Thousandth of an inch
A thousandth of an inch is a derived unit of length in a system of units using inches. Equal to of an inch, a thousandth is commonly called a thou (used for both singular and plural) or particularly in North America a mil (plural mils). The words are shortened forms of the English and Latin words for "thousand" ( in Latin). In international engineering contexts, confusion can arise because "mil" is a formal unit name in North America but "mil" or "mill" is also a common colloquial clipped form of millimetre. The units are considerably different: a  millimetre is approximately 39 mils. Contexts of use. The thou, or mil, is most commonly used in engineering and manufacturing in non-metric countries. For example, in specifying: There are also compound units such as "mils per year" used to express corrosion rates. A related measurement for area known as the circular mil, is based on a circle having a diameter of one mil. Section::::"Tenths". In machining, where the thou is often treated as a basic unit, can be referred to as "one tenth", meaning "one tenth of a thou" or "one ten thousandth". (The metric comparison is discussed below .) Machining "to within a few tenths" is often considered very accurate, and at or near the extreme limit of tolerance capability in most contexts. Greater accuracy (tolerance ranges inside one tenth) apply in only a few contexts: in plug gauge and gauge block manufacturing or calibration, they are typically expressed in millionths of an inch or, alternatively, in micrometres; in nanotechnology, nanometres or picometres are used. Usage notes on "mil" versus "thou". In the United States, "mil" was once the more common term, but as use of the metric system has become more common, "thou" has replaced "mil" among most  technical users to . Today both terms are used, but in specific contexts one is traditionally preferred over the other. Equivalence to other units of length. Unit conversions. 1 thou is equal to: History of usage. The introduction of the thousandth of an inch as a sensible base unit in engineering and machining is generally attributed to Joseph Whitworth who wrote in 1857: Whitworth's main point was to advocate decimalization in place of fractions based on successive halving; but in mentioning thousandths, he was also broaching the idea of a finer division than had been used previously. Up until this  era, workers such as millwrights, boilermakers, and machinists measured only in traditional fractions of an inch, divided via successive halving, usually only as far as 64ths (1, , , , , , ). Each 64th is about 16 thou. Communication about sizes smaller than a 64th of an inch was subjective and hampered by a degree of ineffability—while phrases such as "scant 64th" or "heavy 64th" were used, their communicative ability was limited by subjectivity. Dimensions and geometry "could" be controlled to high accuracy, but this was done by comparative methods: comparison against templates or other gauges, feeling the degree of drag of calipers, or  simply repeatably cutting, relying on the positioning consistency of jigs, fixtures, and machine slides. Such work could only be done in craft fashion: on-site, by feel, rather than at a distance working from drawings and written notes. Although measurement was certainly a part of the daily routine, the highest-precision aspects of the work were achieved by feel or by gauge, not by measuring (as in determining counts of units). This in turn limited the kinds of process designs that could work, because they limited the degree of separation of concerns that could occur. The introduction of thou as  a base unit for machining work required the dissemination of vernier calipers and screw micrometers throughout the trade, as the unit is too small to be measured with practical repeatability using rules alone. (Most rule markings were far too wide to mark a single mil, and even if such dividing is accomplished, it is illegible to the naked eye, being discernible but not useful for measuring.) During the following half century, such measuring instruments went from expensive rarities to widespread, everyday tools among machinists. Bringing more metrology into machining increased the separation of concerns to make possible, for example, designing  an assembly to the point of an engineering drawing, then having the mating parts made at different firms who did not have any contact with (or even awareness of) each other—yet still knowing with certainty that their products would have the desired fit.