What is the voltage drop formula?

Single-phase: VD = 2 × L × I × R ÷ 1000. Three-phase: VD = √3 × L × I × R ÷ 1000. L is the one-way length in feet, I the current in amps and R the wire's resistance in ohms per 1000 ft. For 12 AWG copper, 100 ft and 15 A on 120 V that is 2 × 100 ft × 15 A × 1.98 Ω/1000 ft ÷ 1000 = 5.94 V, or 4.95% of 120 V.

How much voltage drop is acceptable?

The NEC does not set a hard limit for ordinary circuits. Informational Note No. 4 to 210.19(A) says branch-circuit conductors sized so the drop at the farthest outlet is no more than 3%, and the total for feeder and branch circuit together no more than 5%, give reasonable efficiency of operation; an informational note to 215.2(A) says the same for feeders (its number differs between code editions). Informational notes are advice, not requirements, but other rules, equipment instructions and some local codes do set limits.

What wire size keeps 100 ft of a 20 A, 120 V circuit under 3%?

Copper: 8 AWG; aluminum: 6 AWG. For 5% the smallest copper size is 10 AWG. These come from the drop alone: the conductor also needs enough ampacity for a 20 A breaker (12 AWG copper at least), whatever the drop.

Why is the formula 2 × length?

Current flows from the source to the load and back, so a single-phase circuit has two conductors of the length you measure, and both lose voltage. In a balanced three-phase circuit the currents partly cancel, so the total loss is √3 (1.732) times the one-way figure rather than 2. That is why a three-phase run of the same size, length and current loses about 13% less voltage in volts.

Does aluminum have more voltage drop than copper?

Yes, about 1.6 times as much for the same size: 12 AWG aluminum in the example drops 9.75 V (8.13%) against 5.94 V for copper. Aluminum is normally sized one or two steps larger for the same job, and it needs terminals rated for it.

Does a higher voltage reduce the percent drop?

Yes. The volts lost depend on the current, not the source voltage, so the same load on 240 V has half the percent drop of 120 V: the example circuit drops 5.94 V either way but that is 2.48% of 240 V. (A 240 V load draws half the current for the same watts, which halves the drop in volts again.)

How do I calculate three-phase voltage drop?

Use √3 (1.732) in place of 2. For 8 AWG copper, 150 ft and 30 A on 208 V three-phase the drop is 6.06 V, 2.92% of 208 V. This assumes a balanced load and uses the voltage between phases.

Can I enter the length in meters?

Yes: choose meters and the calculator converts at 1 m = 3.2808 ft before using the formula. 30 m of 12 AWG copper at 15 A and 120 V is 98.43 ft and a drop of 5.85 V. The resistance values are per 1000 ft.

Is this enough to size my wire?

No. It estimates the drop only. Wire also has to carry the current within its ampacity (NEC 310.16 and the rules on temperature ratings, conduit fill, bundling and ambient temperature), match the breaker, and meet the code your area has adopted. Have a licensed electrician check any design before you build it, especially anything on a panel, a feeder or a motor.

Voltage Drop Calculator

12 AWG copper carrying 15 A over 100 ft one way on a 120 V single-phase circuit drops 5.94 V (4.95%), leaving 114.06 V at the load. That is over the 3% the NEC informational notes suggest for a branch circuit but within 5%; 8 AWG copper keeps it to 3% or less. Pick copper or aluminum, the wire size, single or three phase, the length, current and source voltage: the calculator shows the drop in volts and percent, the voltage at the load and the smallest size for 3% and for 5%. It is an estimate from published resistance values, not a design: ampacity (NEC 310.16) is a separate requirement, and a licensed electrician or your inspector decides what your installation needs.

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2 × 100 ft × 15 A × 1.98 Ω/1000 ft ÷ 1000 = 5.94 V

5.94 V drop (4.95%)

Over 3% but within 5%. The 5% is meant for feeder and branch circuit together, so a branch circuit this long leaves little for the feeder.

Voltage drop: 5.94 V
Drop as % of source: 4.95%
Voltage at the load: 114.06 V of 120 V
Conductor: 12 AWG copper, 1.98 Ω per 1000 ft
Smallest for 3% or less: 8 AWG copper (2.33 V, 1.95%)
Smallest for 5% or less: 12 AWG copper (5.94 V, 4.95%)

An estimate, not a design. This checks voltage drop only, using the resistance values in NEC Chapter 9, Table 8. It does not check ampacity (NEC 310.16), overcurrent protection or local code, and the 3% and 5% figures come from informational notes, which are recommendations. Have a licensed electrician check any real installation.

