metricated
• 1975: Australia completed metrication
• 1985: New Zealand fully metricated

US Resistance:

• Metric Conversion Act (1975): voluntary metrication—failed
• Square mile remains standard for US geography, census, planning
• All US atlases, maps, and official statistics use square miles
• Real estate still uses acres and square feet

Current Usage:

• United States: Exclusive standard for geographical areas
• United Kingdom: Mixed use (km² official, mi² still common)
• Canada: km² official, mi² understood by older generations
• Myanmar: Uses square mile
• Liberia: Uses square mile

International Organizations:

• UN, WHO, World Bank: use km²
• US Census Bureau: uses mi²
• CIA World Factbook: provides both mi² and km²

Real-World Examples and Applications

Country and State Areas

US States (Selected):

Smallest States:

• Rhode Island: 1,214 mi² (3,144 km²)
• Delaware: 2,489 mi² (6,446 km²)
• Connecticut: 5,543 mi² (14,357 km²)
• New Jersey: 8,723 mi² (22,592 km²)
• New Hampshire: 9,349 mi² (24,214 km²)

Mid-Size States:

• Ohio: 44,826 mi² (116,098 km²)
• Pennsylvania: 46,054 mi² (119,280 km²)
• Virginia: 42,775 mi² (110,787 km²)
• Tennessee: 42,144 mi² (109,153 km²)
• Kentucky: 40,408 mi² (104,656 km²)

Largest States:

• Alaska: 665,384 mi² (1,723,337 km²) — by far the largest
• Texas: 268,596 mi² (695,662 km²)
• California: 163,695 mi² (423,967 km²)
• Montana: 147,040 mi² (380,831 km²)
• New Mexico: 121,590 mi² (314,917 km²)

Comparisons:

• Alaska is larger than Texas, California, and Montana combined
• Rhode Island would fit into Alaska 548 times
• All of New England (6 states) = 71,992 mi² (smaller than Kansas)

Selected Countries (for comparison):

• Singapore: 280 mi² (725 km²) — smaller than New York City
• Andorra: 181 mi² (468 km²)
• United Kingdom: 94,060 mi² (243,610 km²)
• Japan: 145,937 mi² (377,975 km²)
• Germany: 137,988 mi² (357,386 km²)
• France: 248,573 mi² (643,801 km²)
• Ukraine: 233,062 mi² (603,628 km²)
• Canada: 3,855,100 mi² (9,984,670 km²) — 2nd largest country
• United States: 3,796,742 mi² (9,833,520 km²) — 3rd largest country
• China: 3,705,407 mi² (9,596,961 km²) — 4th largest country
• Russia: 6,612,100 mi² (17,098,242 km²) — largest country

Metropolitan Areas and Cities

Major US Metropolitan Areas:

• New York Metropolitan Area: ~13,318 mi² (34,493 km²)

  • Population: ~20 million
  • Density: ~1,500 people/mi²
  • Includes NYC, Long Island, parts of NY, NJ, CT, PA

• Los Angeles Metropolitan Area: ~33,954 mi² (87,940 km²)

  • Population: ~18.7 million
  • Density: ~550 people/mi²
  • Includes LA County, Orange County, Riverside, San Bernardino, Ventura

• Chicago Metropolitan Area: ~10,874 mi² (28,163 km²)

  • Population: ~9.5 million
  • Density: ~870 people/mi²
  • Includes Cook County and surrounding counties in IL, IN, WI

City Proper vs Metropolitan Area:

Dallas:

• City proper: 385 mi² (997 km²)
• Metropolitan area (DFW): 9,286 mi² (24,051 km²)
• 24× larger metropolitan area

Miami:

• City proper: 56 mi² (145 km²)
• Metropolitan area: 6,137 mi² (15,890 km²)
• 110× larger metropolitan area

National Parks and Reserves

Major US National Parks:

