Thousandth of an inch

A thousandth of an inch is a derived unit of length in an inch-based system of units. Equal to 0.001 inches, it is normally referred to as a thou /ˈθaʊ/, 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"). Both words come from roots meaning "1000": "thou" from the English "thousand", which is from the Germanic root for 1000, and "mil" from the Romance root for 1000. 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.

Contexts of use

The thou, or mil, is most commonly used in engineering and manufacturing. For example in specifying:

• The thickness of items such as paper, film, foil, wires, paint coatings, latex gloves, plastic sheeting, and fibers
  • For example, most plastic ID cards are about 30 thou (30 mils in US) in thickness.
  • Card stock thickness in the US is usually measured in points or mils that gives the thickness of the sheet in thousandths of an inch.^[1]
• Manufacturing dimensions and tolerances, such as:
  • In the manufacture of automobile engines (A typical example is the thickness of the head gasket, or the amount of material to be removed from the head to adjust the compression ratio of the cylinders.)
  • In the servicing of automobile engines (Typical examples include a spark-plug gap or ignition points gap.)
  • The manufacture of printed circuit boards (PCBs)^[2] (although the component dimensions are now typically provided in millimetres)
  • Tolerance specifications on hydraulic cylinders

There are also compound units such as "mils per year" used to express corrosion rates.^[3]

A related measurement for area known as the circular mil, is based on a circle having a diameter of one mil.

Tenths

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".^[4] (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

The unit is generally referred to as a thou in United States; mil was once the more common term,^[5][6] although as use of the metric system has become common within U.S. industry in recent decades, thou has replaced mil among most technical users to avoid confusion with millimetres,^[5][6][7] and today both terms are used, but in specific contexts one is traditionally preferred over the other. Thus "mil" tends to be used more than "thou" for the thickness of plastic sheet, while "thou" or "thousandths" tends to be used when discussing machined dimensions.

For the last several decades, the term "thou", or "thousandths" has become normal usage, thus avoiding confusion with the metric system. In the manufacturing sector, the term "mills" is used almost exclusively for millimeters; leaving "thou" for widespread US usage.

Equivalence to other units of length

Unit conversions

1 thou is exactly equal to:

• 0.001 international inches (1 international inch is equal to 1,000 thou)
• 0.0254 mm, or 25.4 μm (1 millimetre is about equal to 39.37 thou)

Heuristics

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.)

• 1 tenth is about 2.5 μm.
• 1 μm can be thought of as half a tenth (although a bit smaller, 40 millionths versus 50 millionths).
• 1 mm is about 40 thou.
• A tolerance of ±0.25 mm is about the same as a tolerance of ±10 thou.

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^[8] who wrote in 1857:

...instead of our engineers and machinists thinking in eighths, sixteenths and thirty-seconds of an inch, it is desirable that they should think and speak in tenths, hundredths, and thousandths...^[9]

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 15 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.

See also

• Angular mil
• Circular mil

References