Formula
Single phase uses 2 in front of K. Three phase uses √3. Length is one way, in feet. Circular mils come from Chapter 9 Table 8.
single-phase VD = 2 · K · I · L / cmil
three-phase VD = √3 · K · I · L / cmil
K = 12.9 (Cu) or 21.2 (Al)
Ohms per foot is about K ÷ cmil, which is why this is called the resistance method in approximate form. Table 9’s AC resistance is a refinement this page does not apply. The size suggestions walk Table 8 from 14 AWG upward and stop at the first size at or under 3%, and again at 5%.
Worked examples
Copper 12 AWG, 20 A, 100 ft, 120 V, single phase. 2 × 12.9 × 20 × 100 / 6,530 = 7.90 V, 6.58%. A 3% branch wants 8 AWG. A 5% total wants 10 AWG.
The same run, three phase. Three phase replaces the 2 with √3, so the drop is √3 / 2 of the single-phase figure. √3 × 12.9 × 20 × 100 / 6,530 = 6.84 V. Single phase is the larger drop.
Aluminum instead of copper. K becomes 21.2, so the single-phase drop scales by 21.2 / 12.9.
Reference
Copper, single phase, 20 A, 100 ft, 120 V.
| Size | cmil | Drop | Percent |
|---|---|---|---|
| 14 AWG | 4,110 | 12.55 V | 10.46% |
| 12 AWG | 6,530 | 7.9 V | 6.58% |
| 10 AWG | 10,380 | 4.97 V | 4.14% |
| 8 AWG | 16,510 | 3.13 V | 2.6% |
| 6 AWG | 26,240 | 1.97 V | 1.64% |
| 4 AWG | 41,740 | 1.24 V | 1.03% |
Questions
How much voltage does 12 AWG copper lose at 20 amps over 100 feet?
7.90 volts on a 120 volt single-phase circuit, which is 6.58%. Circular mils for 12 AWG are 6,530. VD = 2 × 12.9 × 20 × 100 / 6,530.
Is 3% a code violation?
No. NEC 210.19(A) Informational Note 4 and 215.2(A)(1) Informational Note 2 recommend 3% on the branch and 5% total. Informational notes are not requirements. This page still names the smallest Table 8 size that lands on each figure, because that is the question the notes are for.
What is K?
K is 12.9 for copper and 21.2 for aluminum, in ohm-circular-mil per foot. It is the approximate-K form of the resistance method: ohms per foot ≈ K / cmil. A Table 9 AC-resistance calculation can differ by a few tenths of a volt. This page uses K.
Sources
- Voltage drop ≈ 2 K I L / cmil (single phase) or √3 K I L / cmil (three phase). K = 12.9 copper, 21.2 aluminum. Circular mils from NEC Chapter 9 Table 8.
- NEC 210.19(A) Informational Note and 215.2(A) Informational Note: 3% branch, 5% total. Advisory, not a mandatory rule.