Voltage Drop Formula (Single-Phase & Three-Phase)

The single-phase voltage drop formula is VD = (2 × K × I × L) ÷ CM, and the three-phase formula is VD = (1.732 × K × I × L) ÷ CM, where K = 12.9 for copper or 21.2 for aluminum, I is the load current in amperes, L is the one-way circuit length in feet, and CM is the conductor's circular-mil area. The NEC recommends keeping voltage drop to 3% or less on a branch circuit and 5% total including the feeder — a recommendation, not a mandatory limit. The calculator above evaluates the formula instantly; the sections below show the math and a max-run-length chart you can cite directly.

What each term means

Worked example: 20 A at 120 V over 100 ft of 12 AWG copper

A 20 A load at 120 V single-phase, 100 ft one-way on 12 AWG copper (6,530 CM):

VD = (2 × 12.9 × 20 × 100) ÷ 6,530 = 51,600 ÷ 6,530 = 7.90 V, which is 7.90 ÷ 120 = 6.6% — more than double the NEC 3% recommendation.

Upsizing to 10 AWG copper (10,380 CM): VD = 51,600 ÷ 10,380 = 4.97 V = 4.1% — better, but still above 3%. To meet the 3% recommendation at this length and load you need 8 AWG copper (16,510 CM): VD = 51,600 ÷ 16,510 = 3.13 V = 2.6%.

Maximum one-way run length at 20 A, 120 V, for 3% voltage drop

Maximum lengths below solve the formula for L with VD = 3.6 V (3% of 120 V), copper conductors, single-phase: L = (3.6 × CM) ÷ (2 × 12.9 × 20).

Copper wire size (AWG) Circular mils (CM) Max one-way run at 20 A / 120 V, 3% drop (ft)
14 AWG*4,11028
12 AWG6,53045
10 AWG10,38072
8 AWG16,510115
6 AWG26,240183

*14 AWG is shown for comparison only — it is limited to 15 A overcurrent protection (NEC 240.4(D)(3)) and may not be used on a 20 A circuit.

What the NEC actually requires

The 3%/5% figures come from Informational Note 4 to NEC 210.19(A) (branch circuits) and Informational Note 2 to NEC 215.2(A) (feeders): a maximum 3% drop on the branch circuit, and 5% combined for feeder plus branch circuit, "provides reasonable efficiency of operation." Because these appear in informational notes, they are recommendations, not enforceable code requirements — an inspector cannot fail an installation solely for exceeding them (exception: certain specific rules such as fire pumps in NEC 695.7 and sensitive equipment per 647.4(D) do impose mandatory limits). They remain the standard design target for professional work.

When voltage drop matters most

Last verified against NEC 2023 210.19(A) Informational Note 4 and 215.2(A) Informational Note 2, with K constants and circular-mil areas from NEC Chapter 9, Table 8. Results are for planning; confirm with the current NEC edition and your local authority having jurisdiction.