Suppose you had a 100 foot coil of copper wire, and you wanted to know its mass. You could simply weigh it and convert the measurement to mass, but that would give you the mass of the wire and the spindle around which it's coiled. However, you can conveniently calculate the mass without weighing anything. You can do this by using the volume, which can be calculated from the American Wire Gauge (AWG) size and the known density of copper.
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Convert the length to inches. Using the example, multiply 100 feet times 12 inches per feet to calculate 1,200 inches.
Look for the AWG size of the wire, which should be printed on the spindle or documentation. Convert this size to inches using the following formula: Diameter = 0.005 x (92^((36-AWG)/39)). The symbol "^" means "to the power of." For gauge sizes of 00, 000, 0000, etc., use the number -1, -2, -3 etc. In the 1,000 coil example, suppose the wire gauge was AWG 5:
Diameter = 0.005 x (92^((36-5)/39))
Diameter = 0.005 x (92^(31/39))
Diameter = 0.005 x (92^(0.7949)
Diameter = 0.005 x 36.39
Diameter = 0.182 square inches
Multiply the area by the length in inches to get volume. In the example, you would have 218.4 cubic inches.
Multiply the volume times the density of copper, which is 0.147 Kilogram per cubic inch. In the example, this gives you 321 Kilogram. That would be the weight, but mass is measured in grams or kilograms.
Multiply pounds by 0.4536 to convert into kilograms. In the example, this results in 32.1 kilograms.
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