The Voltage Drop Formula, Explained
Every voltage drop calculator runs one formula: VD = 2 x K x I x L / CM. It looks cryptic, but each letter is one thing you already know: the wire metal, the current, the distance, and the wire size. Here is what each part means, with three worked examples you can check by hand.
The voltage drop formula is VD = 2 x K x I x L / CM, where K is 12.9 for copper or 21.2 for aluminum, I is current in amps, L is one-way length in feet, and CM is the wire's circular mil area. Divide volts lost by system voltage and multiply by 100 for the percent. Worked examples: 5.93 V (4.94%), 11.85 V (4.94%), and an aluminum vs copper comparison.
The formula and what each letter means
VD = 2 x K x I x L / CM
VD is the voltage lost in the wire, in volts. 2 accounts for the round trip: current travels out on one conductor and back on the other, so the resistance doubles. K is the resistivity constant of the metal: 12.9 for copper, 21.2 for aluminum (ohms per circular mil-foot at 75 degrees C). I is the load current in amps, what the load actually draws, not the breaker size. L is the one-way length in feet, panel to load. CM is the wire's cross-sectional area in circular mils, from the AWG table: 14 AWG is 4,110, 12 AWG is 6,530, 10 AWG is 10,380, 8 AWG is 16,510, 6 AWG is 26,240, 4 AWG is 41,740, 3 AWG is 52,620, 2 AWG is 66,360, 1 AWG is 83,690, 1/0 is 105,600, 2/0 is 133,100, 3/0 is 167,800, and 4/0 is 211,600.
Worked example 1: a 120 volt branch circuit
120 volts, 100 feet one-way, 15 amps, 12 AWG copper:
VD = 2 x 12.9 x 15 x 100 / 6530 = 38,700 / 6,530 = 5.93 volts.
As a percent: 5.93 / 120 x 100 = 4.94 percent. That exceeds the NEC 3 percent branch-circuit guidance, so this run needs a bigger wire despite 12 AWG being fine on amps alone.
Worked example 2: a 240 volt circuit
240 volts, 150 feet one-way, 20 amps, 12 AWG copper:
VD = 2 x 12.9 x 20 x 150 / 6530 = 77,400 / 6,530 = 11.85 volts.
Percent: 11.85 / 240 x 100 = 4.94 percent. Same percentage as example 1, which is no coincidence: doubling the voltage and the current while lengthening the run scaled everything proportionally. Higher system voltage tolerates more absolute volts lost for the same percentage, which is why 240 volt equipment handles long runs better than 120 volt equipment.
Worked example 3: aluminum vs copper
240 volts, 200 feet one-way, 30 amps, 8 AWG. First aluminum:
VD = 2 x 21.2 x 30 x 200 / 16510 = 254,400 / 16,510 = 15.41 volts, or 6.42 percent.
Now the same run in copper:
VD = 2 x 12.9 x 30 x 200 / 16510 = 154,800 / 16,510 = 9.38 volts, or 3.91 percent.
Aluminum's higher K value (21.2 vs 12.9) drops about 64 percent more voltage on the same size wire. To match copper's drop with aluminum, go roughly two AWG sizes larger.
The percent formula
Volts lost only matters relative to the system voltage: percent drop = VD / system volts x 100. The NEC recommends a maximum of 3 percent on a branch circuit and 5 percent combined on the feeder plus branch circuit (NEC 210.19(A)(1) and 215.2(A)(1) Fine Print Notes). These are recommendations rather than hard rules, but inspectors and engineers treat them as the standard.
The three-phase version
For balanced three-phase circuits, the multiplier changes from 2 to the square root of 3: VD = 1.732 x K x I x L / CM, where I is the line current and L is the one-way length. The 1.732 replaces the round-trip 2 because in a balanced three-phase system the return current cancels in the neutral. Everything else, K values, CM table, and the percent formula, works exactly the same.
A note on safety: wire sizing involves the National Electrical Code, breaker rules, and local amendments. The examples below are planning estimates. Have a licensed electrician review any real installation before you buy wire or pull a permit.
Skip the arithmetic
Do not do this by hand more than once. Enter your voltage, distance, current, and wire gauge to get the drop in volts and percent instantly.
Voltage drop formula questions
What is the K value for copper wire?
12.9 ohms per circular mil-foot at 75 degrees C. Aluminum is 21.2. These constants come from the resistivity of the metals and are the standard values used in the VD = 2 x K x I x L / CM formula.
How do you calculate voltage drop percentage?
First find the volts lost with VD = 2 x K x I x L / CM, then divide by the system voltage and multiply by 100. Example: 5.93 volts lost on a 120 volt circuit is 5.93 / 120 x 100 = 4.94 percent.
What is the voltage drop formula for 3 phase?
VD = 1.732 x K x I x L / CM. The square root of 3 (1.732) replaces the 2 used for single phase, because in a balanced three-phase system the return current cancels. K, I, L, and CM mean the same things as in the single-phase formula.
What is an acceptable voltage drop?
The NEC recommends a maximum 3 percent drop on a branch circuit and 5 percent total from the service to the final outlet (feeder plus branch combined). These are Fine Print Note recommendations, not enforceable code rules, but they are the industry standard.
Why do you multiply by 2 in the voltage drop formula?
Current makes a round trip: it flows out to the load on one conductor and returns on the other (or the neutral). Both legs have resistance, so the total resistance is twice the one-way resistance. That is also why L is the one-way length, not the round-trip length.