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You have possibly heard the term "Fat Quarter" or even "Fat Eighth." This has nothing to do with the weight of the fabric (or of a person!). These are simply one of the ways in which quilting fabric is cut and sold in 1/4 and 1/8 yards (actually, this is the measurement used in the U.S. and Canada. Other countries use the metric system).
Fabric comes rolled in bolts. Usually 100% cotton fabric (the fabric of choice of quilters) measures between 40 to 44 inches wide (approx. 112 cm). A yard of fabric, therefore, would measure 36" x 40", a 1/2 yard cut would measure 18" x 40", a 1/4 yard would measure 9" x 40", and an 1/8 yard would measure 4 1/2" x 40". A Fat Quarter (FQ) is a fourth of a yard of fabric (where the yard measures 36" x 40") cut in half both lengthwise and widthwise to yield four pieces measuring 18" x 20". A Fat Eighth (FE) is a FQ cut in half (9" x 20" or 18" x 10").
Pieces of fabric cut in this way in 1/8, 1/4, and 1/2 a yard are better for many quilting uses than if cut the whole width of the fabric. Let's say, for example, that you need a 16-inch square of fabric. Normally you would have to purchase 1/2 a yard and would have quite a bit left over. There is a lot less waste with a FQ. In addition, specialized fabric and quilting stores in the U.S. and Europe sell pre-cut bundles of these fabric cuts, to such a point that it is a common reference among quilters.