What is a Circular Mil?
A circular mil (cmil) is a unit of area used primarily in electrical engineering to measure the cross-sectional area of wires and cables. One circular mil is defined as the area of a circle with a diameter of one mil (one-thousandth of an inch).
Formula
The area in circular mils is calculated using:
$$\text{Area (cmil)} = \frac{\pi D^{2} / 4}{7.854 \times 10^{-7}}$$
Where:
- D is the diameter in inches
- The value 7.854 x 10^-7 is the conversion factor (area of a 1-mil diameter circle in square inches)
Alternatively, this simplifies to:
$$\text{Area (cmil)} = D^{2} \times 1{,}000{,}000$$
Where D is in mils (thousandths of an inch).
Example Calculation
For a wire with a diameter of 0.075 inches:
- Calculate area in square inches:
$$\text{Area} = \frac{\pi \times 0.075^{2}}{4} = 0.00443 \text{ in}^{2}$$
- Convert to circular mils:
$$\text{Area (cmil)} = \frac{0.00443}{7.854 \times 10^{-7}} = 5{,}638.35 \text{ cmil}$$
Why Use Circular Mils?
Circular mils are particularly useful in the electrical industry because:
- Simplicity: The area in circular mils equals the square of the diameter in mils
- Wire Tables: Standard wire gauges (AWG) are often specified in circular mils
- Current Capacity: Ampacity calculations are simplified when using circular mils
- Resistance: Wire resistance calculations are straightforward with circular mil specifications
This unit eliminates the need to work with pi when dealing with circular cross-sections, making calculations faster and reducing rounding errors in practical applications.