Voltage drop is the volts consumed by the resistance of the wire before the load ever sees them. The resistance values used here are the direct-current resistances in NEC Chapter 9 Table 8, uncoated stranded conductors, at 75°C, in ohms per 1,000 feet. The length is the one-way distance. The multiplier accounts for the path of the current.
Single-phase or DC: VD = 2 × I × R × L / 1,000
Three-phase: VD = √3 × I × R × L / 1,000
I is amperes, R is ohms per 1,000 feet, and L is one-way feet. The 2 is the outgoing conductor plus the return. The √3 converts a phase-conductor drop into a line-to-line drop. Percent is that voltage divided by the source voltage, not by the voltage that arrives at the load.
The 12 AWG example
Table 8 lists 12 AWG stranded uncoated copper at 1.98 ohms per 1,000 feet, and 6,530 circular mils. A 20 A load, 100 feet away, on a 120 V single-phase circuit:
VD = 2 × 20 × 1.98 × 100 / 1,000 = 7.92 V
7.92 / 120 is 6.60%. The load sees about 112.1 V. The same arithmetic with the textbook constant K = 12.9 is 2 × 12.9 × 20 × 100 / 6,530 = 7.90 V. Solid 12 AWG is a different row in Table 8, 1.93 ohms per 1,000 feet, and that run drops 7.72 V. The calculator uses stranded conductors, which is what these circuits are pulled with. Two hundred feet of the same 12 AWG stranded copper is 0.396 ohm, which is the worked resistance example in Mike Holt’s conductor-resistance notes: (1.98 / 1,000) × 200.
A three-phase check
Four AWG copper is 0.308 ohms per 1,000 feet. Fifty amperes, 200 feet, 480 V, three-phase:
VD = √3 × 50 × 0.308 × 200 / 1,000 = 5.33 V
That is 1.11% of 480 V, and about 474.7 V arrives. The square root of three, not two, is the piece that gets swapped by mistake. On a single-phase circuit the current goes out and back. On a three-phase circuit the line-to-line drop is √3 times the drop along one phase conductor.
What the 3% figure is, and is not
Informational notes to NEC 210.19(A) and 215.2(A) suggest about 3% on the branch circuit or the feeder, and about 5% for the two of them together, for reasonable efficiency and operation. Informational notes are not requirements. A long 120 V branch feels the limit much sooner than a 480 V feeder does, because 3% of 120 V is 3.6 V and 3% of 480 V is 14.4 V. Sensitive electronics, motors at the end of a lane, and low-voltage DC all deserve a tighter number than the note. The wire size calculator uses the percent you type, defaults to 3, and will refuse a size that only satisfies ampacity.
Resistance rises with temperature. Table 8 Note 2 is R₂ = R₁ [1 + α (T₂ − 75)], with α = 0.00323 for copper and 0.00330 for aluminum. Sizing and this page stay at 75°C so the numbers match the table. Chapter 9 Table 9 adds reactance for alternating current in conduit. It matters on large feeders with a power factor below 1, and it is optional on the main calculator. At unity power factor the reactance term is zero.
A resistivity shortcut some charts still use, about 11.2 for copper at 127°F, understates the Table 8 resistance at 75°C. On a 240 V, 30 A, 100 ft single-phase run that shortcut points at 10 AWG. Table 8 puts 10 AWG at 7.44 V, which is 3.10%, just past a 3% limit, so the size that actually fits is 8 AWG at 4.67 V. Ampacity was never the constraint. Drop was.