| Square inches (sq in) | Square miles (sq mi) |
|---|---|
| 1 Square inch | 2.49097668605 × 10-10 sq mi |
| 2 Square inches | 4.9819533721 × 10-10 sq mi |
| 3 Square inches | 7.47293005816 × 10-10 sq mi |
| 4 Square inches | 9.96390674421 × 10-10 sq mi |
| 5 Square inches | 0.00000000124548834303 sq mi |
| 10 Square inches | 0.00000000249097668605 sq mi |
| 20 Square inches | 0.0000000049819533721 sq mi |
| 25 Square inches | 0.00000000622744171513 sq mi |
| 50 Square inches | 0.0000000124548834303 sq mi |
| 100 Square inches | 0.0000000249097668605 sq mi |
| Reference | Square inches (sq in) | Square miles (sq mi) |
|---|---|---|
| A sheet of A4 paper | 96.6737 sq in | 0.0000000240812 sq mi |
| A tennis court | 404241 sq in | 0.000100695 sq mi |
| A football pitch | 11067022 sq in | 0.00275677 sq mi |
| One hectare | 15500031 sq in | 0.00386102 sq mi |
| Central Park, New York | 5.28551 × 109 sq in | 1.31661 sq mi |
The square inch is a unit of area equal to 6.4516 square centimetres exactly. Its symbol is sq in, sometimes written in². It is the area of a square one inch on a side, and one hundred and forty-four of them make a square foot. Its most important use is not as an area at all but as the denominator of the pound per square inch, the pressure unit that governs tyres, hydraulics and gas supply across the English-speaking world.
That pressure unit does most of the work. A car tyre is inflated to around 32 pounds per square inch, a bicycle tyre to 80 or more, a domestic water supply arrives at 40 to 60, and hydraulic machinery runs at several thousand. Because a hydraulic cylinder produces a force equal to pressure times piston area, the square inch is what turns a pressure gauge reading into a load, which is why the unit is printed on machinery even in workshops that measure everything else in millimetres.
Materials strength uses a multiple of it. Steel and aluminium are rated in thousands of pounds per square inch, written ksi, and a common structural steel yields near 50 ksi. Concrete in the United States is specified in pounds per square inch, with 3000 to 5000 typical for building work. The corresponding metric figures in megapascals are smaller by a factor of about 6.9, and mixing the two produces some of the most dangerous errors in engineering.
As a plain area it describes small flat things. A postage stamp is about one square inch, a large coin rather less, a credit card about 3.3, and the die inside a large processor around one. Gaskets, contact patches, wound dressings, printed labels and machined faces are all quoted in square inches in American workshops.
The conversion to metric is exact rather than approximate. Because the inch is defined as exactly 2.54 centimetres, one square inch is exactly 6.4516 square centimetres, or 645.16 square millimetres. The exactness is worth knowing, because it means a converted figure can be checked rather than merely trusted.
Its awkwardness lies in the ladder above it. A square foot is 144 square inches and a square yard is 1296, so imperial area arithmetic never reduces to shifting a decimal point. That is the practical reason engineering drawing in Britain moved to millimetres while American practice stayed with the inch and simply accepted the multiplication.
One square inch equals 6.4516 square centimetres, 645.16 square millimetres, or about 0.006944 square feet.
The square mile is a unit of area equal to 640 acres, or 2.589988 square kilometres. Its symbol is sq mi. It is the area of a square one mile on a side, and it is the unit in which American and British counties, cities, parks and disaster zones are described. Its equivalence to exactly 640 acres is not an accident but the foundation of how much of North America was laid out.
The United States Public Land Survey, begun in 1785, divided the western territories into townships of six miles square, each containing thirty-six sections of one square mile. A section holds 640 acres, a quarter section 160, and a quarter of that 40. Those numbers ran through homestead law, land sales and inheritance for a century, and they are still visible from the air in the grid of roads that follows section lines across the Midwest.
Because the survey made the square mile a legal container rather than a mere measurement, it shaped settlement patterns. A quarter section was considered the amount of land a family could work, so farms across the plains came in multiples of 160 acres, and the mile spacing of section-line roads set how far apart towns, schools and grain elevators could usefully sit.
Today its everyday use is descriptive. Population density in American statistics is people per square mile, so around 92 for the country as a whole against nearly 30,000 for Manhattan. Wildfire extent, flood inundation, national park size and metropolitan area are all reported the same way, and British usage matches it for county and national park areas even where other measurements have gone metric.
Converting is straightforward if the factor is remembered: one square mile is 2.59 square kilometres, and one square kilometre is 0.386 square miles. The relationship is not intuitive because it is the square of the length ratio, so a place described as ten times larger in square miles is only about 3.2 times larger in linear extent.
Its awkwardness shows when the three imperial land units are chained. A square mile is 640 acres, an acre is 4840 square yards, and a square yard is nine square feet, so going from a square mile to a square foot means multiplying by 27,878,400. That figure is exactly why land and building are measured with different units even inside the same system.
One square mile equals 640 acres, about 2.59 square kilometres, 259 hectares, or 27,878,400 square feet.