| Centiares (ca) | Square miles (sq mi) |
|---|---|
| 1 Centiare | 0.000000386102158542 sq mi |
| 2 Centiares | 0.000000772204317085 sq mi |
| 3 Centiares | 0.00000115830647563 sq mi |
| 4 Centiares | 0.00000154440863417 sq mi |
| 5 Centiares | 0.00000193051079271 sq mi |
| 10 Centiares | 0.00000386102158542 sq mi |
| 20 Centiares | 0.00000772204317085 sq mi |
| 25 Centiares | 0.00000965255396356 sq mi |
| 50 Centiares | 0.0000193051079271 sq mi |
| 100 Centiares | 0.0000386102158542 sq mi |
| Reference | Centiares (ca) | Square miles (sq mi) |
|---|---|---|
| A sheet of A4 paper | 0.06237 ca | 0.0000000240812 sq mi |
| A tennis court | 260.8 ca | 0.000100695 sq mi |
| A football pitch | 7140 ca | 0.00275677 sq mi |
| One hectare | 10000 ca | 0.00386102 sq mi |
| Central Park, New York | 3410000 ca | 1.31661 sq mi |
The centiare is a unit of area equal to one hundredth of an are, which makes it exactly one square metre. Its symbol is ca. It is the only unit in common use that is an exact duplicate of another under a different name, and the reason it exists at all is a matter of bookkeeping rather than of measurement.
When the French metric law of 1795 established the are as the decimal unit of land, it created a full ladder around it: the hectare above and the centiare below. Land registries then adopted a three-column format, recording every parcel as so many hectares, so many ares and so many centiares. The last column needed a name, and the square metre, though identical, did not fit the pattern.
That format is still in force. French, Belgian, Luxembourgish and Dutch land registers write parcel areas as three numbers in sequence, so 1 ha 25 a 30 ca means 12,530 square metres. The middle and last figures never exceed 99, which makes the notation self-checking: a value like 1 ha 130 a is malformed and signals a transcription error before anyone has to do arithmetic.
Reading it is a matter of place value. Each hectare is 10,000 square metres, each are is 100, and each centiare is one, so the three columns simply spell out a number in base one hundred. A notary's figure of 0 ha 04 a 62 ca is 462 square metres, and a surveyor's plan showing the same plot would print 462 m² without further comment.
Outside the land registry the centiare has no life. Nobody specifies a floor, a wall or a plot of ground in centiares when the square metre says the same thing with a symbol everyone recognises, and no branch of science or engineering has ever adopted it. It is a unit that exists to fill a column.
The one hazard is the symbol. In many documents ca is an abbreviation for the Latin circa, meaning approximately, so a figure that reads ca 400 could mean 400 centiares or about 400 of something else entirely. In land records the position of the number resolves it; in running text, converting to square metres removes the ambiguity for good.
One centiare equals exactly 1 square metre, 0.01 ares, or about 10.764 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.