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Square (unit)
View on Wikipediafrom Wikipedia
 | This article needs additional citations for verification. (November 2025) |
| Square | |
|---|---|
| Unit of | area |
| Symbol | Square |
| Conversions | |
| 1 Square in ... | ... is equal to ... |
| square foot | 100 |
| square metre | 9.3 |
The square is an Imperial unit[citation needed] of area that is used in the construction industry in the United States and Canada,[1][2] and was historically used in Australia. One square is equal to 100 square feet (9.3 m2). Examples where the unit is used are roofing shingles, metal roofing, vinyl siding, and fibercement siding products. Some home builders use squares as a unit in floor plans to customers.[citation needed]
When used in reference to material that is applied in an overlapped fashion, such as roof shingles or siding, a square refers to the amount of material needed to cover 100 square feet when installed according to a certain lap pattern. For example, for a shingle product designed to be installed so that each course has 5 in (130 mm) of exposure, a square would actually consist of more than 100 square feet of shingles in order to allow for overlapping of courses to yield the proper exposed surface. As roofs or siding are unlikely to precisely fit, wastage needs to be taken into account.[3]
Construction in Australia no longer uses the square as a unit of measure, and it has been replaced by the square metre. The measurement was often used by estate agents to make the building sound larger as the measure includes the areas outside under the eaves, and so cannot be directly compared to the internal floor area.[citation needed] Residential buildings in the state of Victoria, Australia are sometimes still advertised in squares.[4]
See also
[edit]References
[edit]- ^ Cleland, Jennifer (October 31, 2025). "What is a Roofing Square in Measurements?". roofr. Retrieved November 1, 2025.
- ^ "What Is A "Square" In Roofing?". Dallas Fort Worth Roofing Blog. March 31, 2016. Archived from the original on January 12, 2018. Retrieved 2016-04-01.
- ^ "How Many Bundles Are in a Roofing Square and What It Means for Your Project". Frontier Foam. October 11, 2025. Retrieved November 1, 2025.
- ^ "One Square, Two Squares… Wait, What's a Roofing Square?". Rocket Renovation. March 5, 2025. Retrieved November 1, 2025.
Square (unit)
View on Grokipediafrom Grokipedia
Definition and Fundamentals
Basic Concept
The square is an imperial unit of area equal to 100 square feet (approximately 9.29 square meters), representing the area of a square with sides of 10 feet each.[3][2] This unit quantifies two-dimensional space, such as roof or wall surfaces in construction, by measuring the extent enclosed by boundaries in flat shapes. For example, a square with sides of 10 feet occupies an area of 1 square (100 ft²), derived from multiplying its length and width in feet. This approach accounts for the two dimensions in area calculations within imperial measurements. In contrast to linear units like the foot, which measure one-dimensional distance, the square requires multiplying two linear dimensions—such as length by width—using feet to yield an area in squared feet, then grouped into units of 100 for the "square."Relation to Linear Units
The square derives from the linear foot through multiplication to calculate area. The area of a rectangle is , where and are length and width in feet, resulting in square feet (). One square equals 100 , specifically the area of a 10 ft by 10 ft square: .[9] This relationship uses dimensional analysis for consistency: a linear foot has dimension , so area has or . The square scales this to a convenient 100 unit for practical applications, ensuring measurements remain in compatible dimensions. To illustrate, a 20 ft by 5 ft rectangle has area , or 1 square, showing how linear measures in feet produce the unit. Squares are non-additive with linear units due to differing dimensions: lengths in feet cannot be added to areas in squares without conversion, maintaining homogeneity in calculations. For example, 10 feet (length) cannot be summed with 1 square (area) directly.Historical Context
Evolution in Modern Systems
The development of the "square" unit as a specific measure of 100 square feet in construction reflects broader efforts to standardize imperial measurements in the United States during the early 20th century. This convention arose in the growing American building sector to streamline estimating and pricing for materials like roofing shingles and siding, where three bundles typically cover one square to account for overlaps and waste.[7] Prior to standardization, measurements relied on direct square footage, but the "square" facilitated quicker calculations and reduced errors in large projects.[10] In parallel, imperial systems were formalized earlier in Britain with the Weights and Measures Act of 1824, which defined the yard as the primary linear unit and derived area measures like the square yard and square foot, with an acre as 4,840 square yards.[11] This influenced US customary units, which evolved from British standards but adapted for American commerce and construction. The 20th century brought further alignment through international agreements. The 1959 international yard and pound agreement, signed by representatives from Australia, Canada, New Zealand, South Africa, the United Kingdom, and the United States, defined the yard precisely as 0.9144 meters, ensuring consistency in derived units like square feet and thus the "square" across imperial-using nations.[12] While metric systems, originating in France in 1795 with the square metre and later formalized in the SI in 1960, gained global prominence for scientific use, the "square" persists in imperial-based construction trades in the US and Canada.[13][14]Common Units and Systems
Metric and SI Units
