Circular Mil (cmil) – What It Is and How It Converts

Definition: 
A circular mil (cmil) is a unit of area used primarily in North America to express the cross-sectional area of round conductors (wires). 
It is defined as the area of a circle with a diameter of one mil (0.001 inches or 0.0254 mm).

Formula for Area: 
For a circular wire:
Area (cmil) = [Diameter (mils)]²

Example:
If a wire has a diameter of 10 mils:
Area = 10² = 100 cmil

Metric System Conversion:

| Unit        | Equivalent Value               |
|-------------|--------------------------------|
| 1 mil       | 0.001 inch = 0.0254 mm         |
| 1 cmil      | π/4 × (0.001 in)² = 7.854×10⁻⁷ in² |
| 1 cmil      | 5.067×10⁻¹⁰ m² = 0.0005067 mm² |
| 1 mm²       | ≈ 1,973.5 cmil                 |

Conversion Formulas:
1 mm² ≈ 1,973.5 cmil
1 cmil ≈ 0.0005067 mm²

Why cmil is Used:

• Avoids using π in wire area calculations
• Widely used in AWG (American Wire Gauge) system
• Makes it easier to compare wire sizes by just squaring the diameter in mils
• Simplifies resistance and current-carrying capacity calculations for round conductors

Practical Engineering Application:
In cable factories, especially in North America, cmil is standard for specifying conductor sizes. It plays a key role in:

• Calculating DC resistance (Ohm/km)
• Determining current rating (ampacity)
• Sizing wires for motors, transformers, and distribution cables

Example Calculation:
A wire has a diameter of 20 mils (0.508 mm):

Area (cmil) = 20² = 400 cmil
In mm²: 400 × 0.0005067 = 0.2027 mm²

Note: For stranded conductors, use equivalent solid area (e.g., cmil or mm²) to compare or calculate resistance, but remember to apply the stranding factor if accuracy is needed.

Useful Tip: 
To quickly estimate AWG size to mm²:

• AWG 10 ≈ 5,260 cmil ≈ 2.66 mm²
• AWG 12 ≈ 3,310 cmil ≈ 1.68 mm²
• AWG 14 ≈ 2,080 cmil ≈ 1.31 mm²