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A circular mil is a
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'' (a ...
of
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 or planar lamina, while '' surface area'' refers to the area of an ope ...
, equal to the area of 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 con ...
with 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 fo ...
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 section. As the definition of the unit contains , it is easy to calculate area values in circular mils knowing the diameter in mils. The area in circular mils, , of a circle with a diameter of  mils, is given by the formula: :A = d^2 In Canada and the United States, the Canadian Electrical Code (CEC) and the National Electrical Code (NEC), respectively, use the circular mil to define wire sizes larger than 0000 AWG. In many NEC publications and uses, large wires may be expressed in thousands of circular mils, which is abbreviated in two different ways: kcmil or MCM. For example, one common wire size used in the NEC has a cross-section of 250,000 circular mils, written as 250 kcmil or 250 MCM, which is the first size larger than 0000 AWG used within the NEC. 1000 circular mil equals , so for many purposes, a ratio of 2 MCM ≈ 1 mm2 can be used with negligible (1.3%) error.


Equivalence to other units of area

As a unit of area, the circular mil can be converted to other units such as square inches or square millimetres. 1 circular mil is approximately equal to: * 0.7854 square mils (1 square mil is about 1.273 circular mils) * 7.854 × 10−7 square inches (1 square inch is about 1.273 million circular mils) * 5.067 × 10−10 square metres * 5.067 × 10−4 square millimetres * 506.7 μm 1000 circular mils = 1 MCM or 1 kcmil, and is (approximately) equal to: * 0.5067 mm, so 2 kcmil ≈ 1 mm (a 1.3% error) Therefore, for practical purposes such as wire choice, 2 kcmil ≈ 1 mm is a reasonable rule of thumb for many applications.


Square mils

In square mils, the area of a circle with a diameter of 1 mil is: :A = \pi r^2 = \pi \left( \frac \right) ^2 = \frac = \rm \frac = \frac~mil^2 \approx 0.7854~mil^2 By definition, this area is also equal to 1 circular mil, so: :\rm 1~cmil = \frac~mil^2 The formula for the area of an arbitrary circle in ''circular mils'' can be derived by applying this conversion factor to the standard formula for the area of a circle (which gives its result in square mils). : \begin A &= \pi r^2 = \pi \left( \frac \right) ^2 = \frac~(\text^2)\\ ex &= \frac \times \frac~(\text)\\ ex &= d^2~(\text) \end


Square inches

To equate circular mils with square inches rather than square mils, the definition of a mil in inches can be substituted: : \begin \rm 1~cmil &= \rm \frac~mil^2 = \frac~(0.001~in)^2\\ ex &= \rm \frac~in^2 \approx 7.854 \times 10^~in^2 \end


Square millimetres

Likewise, since 1 inch is defined as exactly 25.4mm, 1mil is equal to exactly 0.0254mm, so a similar conversion is possible from circular mils to square millimetres: : \begin \rm 1~cmil &= \rm \frac~mil^2 = \frac~(0.0254~mm)^2 = \frac~mm^2 \\ ex &= \rm 1.6129\pi \times 10^~mm^2 \approx 5.067 \times 10^~mm^2 \end


Example calculations

A 0000 AWG solid wire is defined to have a diameter of exactly . The cross-sectional area of this wire is:


Formula 1: circular mil

Note: 1 inch = 1000 mils :\begin d &= \rm 0.46~inches = 460~mils \\ A &= d^2 = \rm (460~mil)^2 = 211,600~circular~mils \end (This is the same result as the AWG circular mil formula shown below for n = −3)


Formula 2: square mil

:\begin d &= \rm 0.46~inches = 460~mils \\ r &= = \rm 230~mils \\ A &= \pi r^2 = \rm \pi \times (230~mil)^2 = 52,900 \pi~mil^2 \approx 166,190.25~mil^2 \end


Formula 3: square inch

:\begin d &= \rm 0.46~inches \\ r &= = \rm 0.23~inches \\ A &= \pi r^2 = \rm \pi \times (0.23~in)^2 = 0.0529 \pi \approx 0.16619~in^2 \end


Calculating diameter from area

When large diameter wire sizes are specified in kcmil, such as the widely used 250 kcmil and 350 kcmil wires, the diameter of the wire can be calculated from the area without using : Note: We first convert from kcmil to circular mil :\begin A &= \rm 250~kcmil = 250,000~\text \\ d &= \sqrt \\ d &= \rm \sqrt = 500~mil = 0.500~inches \end Thus, this wire would have a diameter of a half inch or 12.7 mm.


