How to Calculate Yarn Diameter from Count

How to Calculate Yarn Diameter from Count 

Finding the diameter of a given count of yarn:

The diameter of a yarn can be found out by extracting the square root of the total yards in a pound of the given count and then subtracting 10 per cent from the result. The yarn diameter in inch is the reciprocal. 

For example:
Find out the diameter of a 46s yarn.

Yards in a pound (840 x 46)
Square root 166.6
Less 10% 177.0
Hence the diameter 1/177 inch
In other words, if 177 threads are laid side by side they occupy one inch
Diameter of yarns vary as the square root of the yarn counts
Thus the diameter of 36s is 1/157 inch
And 16s is 1/104 inch

This can be shortened in a simple equation as bellows

Diameter per inch (cotton/spun silk) = √(yards per pound) - 10%
= 0.9 √yards per pound
= 26.1 √count

This calculation of yarn diameter is very useful particularly in weaving for determining the optimum ends and picks per inch. Intersections of warp ends for weft threads and weft threads for warp have to be carefully considered. This is also useful for finding ends and picks while changing from one count to another, for finding the counts in changing from one number of threads per inch to another number of threads per inch and for finding ends and picks per inch in use and in changing from one pattern to another.

Mathematical problem:

Find out the diameter of 20s count of yarn.

Solution:

Diameter per inch = √ ( yards per pound) - 10%
Here yards per pound = (20 x 840)

So, now

Diameter per inch = √(yards per pound) - 10%
= √ (20 x 840 ) - 10%
= 118 per inch (ANS)