Methodology

d(mils) = 5 × 92^((36 − n) / 39)

American Wire Gauge is a geometric series defined in ASTM B258. From the diameter, circular mils is simply the diameter in mils squared, and the metric cross-sectional area follows from the circle area. Sizes 1/0 through 4/0 use gauge numbers 0 through −3. Sizes above 4/0 are specified directly in thousands of circular mils (kcmil).

Confidence: published standard. This is exact, not an approximation.

R = ρ × L / cmil

VD(1φ) = 2 × K × I × L / cmil

VD(3φ) = 1.732 × K × I × L / cmil

DC resistance uses resistivity ρ = 10.371 Ω·cmil/ft for annealed copper and 17.0 for 1350-H19 aluminium, both at 20 °C. Voltage drop uses the trade constant K — 12.9 for copper, 21.2 for aluminium — which folds in a typical operating temperature and stranding effect. L is the one-way run length; the 2 and 1.732 multipliers account for the return path and three-phase geometry respectively.

We flag 3% as the recommended branch-circuit limit and 5% for feeder plus branch combined. These are recommendations in the code, not requirements, but they are what inspectors and engineers expect.

I ≈ 0.0670 × cmil^0.6505 × Ftemp × Fmaterial

Heat dissipation from a conductor in a raceway scales as a power law of its cross-sectional area. We fit that power law across the building-wire range, then scale for insulation temperature rating (75 °C × 1.18, 90 °C × 1.33 relative to 60 °C) and material (aluminium × 0.78). Across 14 AWG to 4/0 the model lands within roughly ±8% of commonly published allowable ampacities.

Confidence: formula estimate. This is the one number on the site you should always cross-check.

Fambient = √((Tc − Ta) / (Tc − 30))

Ambient correction compares the available temperature rise at the actual ambient against the rise at the 30 °C reference. Tc is the insulation rating, Ta the ambient temperature, both in Celsius.

Bundling adjustment for more than three current-carrying conductors follows the standard stepped schedule: 4–6 conductors 80%, 7–9 conductors 70%, 10–20 conductors 50%, 21–30 conductors 45%, 31–40 conductors 40%, 41 or more 35%. Neutral and equipment grounding conductors are generally not counted; the calculator asks you for the count so that judgement stays with you.

A = π × (id / 2)²

Internal areas are computed from published nominal internal diameters: UL 797 / ANSI C80.3 for EMT, UL 1242 / ANSI C80.6 for IMC, UL 6 / ANSI C80.1 for RMC, and NEMA TC-2 / ASTM D1785 for PVC schedules 40 and 80. Conductor areas use manufacturer nominal insulated outside diameters for THHN/THWN-2.

Allowable fill is 53% for one conductor, 31% for two, and 40% for three or more. Nipples 24 inches or shorter are permitted 60% fill; the calculator does not assume a nipple.

Sheet metal gauges use the Manufacturers' Standard Gauge for uncoated steel, the galvanized standard gauge for coated steel, the Brown & Sharpe series for aluminium, and the stainless steel gauge series. Rebar follows ASTM A615 with soft metric designations. Hex nuts follow ASME B18.2.2 and ISO 4032. Pipe threads follow ASME B1.20.1 (NPT). Hex keys follow ASME B18.3. Metric equivalents are computed at 25.4 mm per inch and rounded, with the difference shown so you can judge whether a substitution will round a fastener.