Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 284

■ EXAMPLE 11.43
Problem: Find the cross-sectional area of a large rectangular conductor 5/8 inch thick and 5 inches
wide.

Solution: The thickness may be expressed in mils as 0.625 × 1000 = 625 mils and the width as 5 ×
1000 = 5000 mils. The cross-sectional area is 625 × 5000, or 3,125,000 square mils.

11.7.9.3 Circular Mil
The circular mil is the standard unit of wire cross-sectional area used in most wire tables. To avoid
the use of decimals (because most wires used to conduct electricity may be only a small fraction of
an inch), it is convenient to express these diameters in mils. As an example, the diameter of a wire
is expressed as 25 mils instead of 0.025 inch. A circular mil is the area of a circle having a diameter
of 1 mil, as shown in Figure 11.51B. The area in circular mils of a round conductor is obtained by
squaring the diameter measured in mils. Thus, a wire having a diameter of 25 mils has an area of
(25) 2 or 625 circular mils. By way of comparison, the basic formula for the area of a circle is

A = π r 2 (11.41)

In this example, the area in square inches is

A = π r 2 = 3.14 × (0.0125) 2 = 0.00049 in. 2

If D is the diameter of a wire in mils, the area in square mils can be determined using

A = π × ( D /2) 2 (11.42)

which translates to

A = 3.14/4 × D 2 = 0.785 × D 2 square mils

Thus, a wire 1 mil in diameter has an area of

A = 0.785 × (1) 2 = 0.785 square mils

which is equivalent to 1 circular mil. The cross-sectional area of a wire in circular mils is therefore
determined as

2

0 785
0 785

. D

2

A = = D circular mils

.

where D is the diameter in mils; therefore, the constant π/4 is eliminated from the calculation.
It should be noted that in comparing square and round conductors that the circular mil is a
smaller unit of area than the square mil; therefore, there are more circular mils than square mils in
any given area. The comparison is shown in Figure 11.51C. The area of a circular mil is equal to
0.785 of a square mil.

Note: To determine the circular mil area when the square mil area is given, divide the area in
square mils by 0.785. Conversely, to determine the square mil area when the circular mil area
is given, multiply the area in circular mils by 0.785.