Circular mil

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 inch.

Formula 1: Circular Mil

Note: 1 inch = 1000 mils d = 0.46 inch = 460 mils A = d 2 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

d = 0.46 inch = 460 mils r = d 2 = 230 mils A = π r 2 A = π × 230 2 = 52 , 900 π ≈ 166 , 190.25 square mils

Formula 3: Square Inch

d = 0.46 inch r = d 2 = 0.23 inch A = π r 2 A = π × ( 0.23 ) 2 = 0.0529 π ≈ 0.16619 square inches

Formula 4: Solving for Circular Mil

A = A 211 , 600 circular mils = 52 , 900 × π square mils1 circular mil = 52 , 900 × π 211 , 600 square mils1 circular mil = π 4 square mils

Formula 5: Solving for Square Mil

1 square mil = 4 π circular mils

Therefore, the following conversions apply:

To obtain square mils   ⇒ (# of circular mils) × π ÷ 4

To obtain square inches ⇒ (# of circular mils) × π ÷ 4,000,000

To obtain circular mils ⇒ (# of square mils)   × 4 ÷ π

To obtain circular mils ⇒ (# of square inches) × 4,000,000 ÷ π

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_circular_mil = π × (1e−3 / 2 × 25.4)² = 506.7×10⁻⁶mm²

1_MCM = 1000 circular_mil = 506.7×10⁻³mm²

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 A = 250 kcmil A = 250 , 000 circular mils d = A d = 250 , 000 = 500 mils = 0.500 inch

Thus, this wire would have a diameter of a half inch or 12.7 mm.

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 = ( 5 × 92 36 − n 39 ) 2

For example, a number 12 gauge wire would use n = 12; and the calculated result would be 6530 circular mils

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

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.

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 the Table of AWG wire sizes article.

Circular inch

Cardarelli has asserted that the "circular inch" (cin) was used as a unit for the measurement of wire sizes, with a conversion of 1 circular inch = 1 million circular mil. The Oxford English Dictionary has an entry for "circular mil", but not for "circular inch".

IEEE std 525

Anexo C, C1.2.

1cmil = 5,067x10^⁻⁴ mm²