Fabric Weight from Construction — GSM

The weight of a square metre of woven cloth is nothing but bookkeeping, provided the bookkeeping is done in consistent units. Take one square metre. It contains $n_1$ warp threads per metre of width, each running the full metre of length — except that each one is longer than a metre, because it waves over and under the picks. Each of those metres of yarn weighs $\rho_1$ kilograms. So the warp contributes $n_1 \rho_1 (1+c_1)$ kilograms per square metre, and the weft contributes the same thing with its own numbers. Add them.

\[ G = n_1 \rho_1 (1 + c_1) + n_2 \rho_2 (1 + c_2) \]

The dimensions come out exactly, which is why this page can be trusted across unit systems. Threads per metre is a reciprocal length; kilograms per metre is a linear density; multiply and you have kilograms per square metre, an areal density, with no conversion factor anywhere to be dropped or doubled. That is the reason this site types thread density as a wavenumber rather than as a bare count: enter the sett in ends per inch and the count in tex and the units engine sorts out the inch and the kilometre for you, and the answer is right in both systems.

The crimp terms multiply UP, and this is the sign error that ruins the calculation. A metre of finished cloth contains more than a metre of each yarn, never less, because the yarn takes the long way round its crossing threads. Ignoring crimp altogether under-reports the weight by however many per cent the crimp is — for the mid-weight denim in the anchors, about 20 g/m² out of 319. Worse, if the supplier quoted take-up rather than crimp and it was entered as if it were crimp, the answer is wrong by the difference between the two, which is small in ordinary cloth and large in a heavily crimped one. Convert first.

The ounce weight the North American trade quotes is the same number in different units, and the conversion is exact because both the ounce and the yard are defined exactly: 1 oz/yd² = 33.905 747 474 882 3 g/m². So a 319 g/m² denim is a 9.4 oz denim, and the familiar 12 oz, 14 oz and 16 oz weights are 407, 475 and 543 g/m². Two cautions on that trade usage. Some suppliers quote ounces per linear yard rather than per square yard, which depends on the width of the piece and is therefore not a fabric property at all. And "12 oz denim" is usually a finished, conditioned weight.

Which brings up what this equation does not include. It gives the greige weight from construction. A finished cloth also carries whatever the finishing route added or removed: warp size, which is put on before weaving and taken off in desizing; resin, softener, flame retardant, water repellent; the mass lost in singeing, scouring and mercerizing; and the moisture the atmosphere puts back, which for cotton at standard conditions is several per cent of the whole. Expect the scale to disagree with the calculation by a few per cent in either direction, condition the specimen before weighing it, and treat a large discrepancy as a question about the specification rather than about the arithmetic — a count entered in denier where tex was meant is a factor of nine, and shows up immediately.