Wire resistance used: NEC Chapter 9, Table 8

DC resistance in ohms per 1000 ft at 75 °C, the stranded rows, uncoated copper and aluminum. These are the values the calculator uses; solid 14 to 10 AWG wire reads slightly lower.
Size	Copper (Ω per 1000 ft)	Aluminum (Ω per 1000 ft)
14 AWG	3.14	5.17
12 AWG	1.98	3.25
10 AWG	1.24	2.04
8 AWG	0.778	1.28
6 AWG	0.491	0.808
4 AWG	0.308	0.508
3 AWG	0.245	0.403
2 AWG	0.194	0.319
1 AWG	0.154	0.253
1/0 AWG	0.122	0.201
2/0 AWG	0.0967	0.159
3/0 AWG	0.0766	0.126
4/0 AWG	0.0608	0.1
250 kcmil	0.0515	0.0847
300 kcmil	0.0429	0.0707
350 kcmil	0.0367	0.0605
400 kcmil	0.0321	0.0529
500 kcmil	0.0258	0.0424

Longest one-way run for 3% drop, copper, 120 V single-phase

Feet, rounded down, from L = 3% × 120 V × 1000 ÷ (2 × I × R). Past this length the drop is over 3%. Ampacity is a separate limit: a size can be long enough here and still too small for the current.
Size	10 A	15 A	20 A	30 A	50 A
14 AWG	57 ft	38 ft	28 ft	19 ft	11 ft
12 AWG	90 ft	60 ft	45 ft	30 ft	18 ft
10 AWG	145 ft	96 ft	72 ft	48 ft	29 ft
8 AWG	231 ft	154 ft	115 ft	77 ft	46 ft
6 AWG	366 ft	244 ft	183 ft	122 ft	73 ft
4 AWG	584 ft	389 ft	292 ft	194 ft	116 ft
2 AWG	927 ft	618 ft	463 ft	309 ft	185 ft
1/0 AWG	1,475 ft	983 ft	737 ft	491 ft	295 ft
4/0 AWG	2,960 ft	1,973 ft	1,480 ft	986 ft	592 ft

Longest one-way run for 3% drop, copper, 240 V single-phase

Feet, rounded down, from L = 3% × 240 V × 1000 ÷ (2 × I × R). Past this length the drop is over 3%. Ampacity is a separate limit: a size can be long enough here and still too small for the current.
Size	10 A	15 A	20 A	30 A	50 A
14 AWG	114 ft	76 ft	57 ft	38 ft	22 ft
12 AWG	181 ft	121 ft	90 ft	60 ft	36 ft
10 AWG	290 ft	193 ft	145 ft	96 ft	58 ft
8 AWG	462 ft	308 ft	231 ft	154 ft	92 ft
6 AWG	733 ft	488 ft	366 ft	244 ft	146 ft
4 AWG	1,168 ft	779 ft	584 ft	389 ft	233 ft
2 AWG	1,855 ft	1,237 ft	927 ft	618 ft	371 ft
1/0 AWG	2,950 ft	1,967 ft	1,475 ft	983 ft	590 ft
4/0 AWG	5,921 ft	3,947 ft	2,960 ft	1,973 ft	1,184 ft

How to calculate voltage drop by hand

Find the resistance of the wire. Look up the size in NEC Chapter 9, Table 8. 12 AWG uncoated copper is 1.98 ohms per 1000 ft at 75 °C.
Measure the one-way length and the load current. Length is the run from the source to the load, one way, in feet (meters × 3.2808). Current is the load in amps, not the breaker rating, unless you want the worst case.
Multiply. Single-phase: 2 × length × current × resistance ÷ 1000, because current goes out and back. For the example, 2 × 100 × 15 × 1.98 ÷ 1000 = 5.94 V. Three-phase uses √3 (about 1.732) in place of 2.
Turn it into a percent. Divide the drop by the source voltage and multiply by 100: 5.94 ÷ 120 × 100 = 4.95%.
Compare with 3% and 5%. The informational notes suggest 3% or less on a branch circuit or feeder and 5% or less overall. Try the next size up until it passes: for the example that is 8 AWG copper.
Check ampacity separately. A size that passes the drop test still has to carry the current safely: check NEC 310.16 and the breaker and terminal ratings, or ask an electrician.

