What is the formula for voltage drop?

For single phase, VD = 2 x K x I x L / cmil. For three phase, VD = 1.732 x K x I x L / cmil. K is 12.9 for copper and 21.2 for aluminium, I is the load current in amps, L is the one-way run length in feet, and cmil is the conductor cross-sectional area in circular mils.

How much voltage drop is acceptable?

The widely used guideline is 3% maximum on a branch circuit and 5% total for feeder plus branch circuit combined. These are recommendations rather than hard requirements in the NEC, but inspectors and engineers expect designs to meet them.

Does voltage drop use one-way or round-trip length?

Enter the one-way length. The factor of 2 in the single-phase formula already accounts for current flowing out and back, so doubling the length yourself would double the calculated drop.

What size wire do I need for a 100 ft run at 20 amps?

At 120 V single phase, 20 A over 100 ft one-way, 12 AWG copper drops roughly 4.4% which exceeds the 3% guideline. 10 AWG copper drops about 2.8% and is the usual choice for that run.

Why does aluminium need a larger conductor?

Aluminium has about 61% the conductivity of copper, so its voltage drop constant K is 21.2 against 12.9 for copper. For the same current, length and percent drop, aluminium typically needs to be one to two sizes larger.

Does voltage drop matter more at 120 V or 240 V?

At 120 V. Percent drop is inversely proportional to system voltage, so the same load and run length drops twice the percentage at 120 V that it does at 240 V, and four times what it does at 480 V. Running a long circuit at the higher voltage and splitting it at the far end is usually cheaper than upsizing the conductors.

Do I size wire for ampacity or voltage drop?

Both, and the larger conductor wins. Ampacity governs short runs; voltage drop governs long ones. A 20 A circuit at 120 V is ampacity-limited up to roughly 70 ft on 12 AWG copper, and voltage-drop-limited beyond about 90 ft.

Voltage Drop Calculator

Percent drop, end-of-run voltage, the smallest conductor that stays under 3%, and how far your current conductor can actually go.

Quick answer

Voltage drop for a single-phase circuit is VD = 2 × K × I × L / cmil, where K is 12.9 for copper and 21.2 for aluminium, I is amps, L is the one-way run in feet and cmil is the conductor area in circular mils. Three-phase replaces the 2 with 1.732. Keep branch circuits at or under 3% drop, and feeder plus branch at or under 5% combined.

Circuit inputs

Load current (A)One-way length (ft)System voltage (V)PhaseConductor sizeMaterial

VD = 2 x K x I x L / cmil

Result

Voltage drop

7.90V

Percent drop

6.58%

Voltage at load

112.1V

Max length at 3%

45ft

Over 5% — this run needs a larger conductor.

Ampacity check: 12 AWG copper is estimated at 24 A at 75 °C, against your 20 A load.

Smallest conductor that satisfies both 3% drop and ampacity: 8 AWG.

Published standard

Maximum one-way run length at 3% drop

Size	10 A	15 A	20 A	30 A	40 A	50 A	60 A	80 A	100 A
14	57	38	—	—	—	—	—	—	—
12	91	60	45	—	—	—	—	—	—
10	144	96	72	48	—	—	—	—	—
8	230	153	115	76	57	—	—	—	—
6	366	244	183	122	91	73	—	—	—
4	582	388	291	194	145	116	97	72	—
3	734	489	367	244	183	146	122	91	—
2	926	617	463	308	231	185	154	115	92
1	1167	778	583	389	291	233	194	145	116
1/0	1472	981	736	490	368	294	245	184	147
2/0	1856	1237	928	618	464	371	309	232	185
3/0	2341	1560	1170	780	585	468	390	292	234
4/0	2952	1968	1476	984	738	590	492	369	295

Copper conductors, 120 V single phase, at the 3% branch-circuit guideline. Values in feet.

Source & method: Length solved from the same formula: L = (V × 3% × cmil) / (multiplier × K × I). Cells marked — exceed the estimated ampacity of that conductor at 75 °C, so the run length is irrelevant. Ampacity estimates are described on the methodology page.

Drop per amp per 100 ft — quick mental math

Multiply the cell by your current and by (one-way feet ÷ 100) to get volts dropped, with no calculator needed.

