| Square leagues (sq lea) | Square millimeters (mm²) |
|---|---|
| 1 Square league | 23309892993024 mm² |
| 2 Square leagues | 46619785986048 mm² |
| 3 Square leagues | 69929678979072 mm² |
| 4 Square leagues | 93239571972096 mm² |
| 5 Square leagues | 116549464965120 mm² |
| 10 Square leagues | 233098929930240 mm² |
| 20 Square leagues | 466197859860480 mm² |
| 25 Square leagues | 582747324825600 mm² |
| 50 Square leagues | 1.16549464965 × 1015 mm² |
| 100 Square leagues | 2.3309892993 × 1015 mm² |
| Reference | Square leagues (sq lea) | Square millimeters (mm²) |
|---|---|---|
| A sheet of A4 paper | 0.00000000267569 sq lea | 62370 mm² |
| A tennis court | 0.0000111884 sq lea | 260800000 mm² |
| A football pitch | 0.000306308 sq lea | 7.14 × 109 mm² |
| One hectare | 0.000429002 sq lea | 1 × 1010 mm² |
| Central Park, New York | 0.14629 sq lea | 3.41 × 1012 mm² |
The square league is a unit of area equal to nine square miles, or about 23.31 square kilometres. Its symbol is sq lea. A league here is three statute miles, 4828.032 metres, so a square league is a square three miles on a side and holds 5760 acres. It is an obsolete unit that survives in historical land records and in the names of places whose boundaries were drawn with it.
The league began as a measure of time as much as of distance. In Roman and medieval usage it was roughly the distance a person could walk in an hour, which meant that its length varied with the terrain, the country and the century. English practice eventually fixed it at three miles, but the French lieue, the Spanish legua and the Portuguese légua were all different, and none of them agreed with each other.
That variation matters for anyone reading old documents. A grant recorded in leagues cannot be converted safely without knowing which league the surveyor meant. Spanish colonial grants in Texas and California used the legua based on the vara, giving a league of about 4428 acres rather than 5760, and county boundaries in parts of Texas still follow lines that were laid out on that basis.
At sea the unit lasted longer than on land. The marine league of three nautical miles gave the old three-mile territorial limit its name, and charts and treaties used it into the nineteenth century. The modern territorial sea of twelve nautical miles replaced it, but the phrase survives in older law and in fiction, where a journey of twenty thousand leagues describes distance travelled and not depth reached.
As a plain quantity, a square league is a substantial piece of country: nine square miles is a large parish, a small city, or a block of farmland that would take an hour to walk across. It is the scale at which land stops being a holding and becomes a district, which is precisely why grants of that size were made to found settlements rather than farms.
For conversion, nine square miles, 23.31 square kilometres or 2331 hectares all describe the same area. Any figure taken from a historical source should be checked against the definition in use at the time, because the same word can differ by thirty per cent between two neighbouring jurisdictions.
One square league equals 9 square miles, 5760 acres, about 23.31 square kilometres, or about 2331 hectares.
The square millimetre is a unit of area equal to one millionth of a square metre, written mm². It is the area of a square one millimetre on a side. It is the standard unit of engineering cross-sections, and two of the most consequential numbers in construction and electrical work are expressed in it.
Electrical cable is the first of those. Outside North America, conductors are specified by their cross-sectional area in square millimetres: 1.5 mm² for lighting circuits, 2.5 mm² for socket outlets, 6 mm² for a cooker, and 16 or 25 mm² for a house supply. Current-carrying capacity follows the area closely, so a 2.5 mm² copper conductor safely carries about twenty amperes in ordinary domestic installation, and the whole of wiring regulation is built on that relationship.
North America uses American Wire Gauge instead, where the numbers run backwards and the steps are not proportional: gauge 14 is about 2.08 mm² and gauge 12 about 3.31. Converting between the two systems is one of the more error-prone tasks in electrical work, because a gauge number carries no information about area until it is looked up.
The second consequential use is stress. One newton per square millimetre is exactly one megapascal, which is why structural drawings state steel and concrete strengths in N/mm². A common structural steel is designated S355 because it yields at 355 newtons per square millimetre, and a concrete grade of C30/37 reaches 30 newtons per square millimetre in cylinder testing. Bolts are rated the same way, using their tensile stress area: an M10 bolt has 58 square millimetres of it.
Electronics measures its products here too. A large processor die covers between 300 and 600 square millimetres, and the cost of a chip is driven directly by that number because a wafer holds a fixed area. A full-frame camera sensor is 864 square millimetres against roughly 30 for a phone camera, which is most of the reason the two behave so differently in low light.
Below the square millimetre the metric ladder continues to the square micrometre, used for transistors and cell biology, but almost nothing in ordinary manufacturing needs to go further. Above it, the square centimetre takes over at a hundred square millimetres.
One square millimetre equals 0.01 square centimetres, 0.000001 square metres, or about 0.00155 square inches.