In the International System of Units (SI), the base unit for area is the square metre, denoted as m², which is defined as the area of a square with sides each measuring one metre in length. This derived unit arises coherently from the SI base unit of length, the metre, without requiring additional constants or definitions beyond those establishing the metre itself.[8] The SI employs a system of decimal prefixes to form multiples and submultiples of the square metre, facilitating the expression of areas across vast scales. For instance, the square kilometre (km²) represents the area of a square with 1-kilometre sides and equals 1,000,000 m² (or 10^6 m²), commonly used for measuring large land areas such as countries or continents.[15] Conversely, the square centimetre (cm²), the area of a square with 1-centimetre sides, equals 0.0001 m² (or 10^{-4} m²) and is suitable for smaller measurements, such as cross-sections in engineering or surface areas in biology.[8] Other derived square units include the square decimeter (dm²), which is the area of a square with 1-decimeter sides and equals 0.01 m² (or 10^{-2} m²), often applied in packaging or fabric measurements. The square millimeter (mm²), the area of a square with 1-millimeter sides, equals 0.000001 m² (or 10^{-6} m²) and finds use in precision contexts like microelectronics or medical imaging.[8] These units maintain exact scaling factors based on the prefix powers: for a prefix factor of 10^n applied to length, the area unit scales by 10^{2n}.[15] The square metre and its prefixed variants are universally adopted in scientific research and international standards, with the metric system serving as the official measurement framework in all but three countries—the United States, Liberia, and Myanmar—as of 2025.[16] This widespread implementation ensures consistency in global collaborations, from climate modeling to particle physics experiments.[17]Imperial and US Customary Units
In the Imperial and US Customary systems, area is measured using square units derived from linear measurements, characterized by a non-decimal structure often based on factors of 12 (from inches to feet) and 3 (from feet to yards), leading to irregular scaling such as 144 square inches equaling one square foot.[18] The square foot (ft²) represents the area of a square with sides of one foot each, serving as a fundamental unit for construction, flooring, and general measurements. In US construction, the 'square' is a conventional unit equal to 100 square feet (approximately 9.29 m²), used for estimating coverage of materials like roofing and siding.[19][20] The square yard (yd²) equals nine square feet, reflecting the three-foot length of a yard, and is commonly applied in landscaping and fabric estimation.[18] Larger scales include the square mile (mi²), which encompasses 27,878,400 square feet, used primarily for geographical and land area delineations.[19] Specific to US Customary usage, the acre functions as a key land measurement unit equivalent to 43,560 square feet or 10 square chains (where a chain is 66 feet), historically tied to agricultural plotting rather than a direct square of a linear unit.[19] The square inch (in²), defined as the area of a square with one-inch sides, finds extensive application in manufacturing, engineering drawings, and precision work like electronics assembly.[18] These units remain predominant in the United States for everyday, legal, and industrial contexts, such as real estate and building codes, while in the United Kingdom, they persist for legacy purposes like road signage (in miles) and certain trades despite widespread metric adoption since the 1960s.[17][21]Conversions and Calculations
Formulas for Area Conversion
The conversion between different square units fundamentally relies on the principle that area scales with the square of the linear dimensions. To convert an area from unit A to unit B, where both are derived from the same base linear unit, multiply the value by the square of the ratio of the linear size of unit A to the linear size of unit B: This formula ensures dimensional consistency, as all area units preserve the dimension of length squared, denoted as [L]^2 in physical measurements.[22] Within metric (SI) systems, conversions follow powers of 10 based on prefixes. For example, since 1 kilometer (km) equals 10^3 meters (m), 1 km² equals (10^3)^2 = 10^6 m². Similarly, 1 hectare (ha) equals 10^4 m², as 1 hectometer (hm) = 10^2 m. These relations stem directly from the decimal-based structure of the International System of Units (SI).[22] In imperial and US customary systems, conversions also derive from exact linear relations. For instance, 1 yard (yd) equals exactly 3 feet (ft), so 1 yd² equals 3^2 = 9 ft². Likewise, 1 ft equals 12 inches (in), yielding 1 ft² = 144 in². The square unit, defined as 100 ft², follows directly from this system. These factors are fixed by definition in the US customary system.[22] For cross-system conversions, such as between metric and imperial units, apply the general formula using the established linear factor. The international foot is defined as exactly 0.3048 m, so 1 m equals 1 / 0.3048 ≈ 3.28084 ft. Squaring this gives the area factor: 1 m² ≈ (3.28084)^2 ≈ 10.7639 ft². For the square unit, 1 square = 100 ft² = 100 × 0.09290304 m² = 9.290304 m² exactly. This derivation maintains [L]^2 consistency across systems.[22]Equivalences Between Systems
The equivalences between square units in the metric and imperial systems are derived from precise definitions established by the 1959 International Yard and Pound Agreement, which set the international yard as exactly 0.9144 meters and the inch as exactly 25.4 millimeters, ensuring consistent area conversions.[12] These standards allow for exact calculations of area factors, with values rounded for practical use while maintaining high accuracy.[23] Key conversions between common metric and imperial units include the following:| Unit | Equivalent | Source |
|---|---|---|
| 1 m² | 10.7639 ft² | NIST SP 811[23] |
| 1 ft² | 0.092903 m² | NIST SP 811[23] |
| 1 square | 9.290304 m² | NIST SP 811[22] |
| 1 acre | 4046.86 m² | NIST SP 1038[24] |
| 1 hectare | 2.47105 acres | NIST SP 1038[24] |
| 1 cm² | 0.155000 in² | NIST SP 811[23] |
| 1 in² | 6.4516 cm² | NIST SP 811[23] |