Square Millimeter to Square Mile Conversion Calculator: Free Online Tool
Convert square millimeters to square miles with our free online area converter.
Square Millimeter to Square Mile Calculator
How to Use the Calculator:
- Enter the value you want to convert in the 'From' field (Square Millimeter).
- The converted value in Square Mile will appear automatically in the 'To' field.
- Use the dropdown menus to select different units within the Area category.
- Click the swap button (⇌) to reverse the conversion direction.
How to Convert Square Millimeter to Square Mile
Converting Square Millimeter to Square Mile involves multiplying the value by a specific conversion factor, as shown in the formula below.
Formula:
1 Square Millimeter = 3.8610e-13 square milesExample Calculation:
Convert 10 square millimeters: 10 × 3.8610e-13 = 3.8610e-12 square miles
Disclaimer: For Reference Only
These conversion results are provided for informational purposes only. While we strive for accuracy, we make no guarantees regarding the precision of these results, especially for conversions involving extremely large or small numbers which may be subject to the inherent limitations of standard computer floating-point arithmetic.
Not for professional use. Results should be verified before use in any critical application. View our Terms of Service for more information.
What is a Square Millimeter and a Square Mile?
The Square Millimeter (symbol: mm² or sq mm) is a unit of area in the International System of Units (SI). It represents the area of a square whose sides measure exactly one millimeter (mm) in length.
Key relationships:
- 1 mm² = 1 millimeter × 1 millimeter
- 1 meter (m) = 1,000 millimeters (mm)
- 1 square meter (m²) = (1,000 mm) × (1,000 mm) = 1,000,000 mm²
- 1 square centimeter (cm²) = (10 mm) × (10 mm) = 100 mm² (or 1 mm² = 0.01 cm²)
In terms of imperial/US customary units:
- 1 inch = 25.4 mm exactly
- 1 square inch (in²) = (25.4 mm)² = 645.16 mm²
- Therefore, 1 mm² ≈ 0.00155 square inches (in²)
The Square Mile (symbol: mi² or sq mi) is a unit of area within the British Imperial and United States customary systems. It is defined as the area of a square whose sides each measure exactly one statute mile (mi) in length.
Key relationships within the imperial/US customary system:
- 1 mi² = 1 mile × 1 mile
- 1 mile = 1,760 yards (yd) = 5,280 feet (ft)
- Therefore, 1 mi² = (5,280 ft)² = 27,878,400 square feet (ft²)
- 1 mi² = (1,760 yd)² = 3,097,600 square yards (yd²)
- 1 mi² = 640 acres (ac) (This is a fundamental definition within the system)
In terms of metric units:
- 1 mile = 1.609344 kilometers (km) exactly (based on the international yard)
- Therefore, 1 mi² = (1.609344 km)² ≈ 2.589988 square kilometers (km²)
- 1 mi² ≈ 259 hectares (ha)
Note: The Square Millimeter is part of the metric (SI) system, primarily used globally in science and trade. The Square Mile belongs to the imperial/US customary system.
History of the Square Millimeter and Square Mile
- Origin (Millimeter): The square millimeter is derived directly from the millimeter, which itself is derived from the meter, the base unit of length in the metric system established during the French Revolution. The prefix "milli-" denotes one-thousandth (1/1000).
- Metric System Coherence: The square millimeter arose naturally within the decimal-based metric system as the appropriate unit for measuring very small areas, by squaring the millimeter length unit.
- SI Standardisation: With the formal establishment of the International System of Units (SI) in 1960, the square meter (m²) was confirmed as the derived unit for area. The square millimeter, formed using an SI prefix (milli-) and the base unit (meter) squared, became a standard SI unit for area, suitable for fine-scale measurements.
- Technological Need: The widespread use of the square millimeter grew significantly with advancements in science and technology requiring precise measurement of very small objects and features, such as in microscopy, electronics, and precision engineering.
- Origin (The Mile): The square mile is derived from the mile, a unit of length whose name comes from the Roman mille passus ("thousand paces"). The length of the mile varied considerably until the statute mile was defined by an English Act of Parliament in 1593 as 5,280 feet.
- Imperial System: The square mile became the standard unit for measuring large land areas within the British Empire. Its definition based on the acre (640 acres per square mile) was particularly important for land surveying and administration, especially in the colonization of North America.
- US Public Land Survey System (PLSS): The square mile, referred to as a section, is a fundamental unit in the PLSS, which was established by the Land Ordinance of 1785. This system was used to survey and divide vast amounts of land in the United States. Townships are typically defined as 36 square miles (a 6x6 grid of sections).
- Standardization (International Mile): While the statute mile was legally defined, its exact relationship to metric units was solidified with the international agreement of 1959, which defined the yard (and thus the foot and mile) in terms of the meter. This fixed the conversion to square kilometers.
- Continued Use: Despite global metrication, the square mile remains the primary unit for large land areas and geographical measurements in the United States and is still used in some contexts in the UK, Canada, and other countries with historical ties to the imperial system.
Common Uses for square millimeters and square miles
Explore the typical applications for both Square Millimeter (metric) and Square Mile (imperial/US) to understand their common contexts.
