Circular mil

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.

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 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.

Note: For smaller wires, consult American wire gauge § Tables of AWG wire sizes.

• 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