• Wrangell-St. Elias (Alaska): 13,175 mi² (34,123 km²) — largest US national park, larger than Maryland
• Gates of the Arctic (Alaska): 8,472 mi² (21,942 km²)
• Denali (Alaska): 6,045 mi² (15,656 km²) — larger than Connecticut
• Death Valley (CA/NV): 5,270 mi² (13,650 km²)
• Glacier Bay (Alaska): 5,130 mi² (13,287 km²)
• Yellowstone (WY/MT/ID): 3,472 mi² (8,991 km²) — first national park (1872)
• Everglades (FL): 2,357 mi² (6,105 km²)
• Grand Canyon (AZ): 1,904 mi² (4,931 km²)
• Yosemite (CA): 1,189 mi² (3,080 km²)
• Zion (UT): 229 mi² (593 km²)

State Parks:

• Adirondack Park (NY): 9,375 mi² (24,281 km²) — larger than many national parks

Bodies of Water

Great Lakes (US/Canada):

• Lake Superior: 31,700 mi² (82,100 km²) — largest freshwater lake by surface area
• Lake Huron: 23,000 mi² (59,600 km²)
• Lake Michigan: 22,300 mi² (57,800 km²) — entirely within US
• Lake Erie: 9,910 mi² (25,667 km²)
• Lake Ontario: 7,340 mi² (19,010 km²)
• Total Great Lakes: 94,250 mi² (244,106 km²)

Other Major US Lakes:

• Great Salt Lake (UT): 1,700 mi² (4,400 km²) — varies with water level
• Lake of the Woods (MN/Canada): 1,679 mi² (4,350 km²)
• Lake Okeechobee (FL): 730 mi² (1,900 km²)
• Lake Pontchartrain (LA): 630 mi² (1,630 km²)

Comparison:

• Lake Superior is larger than South Carolina (32,020 mi²)
• All five Great Lakes combined: larger than UK

Population Density

US Population Density by State (People per square mile):

Highest Density:

• New Jersey: 1,263/mi² (most dense state)
• Rhode Island: 1,061/mi²
• Massachusetts: 901/mi²
• Connecticut: 746/mi²
• Maryland: 636/mi²
• Delaware: 508/mi²
• New York: 421/mi²

Lowest Density:

• Alaska: 1.3/mi² (least dense state)
• Wyoming: 5.9/mi²
• Montana: 7.5/mi²
• North Dakota: 11.0/mi²
• South Dakota: 11.9/mi²

US Average: ~94 people/mi² (36/km²)

International Comparisons:

• Monaco: 47,000/mi² (world's densest country)
• Singapore: 21,000/mi²
• Hong Kong: 17,500/mi²
• Bangladesh: 3,000/mi²
• India: 1,200/mi²
• China: 390/mi²
• Germany: 611/mi²
• UK: 725/mi²
• Canada: 11/mi²
• Australia: 8.7/mi²
• Mongolia: 5.3/mi² (least dense country)

Common Uses Across Industries

1. Government and Census

US Census Bureau:

• Reports all geographic areas in square miles
• Population density: people per mi²
• Urban area definitions based on mi² thresholds
• Metropolitan Statistical Areas (MSAs) measured in mi²

Land Management:

• Bureau of Land Management (BLM): 247 million acres = 386,000 mi²
• US Forest Service: 193 million acres = 302,000 mi²
• National Park Service: 84 million acres = 131,000 mi²

2. Geography and Cartography

Map Making:

• US Geological Survey (USGS) maps use mi²
• Topographic maps scale in miles
• GIS software in US defaults to square miles

Geographic Information Systems (GIS):

• Area calculations reported in mi² for US audiences
• Spatial analysis uses mi² for US jurisdictions

3. Urban Planning and Development

City Planning:

• Zoning maps measured in mi²
• Service area calculations (fire, police, schools) in mi²
• Transit system coverage in mi²

Infrastructure:

• Road networks: lane-miles (length × lanes)
• Service territories: utilities measured in mi²
• Emergency response zones: mi² coverage areas

4. Real Estate (Large Tracts)

Rural Land Sales:

• Ranches: sometimes listed in mi² (though acres more common)
• Large timber tracts: mi²
• Mining claims: sections (1 mi² = 640 acres)

Commercial Development:

• Master-planned communities: hundreds to thousands of acres (multiple mi²)
• Industrial parks: often measured in mi²

5. Environmental Science and Conservation

Habitat Measurement:

• Wildlife refuges measured in mi²
• Conservation easements: large tracts in mi²
• Wetland restoration projects: mi²

Disaster Assessment:

• Wildfire extent: acres or mi²
• Flood zones: mi² inundated
• Hurricane damage: mi² affected

Conversion Guide

Square Miles to Acres

Formula: $$ \text{acres} = \text{mi}^2 \times 640 $$

The 640-Acre Rule: This is the most important conversion for square miles.

