Getting to yarn diameter…
We get some measure of the yarn’s thickness from the manufacturer. Yarn thickness is usually given by its grist (yard per pound (ypp), meters per kilogram (m/kg), etc.). As far as sett is concerned, the relevant information is the yarn diameter, as well as various other yarn characteristics that are harder to quantify: how much it compresses and fluffs up, how stiff it is…
But we can get a handle on yarn diameter.
Calculating yarn diameter: the Ashenhurst formula
The Ashenhurst formula uses the grist of the yarn (here, yards per lbs, or ypp) to calculate the number of diameters per inch for the yarn:
#diam/inch = CF x √(ypp),
with the correction factor CF as follows:
CF = 0.92 for silk, cotton and linen yarns
CF = 0.9 for worsted wool
CF = 0.85 for woolen wool
(worsted and woolen describing the type of fiber preparation before spinning).
Estimating yarn diameter: wrapping the yarn
The idea is to wrap the yarn around a ruler or a special device, and to count how many wraps are needed to cover one inch.
The number of wraps is sensitive to how tight the yarn is wound around the ruler, among other things, and is likely to differ from weaver to weaver.
It is not very practical for fine yarns.