Thousandth of an inch
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A thousandth of an inch is a derived
unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatrical presentation Music * ''Unit'' (alb ...
of
length Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Interna ...
in a system of units using inches. Equal to of an
inch Measuring tape with inches The inch (symbol: in or ″) is a unit of length in the British imperial and the United States customary systems of measurement. It is equal to yard or of a foot. Derived from the Roman uncia ("twelfth") ...
, 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 Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...
and
manufacturing Manufacturing is the creation or production of goods with the help of equipment, labor, machines, tools, and chemical or biological processing or formulation. It is the essence of secondary sector of the economy. The term may refer to a r ...
in non-metric countries. 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 in thickness. ** Card stock thickness in the United States, where mils are also called points. **
Gauge Gauge ( or ) may refer to: Measurement * Gauge (instrument), any of a variety of measuring instruments * Gauge (firearms) * Wire gauge, a measure of the size of a wire ** American wire gauge, a common measure of nonferrous wire diameter, es ...
(diameter) of strings in stringed instruments * Manufacturing dimensions and
tolerances Engineering tolerance is the permissible limit or limits of variation in: # a physical dimension; # a measured value or physical property of a material, manufacturing, manufactured object, system, or service; # other measured values (such as t ...
, such as: ** In the manufacture of older 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 older automobile engines. Typical examples include a spark-plug gap or ignition points gap. ** The manufacture of
printed circuit board A printed circuit board (PCB; also printed wiring board or PWB) is a medium used in Electrical engineering, electrical and electronic engineering to connect electronic components to one another in a controlled manner. It takes the form of a L ...
s (PCBs). However, the component dimensions are now typically provided in
millimetres 330px, Different lengths as in respect to the electromagnetic spectrum, measured by the metre and its derived scales. The microwave is between 1 meter to 1 millimeter. The millimetre (American and British English spelling differences#-re, -er, ...
, because they are sold worldwide. ** Tolerance specifications on
hydraulic cylinder A hydraulic cylinder (also called a linear hydraulic motor) is a mechanical actuator that is used to give a unidirectional force through a unidirectional stroke. It has many applications, notably in construction equipment (engineering vehicles ...
s There are also compound units such as "mils per year" used to express corrosion rates. A related measurement for
area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape A shape or figure is a graphics, graphical representation of an obje ...
known as the
circular mil A circular mil is a unit of area, equal to the area of a circle with a diameter of one mil (one thousandth of an inch or ). It corresponds to approximately . It is a unit intended for referring to the area of a wire with a circular cross sectio ...
, is based on a
circle A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ...
having a
diameter In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for ...
of one mil.


''Tenths''

In
machining Machining is a process in which a material (often metal) is cut to a desired final shape and size by a controlled material-removal process. The processes that have this common theme are collectively called subtractive manufacturing, which utilizes ...
, 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 A go/no-go gauge refers to an inspection tool used to check a workpiece against its allowed tolerances via a go/no-go test. Its name is derived from two tests: the check involves the workpiece having to pass one test (''go'') and fail the other ...
and
gauge block Gauge blocks (also known as gage blocks, Johansson gauges, slip gauges, or Jo 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 ...
manufacturing or calibration, they are typically expressed in millionths of an inch or, alternatively, in micrometres; in
nanotechnology Nanotechnology, also shortened to nanotech, is the use of matter on an atomic, molecular, and supramolecular scale for industrial purposes. The earliest, widespread description of nanotechnology referred to the particular technological goal o ...
,
nanometre 330px, Different lengths as in respect to the molecular scale. The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American and British English spelling differences#-re ...
s or
picometre The picometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: pm) or picometer (American spelling) is a unit of length in the International System of Units (SI), equal to , or one trillionth of ...
s 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 .Mil
a
How Many? A Dictionary of Units of Measurement
by Russ Rowlett

/ref> Today both terms are used, but in specific contexts one is traditionally preferred over the other.