Square Miles	Acres	Common Use
1 mi²	640 acres	1 section (PLSS)
0.5 mi²	320 acres	½ section
0.25 mi²	160 acres	¼ section (homestead)
0.125 mi²	80 acres	⅛ section
2 mi²	1,280 acres	Large ranch
10 mi²	6,400 acres	Very large property

Square Miles to Square Kilometers

Formula: $$ \text{km}^2 = \text{mi}^2 \times 2.58999 $$

Quick Mental Math: Multiply by 2.6 (approximately 2.59)

Square Miles	Square Kilometers (Exact)	Square Kilometers (Mental)
1 mi²	2.590 km²	2.6 km²
10 mi²	25.90 km²	26 km²
50 mi²	129.50 km²	130 km²
100 mi²	258.99 km²	260 km²
500 mi²	1,295.00 km²	1,300 km²
1,000 mi²	2,589.99 km²	2,600 km²
10,000 mi²	25,899.88 km²	26,000 km²

Square Kilometers to Square Miles

Formula: $$ \text{mi}^2 = \text{km}^2 \times 0.386102 $$

Quick Mental Math: Multiply by 0.4 (approximately 0.386)

Square Kilometers	Square Miles (Exact)	Square Miles (Mental)
1 km²	0.386 mi²	0.4 mi²
10 km²	3.861 mi²	4 mi²
100 km²	38.610 mi²	40 mi²
1,000 km²	386.102 mi²	400 mi²
10,000 km²	3,861.02 mi²	4,000 mi²

Square Miles to Square Feet

Formula: $$ \text{ft}^2 = \text{mi}^2 \times 27,878,400 $$

The 27.878 Million Rule:

Square Miles	Square Feet
1 mi²	27,878,400 ft²
0.1 mi²	2,787,840 ft²
0.01 mi²	278,784 ft² (about 6.4 acres)

Common Conversion Mistakes

Mistake #1: Not Squaring the Conversion Factor

Wrong: "1 mile = 1.609 km, so 1 mi² = 1.609 km²"

Correct: 1 mile = 1.609 km (linear) 1 mi² = (1.609 km)² = 2.59 km² (area)

Example Error:

• Area: 10 mi²
• Wrong: 10 × 1.609 = 16.09 km² ❌
• Correct: 10 × 2.59 = 25.9 km² ✓

Mistake #2: Confusing Sections with Square Miles

Mostly Correct, But: In the US Public Land Survey System, a "section" is nominally 1 square mile (640 acres). However:

• Survey errors accumulate
• Earth's curvature requires adjustments
• Actual sections may be 630-650 acres
• "Government lots" used to account for discrepancies

Practical Tip: For legal descriptions, always use the actual surveyed area, not the nominal 640 acres.

Mistake #3: Mixing US Survey Foot with International Foot

Two Definitions of the Foot:

• International foot: 0.3048 m (exactly) — standard since 1959
• US survey foot: 1200/3937 m — used for land records

Difference: 2 parts per million (0.0002%)

When It Matters:

• Large surveys spanning many miles
• Legal boundary disputes
• Most states switched to international foot by 2023

Example:

• 1 mi² using international foot: 2.58998811 km²
• 1 mi² using US survey foot: 2.58999847 km²
• Difference: 10.36 m² over 1 mi² (tiny, but legally matters)

Mistake #4: Forgetting the 640-Acre Relationship

The "Quarter Section" Confusion:

• ¼ section = ¼ mi² = 160 acres (not 40 acres)
• ¼ of ¼ section = 1/16 mi² = 40 acres

PLSS Quarter Descriptions:

• NE¼ of Section 10 = 160 acres (northeast quarter)
• NE¼ of NE¼ of Section 10 = 40 acres (northeast quarter of northeast quarter)