25.4 micrometers!
A thou is a unit of length equal to one thousandth of an inch: exactly 25.4 micrometers, or 0.0254 millimeters. A micrometer is a millionth of a meter. The same unit is also called a mil. In the United States it is used to measure the thickness of thin materials, such as plastic sheeting, and the width of wires.
Since 1959, the inch has been exactly 25.4 millimeters. That year, a notice in the U.S. Federal Register fixed the foot at exactly 0.3048 meters, which is 12 inches of 25.4 millimeters each. A thou is a thousandth of an inch, so it is exact too: 25.4 micrometers.
The National Institute of Standards and Technology (NIST), which keeps the measurement standards of the United States, lists the unit under the name mil. It defines 1 mil as exactly 0.001 inch, which is 0.0254 millimeters or 25.4 micrometers. The name mil comes from the Latin word millesimus, meaning "thousandth", and has been recorded in English since the early 1700s. A mil is not a millimeter, which is about 39 thou.
NIST notes that the mil is traditionally used by some U.S. industries to measure thickness. Plastic sheeting is one example.
Guidelines from the U.S. Department of Housing and Urban Development for working safely around old lead paint recommend plastic sheeting 6 mil thick, about 0.15 millimeters. The U.S. Environmental Protection Agency sets no thickness of its own for that work. It requires only that the sheeting keep dust in and not tear.
Wires are measured in thousandths of an inch too. The area of a wire's cut end, its cross-section, is given in circular mils. One circular mil is the area of a circle 1 mil across, about 0.0005 square millimeters.