How the calculation works
Single-phase AC or DC: VD = 2 x K x I x L / CM
Three-phase: VD = 1.732 x K x I x L / CM
- VD is the voltage lost in the wire, in volts.
- K is the resistance of a conductor one circular mil in area and one foot long, in ohm-circular mils per foot: 12.9 for copper and 21.2 for aluminum.
- I is the load current in amperes.
- L is the one-way length from the source to the load, in feet.
- CM is the conductor area in circular mils, from the wire gauge chart (12 AWG = 6,529, 10 AWG = 10,380).
IAEI and NCCER both publish the formula in this form. The 2 counts the trip out to the load and back. For three-phase, NCCER writes the drop as the resistance of one conductor times the current times 1.732, the square root of 3.
Worked example: a 15 A load 100 ft from a 120 V panel on 12 AWG copper. VD = 2 x 12.9 x 15 x 100 / 6,529 = 5.93 V, or 4.9% of 120 V, leaving 114.1 V at the load. The same run in 10 AWG aluminum drops 2 x 21.2 x 15 x 100 / 10,380 = 6.13 V. A three-phase example: 50 A at 480 V over 200 ft of 4 AWG copper drops 1.732 x 12.9 x 50 x 200 / 41,740 = 5.35 V, 1.1%.
Where 12.9 and 21.2 come from
IAEI and NCCER both take the constants from the DC resistance values at 75°C in Chapter 9, Table 8 of the National Electrical Code. IAEI multiplies the resistance per foot by the conductor area in circular mils and notes that for every size in that table the result is close to 12.9 for copper and 21.2 for aluminum. It describes them as the constants for uncoated copper and for aluminum.
The same numbers follow from the NBS wire tables. NBS Handbook 100 gives annealed copper at the international standard, 10.371 ohm-cmil/ft at 20°C (1.7241 microhm-cm), with resistance rising 0.393% per °C. NBS Handbook 109 gives EC-H19 aluminum at 61.0% of that conductivity: 17.002 ohm-cmil/ft and 0.403% per °C.
Raised to 75°C, solid copper reaches 12.61 and solid aluminum 20.77. NBS Handbook 100 adds 2% for stranded conductors up to 2,000,000 circular mils, because each strand spirals and is longer than the cable. That gives 12.87 for copper and 21.19 for aluminum, which round to the published 12.9 and 21.2.
What to enter
- Source voltage: the nominal voltage at the start of the run: 120, 208, 240 or 480 V at a panel, or 12, 24 or 48 V at a battery bank.
- Load current: the current the load actually draws, from its nameplate or a clamp meter reading.
- One-way length: the cable route, not the straight line. Include vertical runs and slack.
- Conductor size and material: the AWG or kcmil size and whether it is copper or aluminum.
- Circuit: single-phase or DC, or three-phase.
The result shows volts lost, the percentage of the source voltage and the voltage left at the load. Results above 5% are flagged; IAEI notes that five percent maximum is generally suggested on a circuit.
Low-voltage DC: RV, solar, van and boat wiring
Volts lost depend on current, length and wire size, not on the system voltage. That is why 12 V circuits need much heavier wire: the same 0.75 V loss is 0.6% of 120 V but 6.2% of 12 V. Take a 20 A load 15 ft from a 12 V battery (30 ft of wire out and back):
| Copper size | Drop | Percent of 12 V |
|---|---|---|
| 10 AWG | 0.75 V | 6.2% |
| 8 AWG | 0.47 V | 3.9% |
| 6 AWG | 0.29 V | 2.5% |
| 4 AWG | 0.19 V | 1.5% |
For the same power, current is watts divided by volts (NCCER's formula wheel gives I = P / E for DC circuits). A 240 W load draws 20 A at 12 V but 10 A at 24 V, so on the same wire it loses half the volts, which is a quarter of the percentage. For an inverter, enter the maximum DC input current from its manual. IAEI points out that equipment instructions often require a minimum voltage at the equipment for it to work as intended; size the wire to keep the voltage at the load above that minimum.
Temperature
Copper resistance rises about 0.39% for every °C and aluminum about 0.40%, per NBS Handbooks 100 and 109. A stranded copper conductor has K = 10.58 at 20°C (68°F), 12.24 at 60°C and 13.49 at 90°C. The calculator uses the published 75°C constant, which IAEI describes as the value for conductors operating at 75°C at rated amperage. In the 12 AWG example above, the same run at 20°C drops 4.86 V instead of 5.93 V. A conductor running cooler than 75°C has lower resistance and loses less than the calculator shows; one running hotter loses more.
Design targets and limits of the formula
IAEI notes that the National Electrical Code mentions voltage drop in informational notes in some sections and requires it to be calculated in others. EC&M (2015) quotes Informational Note No. 4 to 210.19(A): branch-circuit conductors sized to prevent a voltage drop over 3% at the farthest outlet, with no more than 5% total on feeders and branch circuits, provide reasonable efficiency of operation. IAEI points out that informational notes are explanatory and not mandatory Code requirements, and advises choosing the limit acceptable to the authority having jurisdiction. Use the code edition your jurisdiction enforces; NFPA, which publishes the NEC as NFPA 70, offers free read-only access to its codes online.
The formula uses DC resistance. IAEI notes that DC values are used for AC circuits for simplicity and consistency, but large AC circuits can drop more: in its worked example, a 500 kcmil aluminum circuit at 80% power factor carrying 180 A over a 310 ft run drops 13.4 V in steel conduit and 11.9 V in nonmagnetic conduit. For long feeders on large conductors, check the cable manufacturer's AC data. Voltage drop also says nothing about how much current a wire may carry. That is ampacity; look it up in the electrical code adopted where you work. See the wire gauge chart for conductor areas and resistance, and the AWG to mm² converter for metric cable.