Metric equivalent

Some tables give conversions to circular millimetres (cmm). The area in cmm is defined as the square of the wire diameter in mm. However, this unit is rarely used in practice. One of the few examples is in a patent for a bariatric weight loss device. : \rm 1~cmm = \left( \frac \right) ^2~cmil \approx 1,550~cmil


AWG circular mil formula

The formula to calculate the circular mil for any given AWG ( American Wire Gauge) size is as follows. A_n represents the circular mil area for the AWG size n. :A_n = \left (5 \times 92^\right)^2 For example, a number 12 gauge wire would use n = 12: :\left(5 \times 92^\right)^2 = 6530~\textrm Sizes with multiple zeros are successively larger than 0AWG and can be denoted using "number of zeros/0"; for example "4/0" for 0000AWG. For an m/0AWG wire, use :n = -(m - 1) = 1 - m in the above formula. For example, 0000AWG (4/0AWG), would use n = -3; and the calculated result would be 211,600 circular mils.


Standard sizes

Standard sizes are from 250 to 400 in increments of 50kcmil, 400 to 1000 in increments of 100kcmil, and from 1000 to 2000 in increments of 250kcmil.
NFPA 70-2011 National Electrical Code 2011 Edition
''. Table 310.15(B)(17) page 70-155, ''Allowable Ampacities of Single-Insulated Conductors Rated Up to and Including 2000 Volts in Free Air, Based on Ambient Air Temperature of 30°C (86°F)''.
The diameter in the table below is that of a solid rod with the given conductor area in circular mils. Stranded wire is around 5% larger in diameter to allow for gaps between the strands, depending on the number and size of strands. ''Note: For smaller wires, consult .''


See also

*
Thou (length) A thousandth of an inch is a derived unit of length in a system of units using inches. Equal to of an inch, a thousandth is commonly called a thou (used for both singular and plural) or particularly in North America a mil (plural mils). The ...
*
Square mil A square mil is a unit of area, equal to the area of a square with sides of length one mil. A mil is one thousandth of an international inch. This unit of area is usually used in specifying the area of the cross section of a wire or cable. Equi ...
* Wire gauge comparison chart *
IEC 60228 IEC 60228 is the International Electrotechnical Commission (IEC)'s international standard on ''conductors of insulated cables''. the current version is Third Edition 2004-11 Among other things, it defines a set of standard wire cross-sectional a ...
, the metric wire-size standard used in most parts of the world. * American Wire Gauge (AWG), used primarily in the US and Canada * Standard Wire Gauge (SWG), the British imperial standard BS3737, superseded by the metric. *
Stubs Iron Wire Gauge The Birmingham gauge is a wire gauge system, and is also used to specify thickness or diameter of hypodermic needles and tube products. Terminology Birmingham gauge is also known as the Stubs Iron Wire Gauge or Birmingham Wire Gauge. It is not t ...
*
Jewelry wire gauge Jewelry wire is wire, usually copper, brass, nickel, aluminium, silver, or gold, used in jewelry making. Wire is defined today as a single, usually cylindrical, elongated strand of drawn metal. However, when wire was first invented over 2,000 ye ...
*
Body jewelry sizes Body jewelry sizes express the thickness of an item of body jewelry, using one of several possible systems. Background Items of body piercing jewelry have an important common factor: the diameter of the part of the item of jewelry where it will ...
* Electrical wiring *
Number 8 wire Number 8 wire is a gauge of wire on the British Standard Wire Gauge that has entered into the cultural lexicon of New Zealand. Use for farm fencing Early farm fences in New Zealand were generally used to protect crops, gardens, and orchards fr ...
, a term used in the New Zealand vernacular


References

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