| Square centimeters (cm²) | Square miles (sq mi) |
|---|---|
| 1 Square centimeter | 3.86102158542 × 10-11 sq mi |
| 2 Square centimeters | 7.72204317085 × 10-11 sq mi |
| 3 Square centimeters | 1.15830647563 × 10-10 sq mi |
| 4 Square centimeters | 1.54440863417 × 10-10 sq mi |
| 5 Square centimeters | 1.93051079271 × 10-10 sq mi |
| 10 Square centimeters | 3.86102158542 × 10-10 sq mi |
| 20 Square centimeters | 7.72204317085 × 10-10 sq mi |
| 25 Square centimeters | 9.65255396356 × 10-10 sq mi |
| 50 Square centimeters | 0.00000000193051079271 sq mi |
| 100 Square centimeters | 0.00000000386102158542 sq mi |
| Reference | Square centimeters (cm²) | Square miles (sq mi) |
|---|---|---|
| A sheet of A4 paper | 623.7 cm² | 0.0000000240812 sq mi |
| A tennis court | 2608000 cm² | 0.000100695 sq mi |
| A football pitch | 71400000 cm² | 0.00275677 sq mi |
| One hectare | 100000000 cm² | 0.00386102 sq mi |
| Central Park, New York | 3.41 × 1010 cm² | 1.31661 sq mi |
The square centimetre is a unit of area equal to one ten-thousandth of a square metre, written cm². It is the area of a square one centimetre on a side, and it contains one hundred square millimetres. It is the working unit for anything the size of a hand or smaller: wounds, printed circuits, laboratory cultures, sensor chips and postage stamps.
The arithmetic catches people out. Because area scales with the square of length, one hundred square centimetres make a square decimetre and ten thousand make a square metre, not one hundred. A square ten centimetres on a side is 100 cm², and doubling its side to twenty centimetres gives 400 cm², not 200. Nearly every mistake made with this unit comes from applying the linear factor instead of the squared one.
Medicine measures skin in it. Wounds, ulcers, burns and skin lesions are recorded in square centimetres so that healing can be tracked as a shrinking number over weeks, and dermatological treatments are dosed by the area treated. A typical adult palm covers roughly 100 square centimetres, which is why the palm is used as a rough field estimate of burn extent.
Laboratories rely on it for cell culture. Flasks are named by their growth surface, so a T25 offers 25 square centimetres and a T75 offers 75, and cell densities are counted per square centimetre. Photovoltaic research reports efficiency on cells of exactly one square centimetre, precisely so that results from different laboratories describe the same thing.
Engineering uses it for pressure in some traditions. The kilogram-force per square centimetre, close to one atmosphere, is still printed on tyre gauges, pressure vessels and hydraulic equipment in Japan, Korea and parts of eastern Europe, and it survives because the number it produces is conveniently near the values people already knew. Printed circuit boards are quoted and priced by the square centimetre for the same practical reason.
Against the imperial system it faces the square inch, which is 6.4516 square centimetres exactly. That factor comes straight from the inch being defined as exactly 2.54 centimetres, so unlike most imperial conversions this one is not an approximation, merely an awkward number.
One square centimetre equals 100 square millimetres, 0.0001 square metres, or about 0.155 square inches.
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.