Fabric Cover Factor — Warp and Weft Combined

Cover factor answers the plainest question anyone asks about a woven cloth: how much of it is thread and how much is hole? Hold it up to a window and you are measuring cover. It decides whether a fabric is a sheer, a shirting or a sailcloth; it governs air permeability, opacity, wind resistance and how much dye the piece will drink; and it is the single number a cloth designer sets first.

The equation looks like an arbitrary correction with a mysterious 28 in it. It is neither. The 28 is the same 28 as in the yarn-diameter rule, and the whole formula is inclusion–exclusion. Here is the derivation, which is the most useful thing on this page.

Start with one thread system alone — say the warp. The fraction of the cloth's width that is covered by warp is simply the thread diameter divided by the thread spacing, $d/p$. The spacing is the reciprocal of the sett: $p = 1/n$ inches for $n$ ends per inch. The diameter is the old rule, $d = 1/(28\sqrt{N_e})$ inches. So

\[ \text{fractional cover} = \frac{d}{p} = \frac{n}{28\sqrt{N_e}} = \frac{K_1}{28}, \qquad K_1 \equiv \frac{n}{\sqrt{N_e}} . \]

That single line does two things at once. It shows where the cover factor $K_1 = n/\sqrt{N_e}$ comes from — it is not a definition someone invented, it is diameter over spacing with the diameter substituted out — and it shows that $K_1 = 28$ is complete cover. The cover factor is fractional cover written on a scale of 0 to 28 instead of 0 to 1, and the 28 in it is the reciprocal of the constant in the diameter rule, because that is literally where it came from.

Now lay the two systems on top of one another. Let $a = K_1/28$ be the fraction covered by warp and $b = K_2/28$ the fraction covered by weft. If the two are independent, the fraction covered by either is $a + b - ab$ — you add them and subtract the overlap, which would otherwise be counted twice. Substituting and multiplying through by 28:

\[ \frac{K}{28} = \frac{K_1}{28} + \frac{K_2}{28} - \frac{K_1 K_2}{28^{2}} \quad\Longrightarrow\quad K = K_1 + K_2 - \frac{K_1 K_2}{28}. \]

The equation on the page, derived rather than asserted, with the 28 in the last term being the same 28 twice cancelled once. Read the answer as a percentage of complete cover by dividing by 28: under about 55% is a voile or a scrim, 55 to 80% an ordinary shirting or sheeting, 80 to 95% a firm poplin or drill, and above that you are at the practical weaving limit.

Now the error this page exists to correct. The metric statement of the same argument uses the tex diameter relation instead, and it produces a different ceiling: fractional cover $= (\text{threads per cm} \times \sqrt{\mathrm{tex}})/267$, so the tex cover factor $K_{\mathrm{tex}} = (\text{threads/cm})\sqrt{\mathrm{tex}}/10$ reaches complete cover at 26.7 rather than 28. Both numbers are real. They are not the same number and they do not do the same job, and confusing them is one of the most repeated mistakes in the field: "$K_{\mathrm{tex}} = 26.7 \times K_{\text{english}}$" is wrong. The 26.7 is a ceiling, the analogue of the 28. The conversion between the two cover factors is

\[ K_{\mathrm{tex}} = 0.9567 \times K_{\text{english}}, \]

a difference of 4.3%, and the 0.9567 is the same $\sqrt{590.5412}/25.4$ that converts twist factors — necessarily, since both quantities are "sett over the square root of the count" rebuilt in the other system. If a cover calculation comes out a few per cent adrift from a measured one, check this before anything else.

Three limitations to keep the number honest. The geometry assumes flat, circular, non-overlapping threads, so cloths woven past jamming — where the threads deform and ride out of plane — can exceed 28 in reality while the equation says they cannot. The formula knows nothing about weave: a plain cloth, a twill and a satin at identical cover factors have quite different appearance and drape, because a satin's long floats let the threads pack closer. And cover moves in finishing, since shrinkage, compacting and calendering all change the sett of the cloth you started with.