# Relation between Yarn Dia and Yarn Count

Yarn Count:
Yarn count expresses the coarseness or fineness of yarn used in textile. According to Textile Institute, ‘Count is a number indicating the mass per unit length or the length per unit mass of yarn.’’ The relation between yarn dia and yarn count will be discussed below.

### Yarn Dia and Yarn Count Relation

Pierce approached the problem from a consideration of the apparent specific volume of a yarn. By experiment, an apparent specific volume of 1.1 for cotton yarns was obtained.

So, the specific volume of yarn = 1.1 cm3/gm

i.e., The weight of 1.1 cm3 yarn = 1 gm

Let,
yarn count = N tex
Weight of 1000 m yarn is N gm
Length of N gm yarn is 1000 m

…………………………………..1000 m……1000 X 100
Length of 1.0 gm yarn is ………….. Or ……………… cm
………………………………………N…………………N

So, the length of 1.1 cm3 (volume) yarn is 105/N cm

Since, the volume = Cross-section X Length
=> 1.1 cm3 = π X (d/2)2 X (105/N) cm         [Where, d = dia of yarn in cm]

…………………………d2……..105
=> 1.1 cm3 = π X …… X ………… cm
………………………….4……….N

…………….1.1 X 4 X N
=> d2 = ……………………
………………π X 105

=> d = √[(1.1 X 4 X N)/ π X 105] cm

………….0.375
=>d = …………√N cm
…………..100

=> d ∞√N             [For direct system]

Converting cm to inches and Tex to cotton count;

………………….0.375…….√590.5 ……1
d (inches) = ………….. X ………… X ……….         [Tex X Ne = 590.5]
……………………100………..√ Ne……2.54

……………..3.6
=> d = ……………
………….100√Ne

……………..1
=>d = …………
………….28√Ne

…………..1
=>d ∞ …….   [For indirect system]
………….√N

```Author of this Article:
Rakib Hawlader
B.Sc. in Textile Engineer
Noakhali Textile Engineering College
Cell: +8801812478393```

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