Equivalents in other units of length

1 thou is equal to: * 0.001 international
inch Measuring tape with inches The inch (symbol: in or ″) is a unit of length in the British imperial and the United States customary systems of measurement. It is equal to yard or of a foot. Derived from the Roman uncia ("twelfth") ...
es (1 international inch is equal to 1,000 thou) * 0.0254 mm, or 25.4 μm (1 millimetre is about 39.37 thou)


History of usage

The introduction of the thousandth of an inch as a base unit in engineering and machining is generally attributed to
Joseph Whitworth Sir Joseph Whitworth, 1st Baronet (21 December 1803 – 22 January 1887) was an English engineer, entrepreneur, inventor and philanthropist. In 1841, he devised the British Standard Whitworth system, which created an accepted standard for scr ...
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 ... "A Paper on Standard Decimal Measures of Length", Manchester, 1857
Whitworth's main point was to advocate
decimalization Decimalisation or decimalization (see spelling differences) is the conversion of a system of currency or of weights and measures to units related by powers of 10. Most countries have decimalised their currencies, converting them from non-decimal ...
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. Until then, workers such as
millwright A millwright is a craftsperson or skilled tradesperson who installs, dismantles, maintains, repairs, reassembles, and moves machinery in factories, power plants, and construction sites. The term ''millwright'' (also known as ''industrial mecha ...
s,
boilermaker A boilermaker is a tradesperson who fabricates steel, iron, or copper into boilers and other large containers intended to hold hot gas or liquid, as well as maintains and repairs boilers and boiler systems.Bureau of Labor Statistics, US Dep ...
s, and
machinist A machinist is a tradesperson or trained professional who not only operates machine tools, but also has the knowledge of tooling and materials required to create set ups on machine tools such as milling machines, grinders, lathes, and drilling ...
s in the
Anglosphere The Anglosphere is a group of English-speaking world, English-speaking nations that share historical and cultural ties with England, and which today maintain close political, diplomatic and military co-operation. While the nations included in d ...
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 Ineffability is the quality of something that surpasses the capacity of language to express it, often being in the form of a taboo or incomprehensible term. This property is commonly associated with philosophy, aspects of existence, and similar ...
—while phrases such as "scant 64th" or "heavy 64th" were used, they were imprecise. 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 In computer science, separation of concerns is a design principle for separating a computer program into distinct sections. Each section addresses a separate '' concern'', a set of information that affects the code of a computer program. A concern ...
that could occur. The introduction of the thou as a base unit for machining work required the dissemination of vernier calipers and screw
micrometer Micrometer can mean: * Micrometer (device), used for accurate measurements by means of a calibrated screw * American spelling of micrometre The micrometre ( international spelling as used by the International Bureau of Weights and Measures; ...
s throughout the trade, as the unit is too small to be measured with practical repeatability using
rules Rule or ruling may refer to: Education * Royal University of Law and Economics (RULE), a university in Cambodia Human activity * The exercise of political or personal control by someone with authority or power * Business rule, a rule pert ...
alone. (Most rule markings were far too wide to mark a single mil, and even if such dividing is accomplished, it is unclear to the naked eye, being discernible but not useful for measuring.) During the following half century, such measuring instruments, previously expensive rarities, became widespread, everyday tools among machinists. Bringing more
metrology Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in Fran ...
into machining made possible, for example, designing an assembly in the form of an
engineering drawing An engineering drawing is a type of technical drawing that is used to convey information about an object. A common use is to specify the geometry necessary for the construction of a component and is called a detail drawing. Usually, a number of ...
, then having the mating parts made at different firms who did not have any contact with (or even awareness of) each other—yet still being sure that their products would have the desired fit.


See also

*
Angular mil A milliradian ( SI-symbol mrad, sometimes also abbreviated mil) is an SI derived unit for angular measurement which is defined as a thousandth of a radian (0.001 radian). Milliradians are used in adjustment of firearm sights by adjusting ...
*
Circular mil A circular mil is a unit of area, equal to the area of a circle with a diameter of one mil (one thousandth of an inch or ). It corresponds to approximately . It is a unit intended for referring to the area of a wire with a circular cross sectio ...


References

{{United States Customary Units Imperial units Units of length Decimalisation Customary units of measurement in the United States