Size	Copper (V/A/100 ft)	Aluminium (V/A/100 ft)	Copper Ω/1000 ft
14 AWG	0.6282	1.0324	2.5252
12 AWG	0.3951	0.6493	1.5882
10 AWG	0.2485	0.4084	0.9988
8 AWG	0.1563	0.2568	0.6282
6 AWG	0.0983	0.1615	0.3951
4 AWG	0.0618	0.1016	0.2485
3 AWG	0.0490	0.0806	0.1970
2 AWG	0.0389	0.0639	0.1563
1 AWG	0.0308	0.0507	0.1239
1/0 AWG	0.0244	0.0402	0.0983
2/0 AWG	0.0194	0.0319	0.0779
3/0 AWG	0.0154	0.0253	0.0618
4/0 AWG	0.0122	0.0200	0.0490

Volts dropped per amp per 100 ft of one-way run, single phase (multiply by 0.866 for three phase).

Source & method: Each cell is 2 × K × 100 / cmil from the same formula used above, so the columns are internally consistent with the calculator. Example: 12 AWG copper is 0.395 V per amp per 100 ft, so 20 A over 100 ft drops about 7.9 V — roughly 6.6% of 120 V.

When voltage drop actually governs the design

Ampacity and voltage drop are two separate limits on the same conductor, and the larger answer wins. On short runs ampacity governs: 12 AWG copper handles a 20 A circuit comfortably for the first 60 to 70 ft. Past roughly 90 ft at 120 V, the 3% guideline takes over and the conductor has to grow even though it is nowhere near overheating. Detached garages, well pumps, gate operators, RV outlets and yard subpanels are the usual candidates.

Higher voltage is the cheapest fix available. Percent drop scales with the inverse of system voltage, so the same load carried at 240 V drops half the percentage it does at 120 V, and at 480 V a quarter. That is why a long feeder is run at 240 V and split at the far end rather than pulled as two 120 V home runs. When the voltage is fixed, increasing conductor area is the only lever — and area, not diameter, is what counts, so going up two AWG sizes roughly halves the drop.

Motor and compressor loads deserve extra margin. Starting current can be five to seven times running current for a second or two, and the instantaneous drop during that inrush is what causes lights to dim, contactors to chatter and hard-start failures on air conditioning. Sizing the run at 2% rather than 3% at full-load amps is common practice on HVAC and pump circuits for that reason.

Two details separate a rough estimate from an engineered number. The K constant used here — 12.9 for copper, 21.2 for aluminium — is a DC-resistance figure at ordinary conductor temperature, and it is what the trade uses for branch circuits and small feeders. On large conductors, long parallel runs, or circuits with substantial reactive load, an impedance-based method that separates resistance from reactance gives a higher and more accurate drop. Conductor resistance also climbs about 0.4% per °C, so a run through a hot attic or a fully loaded raceway drops more than the table predicts.

Frequently asked

What is the formula for voltage drop?: For single phase, VD = 2 x K x I x L / cmil. For three phase, VD = 1.732 x K x I x L / cmil. K is 12.9 for copper and 21.2 for aluminium, I is the load current in amps, L is the one-way run length in feet, and cmil is the conductor cross-sectional area in circular mils.
How much voltage drop is acceptable?: The widely used guideline is 3% maximum on a branch circuit and 5% total for feeder plus branch circuit combined. These are recommendations rather than hard requirements in the NEC, but inspectors and engineers expect designs to meet them.
Does voltage drop use one-way or round-trip length?: Enter the one-way length. The factor of 2 in the single-phase formula already accounts for current flowing out and back, so doubling the length yourself would double the calculated drop.
What size wire do I need for a 100 ft run at 20 amps?: At 120 V single phase, 20 A over 100 ft one-way, 12 AWG copper drops roughly 4.4% which exceeds the 3% guideline. 10 AWG copper drops about 2.8% and is the usual choice for that run.
Why does aluminium need a larger conductor?: Aluminium has about 61% the conductivity of copper, so its voltage drop constant K is 21.2 against 12.9 for copper. For the same current, length and percent drop, aluminium typically needs to be one to two sizes larger.
Does voltage drop matter more at 120 V or 240 V?: At 120 V. Percent drop is inversely proportional to system voltage, so the same load and run length drops twice the percentage at 120 V that it does at 240 V, and four times what it does at 480 V. Running a long circuit at the higher voltage and splitting it at the far end is usually cheaper than upsizing the conductors.
Do I size wire for ampacity or voltage drop?: Both, and the larger conductor wins. Ampacity governs short runs; voltage drop governs long ones. A 20 A circuit at 120 V is ampacity-limited up to roughly 70 ft on 12 AWG copper, and voltage-drop-limited beyond about 90 ft.