Yarn Count Conversion — Direct and Indirect Systems

There are two ways to say how fine a yarn is, and they run in opposite directions. A direct system states mass per unit length — tex, decitex, denier — so the number gets bigger as the yarn gets coarser. An indirect system states length per unit mass — English cotton count $N_e$, metric count $N_m$, worsted $N_w$, linen lea — so the number gets bigger as the yarn gets finer. Multiply one by the other and the lengths and masses cancel, leaving a constant fixed entirely by which hank length and which unit of mass the system was built on. That constant is $K$, and $\rho_L = K/N$ is the whole of the conversion.

The indirect systems are historical accidents preserved in amber. English cotton count is 840-yard hanks per pound, because the cotton trade's reel made a hank of seven leas of 120 yards. Worsted is 560-yard hanks per pound. Linen lea is 300 yards per pound. Metric count is the one sane member of the family: kilometres per kilogram, so $N_m \times \mathrm{tex} = 1000$ exactly and there is nothing to remember.

Every one of the other constants is an exact rational, and the trade rounds all of them. The yard has been exactly 0.9144 m since 1959 and the pound exactly 453.59237 g, so the cotton constant is not measured, it is computed:

\[ N_e \times \mathrm{tex} = \frac{453.59237 \times 1000}{840 \times 0.9144} = \frac{453592.37}{768.096} = \frac{32399455}{54864} = 590.541\,247\,448\,235\,6\ldots \]

an infinite decimal. The others follow from the hank lengths alone, as exact whole-number ratios: worsted hanks are 560 yd against cotton's 840, so $N_w = 1.5\,N_e$ exactly and $N_w \times \mathrm{tex} = 885.811\,871\,2$; linen hanks are 300 yd, so lea $= 2.8\,N_e$ and lea $\times\,\mathrm{tex} = 1653.515\,492\,9$. Two further conversions fall out of the same arithmetic and are worth memorising: $\mathrm{denier} \times N_e = 5314.871\,227$, published everywhere as 5315, and $N_m / N_e = 1.693\,361\,817$, published as 1.693.

Now the classic mistake, and it is a mistake about precision rather than about arithmetic. A great many references print the cotton constant as 590.5410. That is not a rounding of 590.5412474 — it is wrong in the seventh figure, and it is offered with a confidence no count measurement can support. A yarn count comes from weighing a skein reeled off a wrap reel at a stated tension in a conditioned atmosphere, and it is good to something like a part in a thousand on a careful day. Four significant figures is generous; 590.5 is honest. The right practice is the one this site follows: carry the exact rational inside the arithmetic, where it costs nothing, and quote four figures outside it, where the extra digits would be a claim you cannot back.

The second classic mistake is direction. Coarse is a big tex and a small $N_e$, and a spinner who has spent a career in one system reads the other backwards for about a week. Two landmarks fix it: 20 tex is roughly $N_e$ 30, a shirting yarn; 100 tex is roughly $N_e$ 6, a denim warp. If a conversion moves a number the wrong way, it is this that went wrong, not the constant.