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 0.0254 mm). 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.

The area in circular mils, A, of a circle with a diameter of d mils, is given by the formula:

${\displaystyle A=d^{2}}$

In Canada and the United States the National Electrical Code (NEC) uses 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[1] or MCM.[2] 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 0.5067 mm², so for most 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. A 0000 AWG solid wire is defined to have a diameter of exactly 0.46 inches (11.68 mm).

Formula 1: Circular Mil

Note: 1 inch = 1000 mils

${\displaystyle d=0.46}$ inch = 460 mils

${\displaystyle A=d^{2}}$

${\displaystyle A=460^{2}}$ = 211,600 circular mils

(This is the same result as the AWG circular mil formula shown below for n = −3)

Formula 2: Square Mil

${\displaystyle d=0.46}$ inch = 460 mils

${\displaystyle r={d \over 2}}$ = 230 mils

${\displaystyle A=\pi r^{2}}$

${\displaystyle A=\pi \times 230^{2}=52,900\pi \approx 166,190.25}$ square mils

Formula 3: Square Inch

${\displaystyle d=0.46}$ inch

${\displaystyle r={d \over 2}}$ = 0.23 inch

${\displaystyle A=\pi r^{2}}$

${\displaystyle A=\pi \times (0.23)^{2}=0.0529\pi \approx 0.16619}$ square inches

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 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 mm² is a reasonable rule of thumb for many applications.

1 cmil = π × (1/2 × 0.0254)² = 5.067 × 10⁻⁴ mm²

1 kcmil = 1 MCM = 1000 cmil = 506.7 × 10⁻³ mm²

When large diameter wire sizes such as the widely used 250 kcmil and 350 kcmil wires are specified in kcmil, the wire's diameter can be easily determined with the following formula:

Formula 6: diameter

Note: We first convert from kcmil to circular mil

${\displaystyle A=250}$ kcmil

${\displaystyle A=250,000}$ circular mils

${\displaystyle d={\sqrt {A}}}$

${\displaystyle d={\sqrt {250,000}}}$ = 500 mils = 0.500 inch

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).[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]

${\displaystyle 1\ {\text{cmm}}=\left({1000 \over 25.4}\right)^{2}\ {\text{cmil}}\approx 1,550\ {\text{cmil}}}$

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.

${\displaystyle A_{n}=\left(5\times 92^{\frac {36-n}{39}}\right)^{2}}$

For example, a number 12 gauge wire would use n = 12:

${\displaystyle \left(5\times 92^{\frac {36-12}{39}}\right)^{2}=6530~{\textrm {cmil}}}$

Sizes with multiple zeros are successively larger than the number 0 gauge size and can be denoted using "number of zeros/0"; for example 4/0 for the number 0000 gauge. For an m/0 AWG wire size, use

${\displaystyle n=-(m-1)=1-m}$ in the above formula.

For example, the number 0000 gauge or 4/0 gauge, 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 50 kcmil, 400 to 1000 in increments of 100 kcmil, and from 1000 to 2000 in increments of 250 kcmil.[6]

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.

Standard kcmil wire sizes
& solid copper equivalents

kcmil MCM	mm²	Diameter		NEC copper wire ampacity with 60/75/90 °C insulation (A)[7]
		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, consult American wire gauge § Tables of AWG wire sizes.

See also

• Thou (length)
• Square mil
• Wire gauge comparison chart
• 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

1. "Popular Acronyms" Archived 2011-09-03 at the Wayback Machine. NEMA
2. "Power Plant Siting Acronyms", California Energy Commission
3. Charles Hoare, The A.B.C. of Slide Rule Practice, p. 52, London: Aston & Mander, 1872 OCLC 605063273
4. Edwin James Houston, A Dictionary of Electrical Words, Terms and Phrases, p. 135, New York: W. J. Johnston, 1889 OCLC 1069614872
5. Greg A. Lloyd, Bariatric Magnetic Apparatus and Method of Manufacturing Thereof, US patent US 8481076, 9 July 2013.
6. NFPA 70-2011 National Electrical Code 2011 Edition Archived 2008-10-15 at the Wayback 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).
7. NFPA 70 National Electrical Code 2008 Edition Archived 2008-10-15 at the Wayback 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 from NFPA 70 do not represent the full position of NFPA and the original complete Code must be consulted. In particular, the maximum permissible overcurrent protection devices may set a lower limit.