The National Electrical Code (NEC) expresses conductor size in either AWG (American Wire Gauge) or in kcmils (cmils × 1000) while conductor area is expressed in mm2 and circular mils (NEC Chapter 9, Table 8). Traditionally, American electricians have preferred the circular mil and many standard formulas use the cmil as a standard. Specific resistance, for example, is often expressed in terms of ohms per cmil/ft and serves as the constant (K) in standard voltage drop calculations.
Single Phase Voltage Drop:
Three-Phase Voltage Drop:
Where:
- VD = Voltage Drop
- K = Constant for the specific resistance of the conductor in Ohms per cmil/ft at a given temperature (Approximately 12.9 ohms per cmil/ft for copper and 21.2 ohms per cmil/ft for aluminum).
- I = Current in Amps (intensity).
- L = Length of the conductors in feet from the origin to the point of termination.
- A = Area of the conductor in cmil.
The multipliers (2 for single phase and 1.73 (√3) for 3-phase) are used because the current must travel out AND back. The full current travels on both conductors in a single-phase system, doubling the length (and resistance) of the run, while the current in a 3-phase system divides among 3 conductors, effectively lowering the resistance of the run to about 1.73 times the single wire resistance.
The area can be calculated in circular mils or square mils :
Where:
- A = area in cmils
- d = diameter in mils (a mil is 1/1000 of an inch)
- a = length of one side
A common point of confusion is that the diameter of the circular area is also the length of each side of the square area that encompasses the circle, so it seems that both formulas should give us square mils (see illustration below).
Although the formulas for calculating cmils and square mils are essentially the same, the resulting areas are not the same because different units are used. Circular mils define the area of a circle that fits inside of a square having sides equal to its diameter.
To illustrate this, let’s assume that the diameter of the circle in the illustration above is 1 mil. That makes the length of “a” 1 mil, so the area of the square surrounding the circle would be:
If we want to describe the circle in terms of square mils then the formula would be:
If we want to go the other way and describe the square in terms of circular mils then we can apply our newly calculated ratio of 1:0.785 and derive the number of circular mills in our 1 mil square by taking the number of square mils divided by 0.785 giving us:
(and now we also have the multiplier for converting square mils to cmils).
So, why would you need to know how to convert between square mils and circular mils? One of the most common reasons is to determine the current capacity of a square or rectangular conductor, such as a busbar. For example:
Let’s say that we have a busbar that is 2” wide and ¼” thick. The area in square mills is:
Some of you may be wondering why I used 10002 to calculate square mils. The dimensions of the busbar needed to be converted to mils. Since there are 1000 mils/inch the conversion would be:
Since it is necessary to multiply each side by 1000, it is simpler to take the inch units times 10002.
Now to convert to cmils we use our new multiplier of 1.2732 and get:
The actual conversion formulas to convert between CM and Square Mils are:
Mils2 to CM:
CM to Mils2:
However, it is much easier (though technically less accurate) to use conversion multipliers:
CM to Mils2: 
Mils2 to CM: 
Purists may point out that the multipliers are rounded (and therefore approximate) values; however, using the conversion multipliers will suffice for all general wiring applications and are much easier to use.