Systems for sizing yarn fall into two basic types.

The yarn number is based on the length of yarn needed to make up a specified weight. The finer the yarn, the higher the number. Cotton, wool and linen are numbered with such systems.

The yarn number is based on the mass of a specified length of yarn. The finer the yarn, the lower the number. Silk, synthetic fibers and jute are numbered with such systems.

Wool
Cut system
The yarn number is the number of 300-yard hanks needed to make up a pound. Hence, 600 yards of 2-cut yarn weigh a pound. Symbol, Nac. In practice, coarse yarns are typically five-cut to seven-cut, medium 18-cut to 21-cut, and fine yarns 30-cut to 35-cut.

Run system
The yarn number is the length in yards of one pound of the yarn, divided by 1600. Symbol Nar. So one pound of number 1 run yarn is 1600 yards long, one pound of number 2 run yarn is 3200 yards long, and so on. Numbers 1 through 3 are coarse, 3? to 5 are medium, and numbers 6 to 8 runs are fine.

Resource:
Richard M. Lederer, Jr.
Colonial American English. A Glossary.
Essex, Connecticut: A Verbatim Book, 1985.
Page 200.
ASTM Standard D-123-03. Standard Terminology Relating to Textiles.
Edition approved 10 February 2003.

A fraction is used to describe the weight of multi-ply yarn. The numerator is the number of plies. The denominator is the cut or run number of the yarn as a whole, not of the plies separately. So, for example, 2/10s cut yarn would have two plies, and 3000 yards would weigh a pound. In other words, the plies themselves would be 20-cut.

Count system (worsted yarns)
Worsted yarns have a system of their own, called as "count" and is similar to the above, but with 1-count yarn having a length of 560 yards to the pound. A pound of 2-count yarn is thus 1120 yards long.

Cotton
In the United States, the yarn number for cotton yarns is based on the number of 840-yard hanks in a pound. The convention for indicating plies resembles that for wool. Two-ply 20s would be written 2/20s or 20/2, and would be twice the weight, length for length, of single ply 20s yarn.

Linen, jute, hemp, and ramie
In England and the United States, the yarns of these fibers are described by the number of leas in a pound, each lea of 300 yards.

Linen has been spun as fine as 400s and even 600s, which are used in making fine lace. To achieve such fineness, Belgian hand spinners worked only in damp basements.

Silk and synthetic fibers
Synthetic yarns other than glass, and raw and thrown silk yarns are sized by the metric and denier systems. The metric yarn number is the mass in grams of a 450-meter length of the yarn divided by 0.05, or, another way of saying the same thing, the mass in grams of a 9000-meter length.

The denier was a French coin, equal to 1/12 of a sou, whose mass was used as a weight in calculating yarn numbers. In Great Britain and the United States, denier was originally applied only to raw silk. Being a natural product, silk varies in thickness, so the size is usually given as a range, for example, "13/16 denier."

The Manchester dram system was formerly used for thrown silk, the yarn number being the weight of a 1000-yard skein in drams. Nowadays the denier is used for everything.

International' denier mass in grams of a 500-meter length /0.05
Turin denier mass in grams of a 474-meter length/ 0.05336
Milan denier mass in grams of a 476-meter length/ 0.0511
Old Lyonese denier mass in grams of a 476-meter length/ 0.5311
New Lyonese denier mass in grams of a 500-meter length/ 0.05311

Spun silk yarn, which is made from leftovers after filament silk has been produced, is numbered by a different system in the United States and the United Kingdom, one like that used for cotton. The yarn number is the number of 840-yard lengths (a hank) in a pound. The smaller the number, the heavier the yarn.

Unlike cotton, the count in a fraction representing multi-ply yarn describes the finished yarn, not the plies.

Comparison of systems
The following table gives some very approximate equivalents, by weight, for the various systems.

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