The denier, a traditional textile unit, describes the density of yarn. A 9-km strand of yard that weighs exactly a gram has a density of one denier. Unless you have a team of assistants and a private highway at your disposal, you probably cannot conveniently measure and weigh 9 km of thread. You can, however, calculate the deniers of a sample from its standard density, measured in grams per cubic centimeter.

Square the thread's diameter, measured in centimeters. With a diameter, for instance, of 0.3175 cm:

0.3175^2 = 0.1008

Multiply the result by pi, which equals approximately 3.142:

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0.1008 x 3.142 = 0.3167

Multiply the result by the yarn's density, measured in grams per cubic centimeter. If the density equals, for instance, 0.0157 g per cubic centimeter:

0.3167 x 0.0157 = 0.004972

Divide the result by 4 x 10^-6, a constant conversion factor:

0.004972 / (4 x 10^-6) = 1,243.

This is the yarn's density in deniers.