📏 American Wire Gauge (AWG) – Calculations

1. Definition

• AWG (American Wire Gauge) is a logarithmic stepped system for wire diameters.

• The smallest common size is No. 36 AWG = 0.0050 in (0.127 mm).

• The largest standard size is No. 0000 (4/0) AWG = 0.4600 in (11.684 mm).

• The ratio between these two diameters is 92, across 39 steps.

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2. Formula for Wire Diameter

The diameter (in inches) of an AWG wire size n is:

$$d_n = 0.005 \times 92^{\frac{36-n}{39}}$$

• $n$ = AWG size (integer, can be negative for 0/00… sizes).

• For m/0 AWG (like 4/0), use $n = 1-m$. Example: for 4/0, $n = -3$.

The cross-sectional area (in circular mils) is:

$$A_{CM} = d_n^2 \ (\text{in mils}^2)$$

or in mm²:

$$A_{mm^2} = \frac{\pi}{4} \times d_n^2 \times (25.4)^2$$

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3. ASTM B 258-02 Standard

• Successive size ratio = $92^{1/39} \approx 1.1229322$.

• Diameters tabulated to 4 significant figures.

• Resolution:

  • ≥ AWG 44: 0.0001 in (0.1 mils).

  • ≤ AWG 45: 0.00001 in (0.01 mils).

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4. Rules of Thumb

• Diameter Rule: Doubling diameter = decrease of 6 AWG sizes.

  • Example: No. 8 → No. 2 (2× diameter).

• Area Rule: Doubling area = decrease of 3 AWG sizes.

  • Example: Two No. 14 wires ≈ one No. 11 wire.

• Ten-step Rule: A 10-size decrease multiplies area & weight ×10, and reduces resistance by ÷10.

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5. AWG vs kcmil (MCM)

• For wires larger than 4/0, size is given in thousands of circular mils (kcmil).

• $1 \text{ kcmil} = 1000 \text{ circular mils} = 0.5067 \, \text{mm}^2$.

• Example: 500 kcmil ≈ 253 mm².

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6. Global Equivalent (IEC 60228)

• North America → AWG (logarithmic diameter-based).

• Europe / IEC → Nominal mm² cross-sectional area.

• AWG-to-mm² conversion is approximate (depends on strand count).

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7. Quick Reference Chart (excerpt)

AWG	Diameter (mm)	Area (mm²)	Resistance (Ω/km @ 20°C)	Ampacity (A, PVC insulation @ 60Hz)
36	0.127	0.0127	1339	0.14
20	0.812	0.518	33.61	11
14	1.628	2.08	8.286	32
10	2.588	5.26	3.277	55
4	5.189	21.2	0.823	135
1/0	8.251	53.5	0.321	170
4/0	11.684	107	0.160	230

⚡ Key Takeaway:
AWG is a logarithmic sizing system—each step changes diameter by about 12% and area by about 26%. For global projects, always cross-check with IEC 60228 mm² equivalents.

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Would you like me to design this into a full infographic set (like:
✅ formula flowchart,
✅ AWG vs mm² comparison chart,
✅ AWG-to-ampacity quick lookup table),
so you can directly drop it into your article or presentation?