Derived weight is the average weight per area measure within a roll of fabric. In the United States this is most commonly expressed in ounces or grams per square yard. It is calculated by weighing a roll of fabric and subtracting out the weight of the core. This net weight is then divided by the number of square yards of fabric on the roll. Squared yards is calculated by measuring the width of the roll in inches, dividing by 36 to convert to yards and them multiplying by the length of the roll in yards.
Here is an example:
The roll weighs 717 lbs. We know the core weighs 4.7 lbs. Subtracting we get the net weight which is 712.3 lbs. From the counter on the winder, we know the roll is 650 yards long. We measure the roll and it is 58.5 inches wide. We divide 58.5 by 36 inches per yard and we find the roll is 1.625 yards wide. Multiply the width in yards by the length in yards and we come up with 1,056.25 square yards of fabric on the roll. Convert the pounds the roll weighs (712.3) to ounces by multiplying by 16 since there are 16 ounces in a pound. This gives us 11,396.8 ounces. Divide by the square yards and we come up with a derived weight of 10.79 ounces per square yard.
Note that this is an average weight. There could be variations within the roll. Calculating the derived weight roll to roll gives a good indication how accurately the machine is maintaining its weight setting.