In wire sizing, the cross-sectional area of a round conductor measured in circular mils (cmils) equals the square of its diameter in mils. What is the area for a conductor 1 inch in diameter (1000 mils)?

Introduction / Context:
Electrical conductors are often specified using circular mils (cmils), a convenient unit for circular cross-sections. It simplifies area calculations because the area in cmils is the square of the diameter in mils, avoiding use of pi for quick estimates and tables.

Given Data / Assumptions:

• Diameter d = 1 inch.
• 1 inch = 1000 mils (since 1 mil = 0.001 inch).
• Area (cmils) = d^2 (with d in mils).

Concept / Approach:
Use the circular mil definition: A_cmils = d_mils^2. This is a unit definition used widely in NEC tables and cable datasheets. It provides a direct proportional relationship for comparing conductor sizes without converting to square inches each time.

Step-by-Step Solution:
Convert diameter: d = 1 inch = 1000 mils.Apply definition: A = d^2 = (1000)^2 cmils.Compute: A = 1,000,000 cmils.

Verification / Alternative check:
Relate to square inches: 1 circular mil = (pi/4) * (0.001 in)^2 scaled factor; however, by definition, the shortcut d^2 in mils gives cmils directly, confirming 1,000,000 cmils for 1 inch diameter.

Why Other Options Are Wrong:

• 500 or 100,000 cmils: Far too small for a 1 inch diameter.
• 500,000,000 cmils: Off by a factor of 500 from the correct square relationship.

Common Pitfalls:

• Forgetting that diameter (not radius) is squared in the cmils definition.
• Mixing mils and inches without converting; always convert inches to mils first.

Final Answer:
1,000,000 cmils