[ENG] AWG System: Behind the scenes

In the electrical design engineering, conductor is one of the most important things to be considered. It can be in the form as wires or cables, and sometimes optical fiber for small-power low-voltage requirement. Simply says, cable is a wire veiled with the insulators, which can be polyethylene or PVC, etc.

There are two major systems that often used in the electrical power design engineering, especially in the construction for refinery and petrochemical plant, power plant, and mining.

First one is usually called as “AWG System” used for American standard environment and the second one is “Metric System” mostly used by European practitioner (and generalized to be non-American standard user).

In this occasion, I will talk about Size of Wire in American standard.

Diameter of AWG Systems

It stands for American Wire Gauge. Originally, AWG systems had only 40 gauges (size). They were 4/0 (4 “aught” or four of zeros) to 36 AWG. Originally, number 36 AWG and 4/0 AWG were considered as basis, which is 0.005” (0.005 inches) and 0.46” (0.46 inches) in diameter respectively. The diameter of another AWG number is determined by multiplying 0.005” by (1.22932)^(36-n), hence we have d_n=0.005×(1.22932)^(36-n), where “n” is the index number of AWG. For example, number 35 AWG will have diameter of 0.005 x 1.123 = 0.005615”; with the same rule, we find number 12 AWG and 1 AWG is 0.080808” and 0.289297” respectively. And for number 0 AWG which is known also as 1/0 AWG (1 aught or one of zero) has diameter of 0.324861”. As for number greater than 0 AWG, it can be sorted to the next integer number, like 4 AWG; 3 AWG; 2 AWG; 1 AWG; 1/0 AWG; 2/0 AWG; 3/0 AWG; 4/0 AWG will have “n” as 4; 3; 2; 1; 0; -1; -2; -3. By this “n” number, we can find the diameter of number 2/0 AWG and number 4/0 AWG is 0.364797” and 0.46” respectively.

For more details, refer to International Standard ASTM B258-02 (R2008) Standard Specification for Standard Nominal Diameters and Cross-Sectional Areas of AWG Sizes of Solid Round Wires Used as Electrical Conductors.

Cross-sectional Area of AWG Systems

The next step is to determine the cross section area of the wire. General formula as A=πr^2 can be used, by changing the radius r with half of diameter as mentioned above, we get A=0.000019625×(1.260976718)^(36-n), this area is in square-inches.

General term used to describe cross-sectional area in AWG system is “circular mils”. Definition of one circular mil is equal to area of one mil in diameter. While, one inch is equal to one thousand mil (1inch = 1000 mils = 1kmil), therefore cross-section area with one inch in diameter will be one million circular mils (1MCM = 1kcmil).

Easy explanation is as below:

d=1 mil; A=d^2=1 cmil
d=10 mils; A=d^2=100 cmils
d=100 mils; A=d^2=10,000 cmils
d=1,000 mils; A=d^2=1,000,000 cmils

By this, it will give us

d=1,000 mils=1 kmil=1 inch
A=d^2=1,000,000 cmils=1,000 kcmil=1,000 MCM=0.785398 in^2

By an example, number 4/0 AWG wire, which has 0.46” diameter, equal to 460 mils, will have d^2= 211,600 cmils cross-section area, which is equal to 211.6 MCM, to be rounded as 212 MCM, and equal to 0.16619 in^2.

Take a look conversion below:

Length Unit, one dimension

1 inch = 1,000 mils
1 inch = 1 k-mil

Area Unit, two dimensions

1 square-inches = 1,273,239.5447352 circular-mils
1 circular-mil = 0.000000785 square-inches
1 k-cmil = 1 MCM
1 k-cmil = 1,000 circular-mil
1 k-cmil = 0.000785938 square-inches

To remember:

1. Mil is a one-dimension-length unit, whereas circular-mil is two-dimension-area unit.
2. Circular-mil is proportional to quadratic of diameter, whereas square-inch is proportional to quadratic of radius.
3. MCM is preferred expression instead of kcmil. This is because “k” from kcmil means “kilo” which actually a prefix in the Metric System, while the AWG system is NON-metric systems. “M” from MCM doesn’t mean “mega”, but “million”. (Thanks to Joe, he called it pseudo-metrification, where I got the knowledge from http://www.controlbooth.com/threads/dumb-qotd-mcm-kcmil.9376/).
4. Easy way to remember for Metric User: 2 MCM ~ 1 sqmm.

AWG System for stranded wires

Previously, AWG systems were only used to describe the size of solid wires. However, nowadays it also can be used to represent stranded wires.

The cross-sectional area of a stranded wire in AWG system is equal to the total of cross-sectional area of individual strands; the gaps between strands are not counted. Stranded wire will have larger cross-sectional area (including gap) rather than the solid wire with the same AWG number. Even though, it depends on the method of twisting and stranding.

Stranded wires in AWG system are specified by three numbers, such as number “2 AWG 7/10”. The description is “2 AWG” as the he overall AWG size, “7” is the number of strands, and “10” is the AWG size of a strand.

IMPORTANT: This is just for additional knowledge. In electrical design engineering, this kind of calculation is not needed, we can easily use the table already provided by many manufacturers. Just in case you are curious with the history of this method. 

(Collected from many sources such as Wikipedia, ASTM, and forum of discussions)