| Square millimeters (mm²) | Square hands (sq hh) |
|---|---|
| 1 Square millimeter | 0.0000968751937504 sq hh |
| 2 Square millimeters | 0.000193750387501 sq hh |
| 3 Square millimeters | 0.000290625581251 sq hh |
| 4 Square millimeters | 0.000387500775002 sq hh |
| 5 Square millimeters | 0.000484375968752 sq hh |
| 10 Square millimeters | 0.000968751937504 sq hh |
| 20 Square millimeters | 0.00193750387501 sq hh |
| 25 Square millimeters | 0.00242187984376 sq hh |
| 50 Square millimeters | 0.00484375968752 sq hh |
| 100 Square millimeters | 0.00968751937504 sq hh |
| Reference | Square millimeters (mm²) | Square hands (sq hh) |
|---|---|---|
| A sheet of A4 paper | 62370 mm² | 6.04211 sq hh |
| A tennis court | 260800000 mm² | 25265.1 sq hh |
| A football pitch | 7.14 × 109 mm² | 691689 sq hh |
| One hectare | 1 × 1010 mm² | 968752 sq hh |
| Central Park, New York | 3.41 × 1012 mm² | 330344411 sq hh |
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.
The square hand is a unit of area equal to sixteen square inches, or 103.2256 square centimetres. Its symbol is sq hh. A hand is four inches, so a square hand is a square four inches on a side, roughly the area of an adult palm. It is a complete and consistent unit that almost nobody has ever needed, because the hand it derives from measures one thing only.
That one thing is horses. The height of a horse or pony is measured at the withers, the ridge between the shoulder blades, and it is given in hands almost everywhere in the world, including in countries that are otherwise entirely metric. A hand was fixed at four inches by an English statute of 1541 under Henry VIII, and the equestrian world has held to that figure ever since.
The notation contains a trap worth knowing. A horse described as 15.2 hands is not fifteen and two tenths but fifteen hands and two inches, which is 62 inches or 157.5 centimetres. The digit after the point runs from 0 to 3 and then rolls over, so 15.3 is followed by 16.0. Anyone converting a list of horse heights with ordinary decimal arithmetic will produce numbers that are wrong by up to three inches.
Where the boundary between pony and horse falls is decided by this measurement. Most classifications put it at 14.2 hands, which is 58 inches or 147.3 centimetres, and competition classes at every level are drawn on the same scale. Because a placing can depend on a fraction of an inch, official measurement is a regulated procedure carried out on a level surface by an approved measurer.
The area form has never followed the length into use. Body-derived units were invented for laying along things, the height of an animal, the length of a cloth, the depth of water, and not for enclosing ground, which is why the acre and the chain came from ploughing rather than from anatomy. A square hand is simply what appears when the rule for forming areas is applied to a unit that had no such purpose.
As a quantity it is easy enough to place. A hundred square centimetres is a large sticky note, a beer mat and a half, or the palm of a hand, which is the same comparison used to estimate burn area in first aid. Sixteen square hands make a square foot, and 2304 of them make a square yard.
One square hand equals 16 square inches, about 103.23 square centimetres, or about 0.0103 square metres.