Common Uses for square millimeters
The square millimeter is used for measuring extremely small areas, primarily in technical and scientific contexts:
- Engineering and Manufacturing: Specifying cross-sectional areas of fine wires, optical fibers, and small mechanical components; defining surface areas of micro-electromechanical systems (MEMS); measuring surface roughness features.
- Material Science: Quantifying the area of microscopic structures like crystal grains, pores, or defects in materials under microscopic analysis; measuring the area of test indentations (e.g., in hardness testing).
- Electronics: Defining the area of contact pads, traces, vias, and components on printed circuit boards (PCBs) and integrated circuits (ICs).
- Optics: Measuring the effective area of small apertures, detector pixels, laser beam cross-sections, or optical fiber cores.
- Medicine and Biology: Measuring the cross-sectional area of fine capillaries, nerve fibers, or cells under a microscope; quantifying the area of small lesions or tissue samples.
- Physics: Used in calculations involving small surfaces, pressures on small areas, or flux densities.
It is generally far too small for everyday measurements like room sizes or land areas.
Common Uses for square miles
The square mile is used for measuring large areas, particularly land:
- Geography and Cartography (US, UK, etc.): Measuring the area of cities, counties, states (in the US), national parks, large lakes, islands, and administrative regions in countries using imperial/US customary units.
- Demography (US, UK, etc.): Calculating population density, typically expressed as inhabitants per square mile (people/mi²).
- Land Surveying (US): A fundamental unit (section) in the Public Land Survey System used for defining property boundaries over large parts of the United States.
- Real Estate (Large Tracts): Sometimes used for very large rural properties or ranches, although acres are often preferred.
- Historical Documents: Common in older maps, land deeds, and geographical descriptions in relevant countries.
- Environmental Science: Measuring the extent of large reserves, habitats, or areas affected by large-scale phenomena (e.g., wildfire extent) in relevant regions.
It is generally too large for measuring individual residential properties (acres or square feet are used) or room sizes.
Frequently Asked Questions
Questions About Square Millimeter (mm²)
How many square millimeters are in a square centimeter?
There are exactly 100 square millimeters (mm²) in one square centimeter (cm²). This is because 1 cm = 10 mm, so 1 cm² = (10 mm) × (10 mm) = 100 mm².
How many square millimeters are in a square meter?
There are exactly 1,000,000 square millimeters (mm²) in one square meter (m²). This is because 1 m = 1000 mm, so 1 m² = (1000 mm) × (1000 mm) = 1,000,000 mm².
How do you convert square millimeters to square inches?
To convert square millimeters to square inches, multiply the area in square millimeters by approximately 0.00155 (or divide by 645.16).
- Conversion formula: Area [in²] ≈ Area [mm²] × 0.00155
- Example: 500 mm² ≈ 500 × 0.00155 in² ≈ 0.775 in²
Is the square millimeter an official SI unit?
Yes, the square millimeter (mm²) is an SI unit of area. It is derived from the SI base unit of length, the meter, using the standard SI prefix "milli-". While the square meter is the fundamental SI unit of area, square millimeters are standard for measuring very small areas.
Is mm² commonly used for paper sizes?
No. Standard paper sizes (like A4, Letter) are typically defined using millimeters (mm) for their dimensions (length and width), but their area is usually expressed in square meters (m²) or square centimeters (cm²) if needed, not typically square millimeters.
About Square Mile (mi²)
How many acres are in one square mile?
There are exactly 640 acres in one square mile. This is a defining relationship in the imperial and US customary systems.
How do you calculate the area of a square mile?
It is the area of a square with sides of one mile each. Since 1 mile = 5,280 feet: Area = 5,280 ft × 5,280 ft = 27,878,400 square feet (ft²).
How many square kilometers are in one square mile?
One square mile is equal to approximately 2.589988 square kilometers (km²). For practical purposes, it is often rounded to 2.59 km².
- Conversion formula: Area [km²] ≈ Area [mi²] × 2.589988
Is the square mile an SI unit?
No, the square mile is not part of the International System of Units (SI). It belongs to the British Imperial and US customary systems. The corresponding SI-accepted unit for large areas is the square kilometer (km²) or the hectare (ha).
What is a "section" of land in the US?
In the US Public Land Survey System (PLSS), a section is a unit of land area nominally equivalent to one square mile (640 acres). Townships are typically formed from a 6-mile by 6-mile square, containing 36 sections.
How to convert 3 square miles to square yards
To convert 3 square miles to square yards, we need to use the conversion factor between square miles and square yards. 1 square mile = 3,097,600 square yards So, to convert 3 square miles to square yards, we multiply 3 by 3,097,600: 3 square miles = 3 * 3,097,600 = 9,292,800 square yards Therefore, 3 square miles is equal to 9,292,800 square yards.
Conversion Table: Square Millimeter to Square Mile
| Square Millimeter (mm²) | Square Mile (mi²) |
|---|---|
| 1 | 0 |
| 5 | 0 |
| 10 | 0 |
| 25 | 0 |
| 50 | 0 |
| 100 | 0 |
| 500 | 0 |
| 1,000 | 0 |