Conversion from 3 Square yards to Square millimeters

Information about the Square yard (sq yd)

The square yard is a unit of area equal to nine square feet, or 0.83612736 square metres exactly. Its symbol is sq yd, sometimes written yd². It is the area of a square one yard on a side, and 4840 of them make an acre. It occupies the awkward middle of the imperial ladder: too large for a workshop, too small for a field, and used mainly for surfaces that are laid rather than built.

Ground coverings are its main business. Turf is sold and laid by the square yard, asphalt paving and road resurfacing are measured in square yards in the United States, and carpet was priced that way for most of the twentieth century before American retailers moved to the square foot. Anything that arrives on a roll or a pallet and is spread out tends to be counted in this unit.

Textiles use it in an indirect but important way. Cloth is bought by the linear yard off a roll of known width, but its weight is specified in ounces per square yard, which is what allows two fabrics of different widths to be compared. A shirting might be four ounces per square yard and a heavy canvas eighteen, and those numbers describe the cloth more usefully than any measurement of the bolt does.

It also carries a large part of the South Asian property market. In Pakistan and northern India, plots are commonly sold in gaz, which is the square yard under a local name, so a house plot might be advertised at 240 gaz. Larger holdings switch to the marla and the kanal, both of which are defined as multiples of the square yard, so the whole regional system rests on this unit even where the English name is never used.

Its relationship to the rest of the imperial ladder is unusually clean at one step and unusually messy at the next. Nine square feet is easy; 1296 square inches and 4840 to the acre are not. That mixture is characteristic of a system built from body measures and ploughing practice rather than from a single decimal idea.

Conversion to metric is exact but not memorable: one square yard is 0.83612736 square metres and one square metre is 1.19599 square yards. A rough rule that a square metre is about a fifth larger than a square yard is close enough for judging a room, though not for ordering material.

One square yard equals 9 square feet, 1296 square inches, about 0.8361 square metres, or about 0.000207 acres.

Information about the Square millimeter (mm²)

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.