Thousandth of an inch

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Thousandth of an inch
1 thou in ...... is equal to ...
    imperial and US customary systems   0.001  in
    SI units    25.4  μm

A thousandth of an inch is a derived unit of length in a system of units using inches. Equal to 11000 of an inch, a thousandth is commonly called a thou /ˈθ/ (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" (mille). In international engineering contexts, confusion can arise from the fact that mil is a formal unit name in North America but mil or mill is also a common colloquial clipped form of millimetre. [1] 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. [5]

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


In machining, where the thou is often treated as a basic unit, 0.0001 inches (2.54 micrometres ) can be referred to as "one tenth", meaning "one tenth of a thou" or "one ten thousandth". [6] (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, [7] [8] but as use of the metric system has become more common, thou has replaced mil among most technical users to avoid confusion with millimetres. [7] [8] [9] 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 [10] 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... [11]

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, 12, 14, 18, 116, 132, 164). 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.

See also

Related Research Articles

Inch Unit of length

The inch is a unit of length in the (British) imperial and United States customary systems of measurement. It is equal to ​136 yard or ​112 of a foot. Derived from the Roman uncia ("twelfth"), the word inch is also sometimes used to translate similar units in other measurement systems, usually understood as deriving from the width of the human thumb.

Litre Unit of volume

The litre or liter is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metre (m3). A cubic decimetre occupies a volume of 10 cm × 10 cm × 10 cm and is thus equal to one-thousandth of a cubic metre.


The micrometre or micrometer, also commonly known as a micron, is an SI derived unit of length equalling 1×10−6 metre ; that is, one millionth of a metre.

A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The prefix kilo-, for example, may be added to gram to indicate multiplication by one thousand: one kilogram is equal to one thousand grams. The prefix milli-, likewise, may be added to metre to indicate division by one thousand; one millimetre is equal to one thousandth of a metre.

United States customary units System of units of measurement commonly used in the United States

United States customary units are a system of measurements commonly used in the United States since it was formalized in 1832. The United States customary system developed from English units which were in use in the British Empire before the U.S. became an independent country. The United Kingdom's system of measures was overhauled in 1824 to create the imperial system, which was officially adopted in 1826, changing the definitions of some of its units. Subsequently, while many U.S. units are essentially similar to their imperial counterparts, there are significant differences between the systems.


A micrometer, sometimes known as a micrometer screw gauge, is a device incorporating a calibrated screw widely used for accurate measurement of components in mechanical engineering and machining as well as most mechanical trades, along with other metrological instruments such as dial, vernier, and digital calipers. Micrometers are usually, but not always, in the form of calipers. The spindle is a very accurately machined screw and the object to be measured is placed between the spindle and the anvil. The spindle is moved by turning the ratchet knob or thimble until the object to be measured is lightly touched by both the spindle and the anvil.

Millimetre Unit of length 1/1000 of a metre

The millimetre or millimeter is a unit of length in the metric system, equal to one thousandth of a metre, which is the SI base unit of length. Therefore, there are one thousand millimetres in a metre. There are ten millimetres in a centimetre.


A machinist is a tradesperson or trained professional, who not only operates machine tools, but has the knowledge of tooling and materials required to create set ups on machine tools including, but not limited to milling machines, grinders, lathes, and drilling machines.

Unit of length Reference value of length

A unit of length refers to any arbitrarily chosen and accepted reference standard for measurement of length. The most common units in modern use are the metric units, used in every country globally. In the United States the U.S. customary units are also in use. British Imperial units are still used for some purposes in the United Kingdom and some other countries. The metric system is sub-divided into SI and non-SI units.

Tape measure Flexible ruler used to measure size or distance

A tape measure or measuring tape is a flexible ruler used to measure size or distance.

Feeler gauge

A feeler gauge is a tool used to measure gap widths. Feeler gauges are mostly used in engineering to measure the clearance between two parts.

Calipers Tool to measure dimensions of an object

A caliper is a device used to measure the dimensions of an object.

Indicator (distance amplifying instrument) Distance amplifying instrument

In various contexts of science, technology, and manufacturing, an indicator is any of various instruments used to accurately measure small distances and angles, and amplify them to make them more obvious. The name comes from the concept of indicating to the user that which their naked eye cannot discern; such as the presence, or exact quantity, of some small distance.

Gauge block A system for producing precision lengths by stacking components

Gauge blocks are a system for producing precision lengths. The individual gauge block is a metal or ceramic block that has been precision ground and lapped to a specific thickness. Gauge blocks come in sets of blocks with a range of standard lengths. In use, the blocks are stacked to make up a desired length.

Drill bits are the cutting tools of drilling machines. They can be made in any size to order, but standards organizations have defined sets of sizes that are produced routinely by drill bit manufacturers and stocked by distributors.

Wire gauge

Wire gauge is a measurement of wire diameter. This determines the amount of electric current a wire can safely carry, as well as its electrical resistance and weight.

Circular mil Unit of area

A circular mil is a unit of area, equal to the area of a circle with a diameter of one mil. It corresponds to approximately 5.067×10−4 mm2. It is a unit intended for referring to the area of a wire with a circular cross section. As the definition of the unit contains π, it is easy to calculate area values in circular mils knowing the diameter in mils.

Standard wire gauge imperial unit for wire diameters, as defined in British Standard 3737

British Standard Wire Gauge is a unit for denoting wire size given by BS 3737:1964. It is also known as the Imperial Wire Gauge or British Standard Gauge. Use of SWG sizes has fallen greatly in popularity, but is still used as a measure of thickness in guitar strings and some electrical wire. Cross sectional area in square millimetres is now the more usual size measurement for wires used in electrical installation cables. The current British Standard for metallic materials such as wire and sheet is BS 6722:1986, which is a solely metric standard.

The distinction between real value and nominal value occurs in many fields. From a philosophical viewpoint, nominal value represents an accepted condition, which is a goal or an approximation, as opposed to the real value, which is always present.

Sweden decided to adopt the metric system in 1876. After a ten-year transition period starting 1879, usage of legacy units were outlawed by the beginning of 1889.


  1. Oxford English Dictionary , 3rd edition, March 2002, s.v. mill8
  2. "Paper weight comparison and more". Micro Format. Retrieved 2016-01-18.
  3. "Guitar Strings". FaChords Guitar. July 2020. Retrieved 2020-07-31.
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  5. "Corrosion Rate Conversion",
  6. "...the smallest move of one-tenth (not 0.1 but 0.0001 of an inch)...", Dan Nelson, The CNC Toolbox, p89
  7. 1 2 Mil at How Many? A Dictionary of Units of Measurement by Russ Rowlett
  8. 1 2 University of Queensland: PCB design FAQ
  9. Thou at How Many? A Dictionary of Units of Measurement by Russ Rowlett
  10. Edkins, Jo. "Small units". Imperial Measures of Length. Jo Edkins. Retrieved 2009-09-23.
  11. "A Paper on Standard Decimal Measures of Length", Manchester, 1857