Frequently asked questions

What is the voltage drop formula?: Single-phase: VD = 2 × L × I × R ÷ 1000. Three-phase: VD = √3 × L × I × R ÷ 1000. L is the one-way length in feet, I the current in amps and R the wire's resistance in ohms per 1000 ft. For 12 AWG copper, 100 ft and 15 A on 120 V that is 2 × 100 ft × 15 A × 1.98 Ω/1000 ft ÷ 1000 = 5.94 V, or 4.95% of 120 V.
How much voltage drop is acceptable?: The NEC does not set a hard limit for ordinary circuits. Informational Note No. 4 to 210.19(A) says branch-circuit conductors sized so the drop at the farthest outlet is no more than 3%, and the total for feeder and branch circuit together no more than 5%, give reasonable efficiency of operation; an informational note to 215.2(A) says the same for feeders (its number differs between code editions). Informational notes are advice, not requirements, but other rules, equipment instructions and some local codes do set limits.
What wire size keeps 100 ft of a 20 A, 120 V circuit under 3%?: Copper: 8 AWG; aluminum: 6 AWG. For 5% the smallest copper size is 10 AWG. These come from the drop alone: the conductor also needs enough ampacity for a 20 A breaker (12 AWG copper at least), whatever the drop.
Why is the formula 2 × length?: Current flows from the source to the load and back, so a single-phase circuit has two conductors of the length you measure, and both lose voltage. In a balanced three-phase circuit the currents partly cancel, so the total loss is √3 (1.732) times the one-way figure rather than 2. That is why a three-phase run of the same size, length and current loses about 13% less voltage in volts.
Does aluminum have more voltage drop than copper?: Yes, about 1.6 times as much for the same size: 12 AWG aluminum in the example drops 9.75 V (8.13%) against 5.94 V for copper. Aluminum is normally sized one or two steps larger for the same job, and it needs terminals rated for it.
Does a higher voltage reduce the percent drop?: Yes. The volts lost depend on the current, not the source voltage, so the same load on 240 V has half the percent drop of 120 V: the example circuit drops 5.94 V either way but that is 2.48% of 240 V. (A 240 V load draws half the current for the same watts, which halves the drop in volts again.)
How do I calculate three-phase voltage drop?: Use √3 (1.732) in place of 2. For 8 AWG copper, 150 ft and 30 A on 208 V three-phase the drop is 6.06 V, 2.92% of 208 V. This assumes a balanced load and uses the voltage between phases.
Can I enter the length in meters?: Yes: choose meters and the calculator converts at 1 m = 3.2808 ft before using the formula. 30 m of 12 AWG copper at 15 A and 120 V is 98.43 ft and a drop of 5.85 V. The resistance values are per 1000 ft.
Is this enough to size my wire?: No. It estimates the drop only. Wire also has to carry the current within its ampacity (NEC 310.16 and the rules on temperature ratings, conduit fill, bundling and ambient temperature), match the breaker, and meet the code your area has adopted. Have a licensed electrician check any design before you build it, especially anything on a panel, a feeder or a motor.

How it works

Voltage drop is current × resistance, counted over the whole conductor path. Single-phase: VD = 2 × L × I × R ÷ 1000; three-phase: VD = √3 × L × I × R ÷ 1000, with L the one-way length in feet, I in amps and R in ohms per 1000 ft. R is the DC resistance of uncoated copper or aluminum at 75 °C from NEC Chapter 9, Table 8, using the stranded-conductor rows (solid 14, 12 and 10 AWG wire reads slightly lower, so the estimate errs high for it); the full list is in the table above. The percent is the drop divided by the source voltage you pick. The smallest size is the first in the list from 14 AWG to 500 kcmil whose drop is 3% (or 5%) or less of that voltage, using the same length and current. Simplifications: it uses DC resistance, so it ignores the inductive reactance that matters for large conductors in steel conduit and at a poor power factor (NEC Chapter 9 Table 9 gives AC values); real wire is usually cooler than 75 °C and so loses slightly less; the load is treated as one lump at the end of the run with a steady current; a three-phase load is assumed balanced; and starting current of motors is not considered. This is an estimate for planning, not a design or a code check. It does not check ampacity (NEC 310.16), overcurrent protection, conduit fill or the code in force where you live, and the 3% and 5% figures come from informational notes, which are recommendations. A licensed electrician or your inspector decides what is right for an installation. Everything runs in your browser.

Sources

NFPA 70, National Electrical Code, Chapter 9, Table 8 Conductor Properties (DC resistance at 75 °C); values cross-checked against published reproductions of the table
NFPA 70, 210.19(A) Informational Note No. 4 (3% at the farthest outlet, 5% total for feeder and branch circuit) and the matching informational note to 215.2(A) for feeders
NFPA 70, Table 310.16 Allowable ampacities of insulated conductors (a separate requirement from voltage drop)
EC&M, How to Use Chapter 9 in Your Next Design (Table 8 and voltage drop)

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