Circular mil
Encyclopedia
A circular mil is a unit
Units of measurement
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...
of area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...
, equal to the area of a circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
with a diameter
Diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle...
of one mil
Thou (unit of length)
A thou also known as a mil or point, is the verbalized abbreviation for "thousandth of an inch." It is a unit of length equal to 0.001 inch....
(one thousandth of an inch). It is a convenient unit for referring to the area of a wire with a circular cross section, because the area in circular mils can be calculated without reference to pi
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
(π).
The area in circular mils, A, of a circle with a diameter of d mils, is given by the formula:
Electrician
Electrician
An electrician is a tradesman specializing in electrical wiring of buildings, stationary machines and related equipment. Electricians may be employed in the installation of new electrical components or the maintenance and repair of existing electrical infrastructure. Electricians may also...
s in Canada
Canada
Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...
and the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
are familiar with the circular mil because the National Electrical Code (NEC) uses the circular mil to define wire sizes larger than 0000 AWG
American wire gauge
American wire gauge , also known as the Brown & Sharpe wire gauge, is a standardized wire gauge system used since 1857 predominantly in the United States and Canada for the diameters of round, solid, nonferrous, electrically conducting wire...
. In many NEC publications and uses, large wires may be expressed in thousands of circular mils, which is abbreviated in two different ways: MCM or kcmil. 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.
Equivalence to other units of area
Although square mils are rarely used, it is convenient to convert between square inches and circular mils. As a classic example taken from the NEC, a 0000 AWG solid wire is defined to have a diameter of exactly 0.46 inch.Formula 1: Circular Mil
inch = 460 mil
= 211,600 circular mils Formula 2: Square Mil
inch = 460 mil
= 230 mil
square milsFormula 3: Square Inch
inch
= 0.23 inch
square inchesFormula 4: Solving for Circular Mil
circular mils
square mils
- 1 circular mil
square mils - 1 circular mil
square mils
Formula 5: Solving for Circular Mil
- 1 square mil
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 metreSquare metreThe square metre or square meter is the SI derived unit of area, with symbol m2 . It is defined as the area of a square whose sides measure exactly one metre...
s - 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.
AWG circular mil formula
The formula to calculate the circular mil for any given AWG (American Wire GaugeAmerican wire gauge
American wire gauge , also known as the Brown & Sharpe wire gauge, is a standardized wire gauge system used since 1857 predominantly in the United States and Canada for the diameters of round, solid, nonferrous, electrically conducting wire...
) size is as follows. An represents the circular mil area for the AWG size n.
- For example, a number 12 gauge wire would use n = 12; and the calculated result would be 6529.946789 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
- Were it possible to use n = -4 in this equation (assuming there was a size larger than 4/0 AWG), the calculated result would be about 255 kcmil, which is similar to the 250 kcmil wire size actually in use