Avoid The Wrap: How To Use Math To Estimate Yarn Diameter

Figuring out yarn weight—a term for the thickness or diameter of our yarn—is a pain. No matter which tool you choose to use, you need to be consistent… and if your yarn is fiddly or slippery or soft, then measuring yarn diameter consistently feels impossible. What if I told you that there was another way? A way where you didn’t even need to handle the yarn and that all you needed was some commonly available information and a calculator? Well, let me introduce you to a little math.

Ashenhurst’s Formula for Yarn Diameter

Ashenhurst’s formula for Yarn Diameter was originally developed for industry but it is easy to use at home too.

Here it is:

where, for imperial units:

y = yarn diameter per inch (same as wraps per inch, or ends per inch)
l = length of yarn, in yards
m = weight of yarn, in pounds
d = density adjustment, depending on type of yarn
- for soft yarns, such as woollen yarns, d = 0.85
- for firm yarns, such as worsted yarns, d = 0.90
- for very firm yarns, such as silk, cotton, or linen yarns, d = 0.91

or, for metric units:

y = yarn diameter per centimetres (same as wraps per cm, or ends per cm)
l = length of yarn, in metres
m = weight of yarn, in kilograms
d = density adjustment, depending on type of yarn
- for soft yarns, such as woollen yarns, d = 0.236
- for firmer yarns, such as worsted yarns, d = 0.25
- for very firm yarns, such as silk, cotton, or linen yarns, d =255

As an example, SweetGeorgia Yarns Tough Love Sock, a worsted-spun fingering-weight yarn, comes in skeins of 425 yards, weighing 4 ounces (0.25 pounds).

Depending on how you wrap yarn to measure yarn diameter, you will typically get a lower number than if you use Ashenhurst’s formula to calculate the yarn diameter. It is worth comparing your results using each method for a while to see what that difference is for you. If you wrap your yarn to find yarn weight, like Tabetha Hedrick demonstrates in her recent article on yarn weight over on the SweetGeorgia Yarns blog, you’ll most likely end up with a wraps per inch amount that is about 65–70% of what you would get if you calculated it using the Ashenhurst formula.

Yarn Diameter for Weave Sett

Ashenhurst’s formula for yarn diameter is best thought of as the first step to calculating the maximum weaving sett for a yarn, but since it is so easy to be inconsistent when we use other ways of measuring yarn diameter at home, we can use Ashenhurst’s formula as a consistent baseline. That 65–70% number we get when we wrap just right, when used to find our starting sett, produces a medium-sett cloth with a lovely drape.

weaving cloth to demonstrate yarn diameter — Cotton Ne 20/2 in the warp and as ground weft. Using the formula, Ne 20/2 cotton has a yarn diameter of approximately 82 wraps per inch.

For a balanced plain weave, the number of ends per inch is equal to half the wraps per inch. Using the value for yarn diameters that I calculated above, my maximum plain weave sett for Tough Love Sock is 18.5 ends per inch. For a nice light-to-medium density cloth with drape, say for a woolly scarf or throw blanket for winter (not too much wear and tear, but still quite functional), I would try setting it at 65% of maximum, so 65% x 18.5 epi = 12 epi.

You can find projects, such as the Sock Blank Scarves by Felicia Lo, in the School of SweetGeorgia which use yarns just like this at 12 ends per inch. Have fun exploring and sampling to see what combinations of yarns and set have been used to create different projects.

If the numbers are so different from wrapping, why bother with the formula?

If we know how we wrap, and that it gives us a medium-density cloth (woven or knitted) then we can go up or down in reeds or knitting needles to produce the fabric we want. That is great if you always manage to wrap the yarn the same way when measuring yarn diameter.

Blue and white woven cloth in progress to demonstrate yarn diameter calculations — Cotton Ne 30/2 in the warp and as ground weft. Using the formula, Ne 30/2 cotton has a yarn diameter of approximately 102 wraps per inch.

I personally find it harder to be consistent across different types and sizes of yarn.

Sometimes, our hand dexterity (or eyesight) just isn’t that good.

And sometimes, like for the weaving I was working on recently, the yarn is just too fine. It is hard to wrap the yarn consistently, and count the number of threads without error, when you are dealing with Ne 30/2 cotton!

Using the formula is easy and consistent. I like easy and consistent… don’t you?