Circular mil
circular mil | |
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General information | |
Unit of | Area |
Symbol | cmil |
Derivation | 1 cmil =π/4(0.001 in)2 |
Conversions | |
1 cmilin... | ... is equal to... |
SI units | 506.7075 μm2 |
FPS units | 7.853982×10−7in2 |
Acircular milis aunitofarea,equal to the area of acirclewith adiameterof onemil(one thousandth of an inch or0.0254 mm). It corresponds to approximately5.067×10−4mm2.It is a unit intended for referring to the area of a wire with a circular cross section. As the definition of the unit containsπ,it is easy to calculate area values in circular mils when the diameter in mils is known.
The area in circular mils,A,of a circle with a diameter ofdmils, is given by the formula:
In Canada and the United States, theCanadian Electrical Code(CEC) and theNational Electrical Code(NEC), respectively, use the circular mil to define wire sizes larger than 0000AWG.In many NEC publications and uses, large wires may be expressed in thousands of circular mils, which is abbreviated in two different ways:kcmil[1]orMCM.[2]For example, one common wire size used in the NEC has a conductor diameter of 0.5 inches, or 500 mils, and thus a cross-section ofcircular 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 approximately0.5067 mm2,so for many purposes, a ratio of 2 MCM ≈ 1 mm2can be used with negligible (1.3%) error.
Equivalence to other units of area
[edit]As a unit of area, the circular mil can be converted to other units such as square inches or square millimetres.
1 circular milis approximately equal to:
- 0.7854 square mils (1 square mil is about 1.273 circular mils)
- 7.854 × 10−7square inches (1 square inch is about 1.273 million circular mils)
- 5.067 × 10−10square metres
- 5.067 × 10−4square millimetres
- 506.7 μm2
1000 circular mils= 1 MCM or 1 kcmil, and is (approximately) equal to:
- 0.5067 mm2,so 2 kcmil ≈ 1 mm2(a 1.3% error)
Therefore, for practical purposes such as wire choice, 2 kcmil ≈ 1 mm2is a reasonable rule of thumb for many applications.
Square mils
[edit]In square mils, the area of a circle with a diameter of 1 mil is:
By definition, this area is also equal to 1 circular mil, so:
The formula for the area of an arbitrary circle incircular milscan be derived by applying this conversion factor to the standard formula for the area of a circle (which gives its result in square mils).
Square inches
[edit]To equate circular mils with square inches rather than square mils, the definition of a mil in inches can be substituted:
Square millimetres
[edit]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:
Example calculations
[edit]A 0000 AWG solid wire is defined to have a diameter of exactly 0.46 inches (11.68 mm). The cross-sectional area of this wire is:
Formula 1: circular mil
[edit]Note: 1 inch = 1000 mils
(This is the same result as the AWG circular mil formula shown below forn= −3)
Formula 2: square mil
[edit]Formula 3: square inch
[edit]Calculating diameter from area
[edit]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 usingπ:
We first convert from kcmil to circular mil
Thus, this wire would have a diameter of a half inch or 12.7 mm.
Metric equivalent
[edit]Some tables give conversions to circular millimetres (cmm).[3][4]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.[5]
AWG circular mil formula
[edit]The formula to calculate the area in circular mil for any given AWG (American Wire Gauge) size is as follows.represents the area of numberAWG.
For example, a number 12 gauge wire would use:
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/0AWG wire, use
- in theabove formula.
For example, 0000AWG (4/0AWG), would use;and the calculated result would be 211,600 circular mils.
Standard sizes
[edit]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.[6]
The diameter in the table below is that of a solid rod with the given conductor area in circular mils. Stranded wire is larger in diameter to allow for gaps between the strands, depending on the number and size of strands.
Area | Diameter | NECcopper wire ampacitywith 60/75/90 °C insulation (A)[7] | ||||
---|---|---|---|---|---|---|
(kcmil, MCM) |
(mm2) | (in) | (mm) | |||
250 | 126.7 | 0.500 | 12.70 | 215 | 255 | 290 |
300 | 152.0 | 0.548 | 13.91 | 240 | 285 | 320 |
350 | 177.3 | 0.592 | 15.03 | 260 | 310 | 350 |
400 | 202.7 | 0.632 | 16.06 | 280 | 335 | 380 |
500 | 253.4 | 0.707 | 17.96 | 320 | 380 | 430 |
600 | 304.0 | 0.775 | 19.67 | 355 | 420 | 475 |
700 | 354.7 | 0.837 | 21.25 | 385 | 460 | 520 |
750 | 380.0 | 0.866 | 22.00 | 400 | 475 | 535 |
800 | 405.4 | 0.894 | 22.72 | 410 | 490 | 555 |
900 | 456.0 | 0.949 | 24.10 | 435 | 520 | 585 |
1000 | 506.7 | 1.000 | 25.40 | 455 | 545 | 615 |
1250 | 633.4 | 1.118 | 28.40 | 495 | 590 | 665 |
1500 | 760.1 | 1.225 | 31.11 | 520 | 625 | 705 |
1750 | 886.7 | 1.323 | 33.60 | 545 | 650 | 735 |
2000 | 1013.4 | 1.414 | 35.92 | 560 | 665 | 750 |
Note: For smaller wires, consultAmerican wire gauge § Tables of AWG wire sizes.
See also
[edit]- Thou (length)
- Square mil
- IEC 60228,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
- Jewelry wire gauge
- Body jewelry sizes
- Electrical wiring
- Number 8 wire,a term used in the New Zealand vernacular
References
[edit]- ^"Popular Acronyms"Archived2011-09-03 at theWayback Machine.NEMA
- ^"Energy Acronyms",California Energy Commission
- ^Charles Hoare,The A.B.C. of Slide Rule Practice,p. 52, London: Aston & Mander, 1872OCLC605063273
- ^Edwin James Houston,A Dictionary of Electrical Words, Terms and Phrases,p. 135, New York: W. J. Johnston, 1889OCLC1069614872
- ^Greg A. Lloyd,Bariatric Magnetic Apparatus and Method of Manufacturing Thereof,US patentUS 8481076,9 July 2013.
- ^NFPA 70-2011 National Electrical Code 2011 EditionArchived2008-10-15 at theWayback Machine.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).
- ^NFPA 70 National Electrical Code 2008 EditionArchived2008-10-15 at theWayback Machine.Table 310.16 page 70-148,Allowable ampacities of insulated conductors rated 0 through 2000 volts, 60°C through 90°C, not more than three current-carrying conductors in raceway, cable, or earth (directly buried) based on ambient temperature of 30°C.Extracts fromNFPA 70do not represent the full position ofNFPAand the original complete Code must be consulted. In particular, the maximum permissibleovercurrent protectiondevices may set a lower limit.