A thousandth of an inch is a derived unit of length in an inch-based system of units. Equal to 1⁄1000 of an inch, it is normally referred to as a thou //, a thousandth, or (particularly in the United States) a mil.
The plural of thou is also thou (thus one hundredth of an inch is "10 thou"), while the plural of mil is mils (thus "10 mils"). The words are shortened forms of the English and Latin words for "thousand" (mille). The US Customary mil can be confused with the millimetre, which is the standard meaning for "mil" or "mils" (plural) in British English and European engineering circles. This can cause problems with spoken dimensions or with those who are not familiar with alternative uses of the term. One US mil is approximately 1/40th of a millimetre at 0.0254 mm, or 25.40 μm.
There are also compound units such as "mils per year" used to express corrosion rates.
In machining, where the thou is often treated as a basic unit, 0.0001 inches can be referred to as "one tenth", meaning "one tenth of a thou". (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.
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 avoid confusion with millimetres. Today both terms are used, but in specific contexts one is traditionally preferred over the other.
1 thou is exactly equal to:
For machinists who need to maintain a continual "horse sense" of relative size, it is useful to have a gut feeling for the following. (Each of these "equivalents" is off by an amount that is negligible for most practical purposes—for example, 2 tenths on a plus-minus-10-thou tolerance. But the point here is horse sense on the fly—quick common-sense mental math to keep oneself oriented when machining and inspecting.)
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, 1⁄2, 1⁄4, 1⁄8, 1⁄16, 1⁄32, 1⁄64). 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 use 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.