How voltage drop is worked out

The formula

Current flowing through a resistance loses voltage across it. A run has resistance because a conductor does, and the current has to get back, so the length that matters is the round trip.

Length in feet, current in amperes, R in ohms per 1,000 ft. Divide the result by supply voltage for a percentage. The √3 in the three-phase case is the line-to-line relationship, not a fudge factor.

Where R comes from, and why it is computed

Most sites print a resistance table and ask you to trust it. A printed table cannot be checked by the person reading it, and copying one is how a wrong figure travels. So this site computes R instead, from two things that are published and citable.

The conductor's area is a definition, not a measurement

American Wire Gauge is a geometric series, ASTM B258, the American Wire Gauge geometric series. The diameter of gauge n is 0.005 × 92^{(36 − n)/39} inches, and the area in circular mils is that diameter in thousandths of an inch, squared. Nothing is looked up: 12 AWG works out to 6,530 circular mils because the definition says so.

Resistivity is a published constant

Resistance is resistivity times length over area. In the units the trade uses, resistivity is given in ohm-circular-mils per foot and rises with temperature:

The computation is checked against its own source

Tech Note 212 also prints a resistance table. The build recomputes every value in it from the resistivity above and stops if any has moved more than 1% apart. That check is the reason to compute rather than copy: a copied table is taken on faith, and a computed one proves itself every time the site is built.

What this does not model

dc resistance for a conductor of the nominal circular-mil area at the stated temperature. Stranding, ac skin effect, raceway material and actual operating temperature all move the real figure. A conductor running at 40 °C rather than 75 has roughly 11% less resistance, so a result here is conservative for a lightly loaded run and close for a fully loaded one. Reactance is not in the figure at all, which matters on long high-current runs and in steel raceway.

The 3% and 5% figures quoted everywhere are informational notes in the National Electrical Code, not enforceable requirements. That distinction is on the calculator too, because it is the single thing most charts get wrong.