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.

Square inch conversion table