Thou (length)

1 thou =

SI units
25.4×10^−6 m	25.40 μm
US customary / Imperial units
83.3×10^−6 ft	1.00×10^−3 in

A thou ( /ˈθaʊ/), also known as a mil, is the verbalized abbreviation for "thousandth(s) of an inch." It is a unit of length equal to 0.001 inch.

The plural of thou is also thou; e.g., a measurement of one hundredth of an inch is written as 10 thou, while the plural of mil is mils. The th in thou is pronounced as in thousand, /ˈθaʊ/, unlike the pronoun thou, /ðaʊ/, where the th is pronounced as in that.

The introduction of the thou in 1844 is generally attributed to Joseph Whitworth.

Both words come from roots meaning "10³": "thou" from the English "thousand", which is from the Germanic root for 1000, and "mil" from the Romance root for 1000.

Contexts of use

The thou (or mil) is sometimes used in engineering, machining, and in the specification of:

• The thickness of items such as paper, film, foil, wires, paint coatings, latex gloves, plastic sheeting, and fibers
• 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)
  • Tolerance specifications on hydraulic cylinders

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

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

In machining

In machining, it is common to work to positions with accuracies of one thou, several thou, or even a fraction of a thou. One tenth of a thou is one ten-thousandth of an inch (0.0001 inch). Because machinists often think in terms of the thou as the "base unit" in their context, it follows that they call 0.0001 inches "one tenth", meaning "one tenth of a thou". Machining "to within a few tenths" is usually considered very accurate, with a few exceptions. This level of accuracy is more common in tool and die work than in production or MRO work. Gagemakers' tolerances, such as for gauge blocks or pins, are a somewhat special realm, being typically from 0.2 tenths (most expensive class) to 2 tenths (workshop grade), which is one to two orders of magnitude smaller than typical production tolerances. However, in recent decades production tolerances for many parts have been trending downward, and production-run tolerance ranges of 2 tenths are no longer rare.

When machinists speak to each other (or think to themselves silently or subvocally) with thou in mind as the base units, one naturally hears, for example, "seven-fifty", "five-ten", and "six-twenty-five" in speech, meaning 0.750 (three-quarters of an inch, ³⁄₄ inch), 0.510 (a bit over a half inch), and 0.625 (five-eighths of an inch, ⁵⁄₈ inch). It is standard practice in inch-unit machining to omit the leading zero before the decimal point, although not in metric-unit machining. Thus .750, .510, and .625. For measurements under 100 thou, the leading zero after the decimal point is said aloud (or, in one's own head, thought explicitly) to prevent confusion. For example, 0.093 is spoken as "oh-ninety-three" (or "aught-ninety-three"; it corresponds to ³⁄₃₂ inch as a fraction); "oh-sixty-two" is 0.062 (¹⁄₁₆ inch). The "oh" for leading zero is important especially because the common engineering drawing convention of expressing tolerances by number of decimal places (in other words, significant figures) yields, for example, 1.30 meaning "one and three hundred [1.300]", which, being "one point thirty", could easily be confused with "one and thirty" or "one and oh-thirty", which is quite different [1.030]. Familiarity with decimal-fraction equivalents is helpful not only in general but also specifically because one can cross-check oneself and force the numbers to "sink in" mentally, making sure that the dimension figures are visualized spatially and do not remain mere forgettable abstractions. For example, in the 1.30 / 1.03 example, one visualizes the shapes and prevents mistakes in several ways: (1) by saying/thinking "one point oh-thirty" instead of "one and thirty" or "one point oh three"; or "one point three hundred" instead of "one point thirty"; and (2) by also noting parenthetically "one and a thirty-second" (1 ¹⁄₃₂, corresponding to 1.03 in decimal with sig figs) versus "one and five-sixteenths" (1 ⁵⁄₁₆, corresponding [as a nominal, at least] to 1.30 in decimal with sig figs).

The metric analog of thou and tenths [referring back to the inch] is hundredths and microns [referring back to the millimeter]. (The name "micron" is now deprecated by SI in favor of "micrometre", but "micron" is still commonly heard in industry.) This metric "scale of thinking" represents slightly smaller distances than does the corresponding inch-based scale of thinking (thou and tenths). Therefore, machining in metric units is occasionally preferred to working in thou for extremely precise work. But there are other factors involved in deciding which one is used in any particular case, and this difference rarely matters. On CNC machine tools, all linear motion is based on the minimum increment of the control system, which is either one "micron" (one micrometre, 0.001 mm) or one "tenth" (0.0001 inch). The metric standard widely prevails today, both because it is physically smaller and because SI prevails in measurement worldwide, and globalized manufacturing uses ISO standards as its benchmarks. But the control allows the user to work in either system, because the computer does the unit conversions automatically (rounded to the nearest minimum increment).

Usage notes on mil versus thou and thousandths

Some sources say that the usual term has been mil in the United States, whereas thou has been more common elsewhere. These sources say that as use of the metric system became more common thou has begun to replace mil among some technical users to avoid confusion with millimeters.

This usage transition, if it was still unfinished 20 years ago, is certainly quite advanced nowadays. Regarding usage today within U.S. industry, it is accurate to say that both terms are used, but that in specific contexts one is preferred over the other. Thus "mil" tends to be used more than "thou" for the thickness of plastic sheet (e.g., "buy some 20-mil sheet"), while "thou" or "thousandths" tends to be used by machinists when discussing machined dimensions (e.g., "take another 8 thousandths off this face"). In the latter sense it is now quite unusual to hear "mil". The reason cited above is probably the driving factor in this usage shift.

Equivalence to other units of length

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 millimeter is about equal to 39.37 thou)

The most common thickness of most plastic ID cards, 30 thou (30 mils in US), is equal to 0.03 inches (0.76 mm).

See also

• Angular mil