Conversion from Square leagues to Square inches

Information about the Square league (sq lea)

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.

Information about the Square inch (sq in)

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.