FAT QUARTER: MEASURES: 18X21" INCHES
A fat quarter of fabric is a half of a half yard. A regular quarter of fabric is a 1/4 yard piece measuring 9 inches by 44 inches. The larger dimension in each case varies if the fabric is not 44 inches wide.Many crafters find fat quarters easier to handle and store than regular quarters. Fat quarters are often used for sampler quilts and scrap quilts and may be more versatile for patchwork and appliqué.

HALF YARD - MEASURES: 18X44"
1 YARD - MEASURES: 36X44"
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Fabric is usually measured by the yard.
How much is a yard of fabric? Your quick conversion is:
1 yard = 3 feet = about 90 cm ​This means that when you buy a yard of fabric you’re getting 1 yard x the width of the fabric (usually measured in inches).
The most common widths of fabrics are 36″, 45″, 54″, 60″, 72″, and 118″.
Be sure you know what the usuable widths are as some fabrics have borders. Usable widths are usually 1-2 inches less than the full width, though in some cases the entire width is usable.
You can also estimate a yard of fabric by holding one end of the fabric to your chin while fully extending your other arm which should hold the other end of the fabric.