Voltage Drop Calculator

How do you calculate voltage drop?

Multiply the current by the resistance of the wire. For a single-phase or DC circuit, V_d = 2 × I × R × L, with I the current in amperes, R the resistance of one conductor per foot or meter, and L the one-way length. Balanced three-phase circuits use √3 instead of 2. Percent drop is V_d ÷ supply voltage × 100.

From wire gauge to ohms per foot

The American Wire Gauge is fixed by two sizes: 0000 is 0.4600 in across and 36 is 0.0050 in, with 38 sizes between them in a geometric series (NBS Handbook 100, Copper Wire Tables, 1966). Each step changes the diameter by the 39th root of 92, so d = 0.127 mm × 92^((36 − n)/39), with 1/0 to 4/0 counted as n = 0 to −3. Three steps multiply the area by 2.005, which is why going three gauge sizes larger halves the resistance, and with it the drop.

Above 4/0, sizes are named by area in kcmil, thousands of circular mils, up to 2,000 kcmil here. A circular mil is the area of a circle one mil, 0.001 in, across, so a round wire’s area in circular mils is its diameter in mils squared: 12 AWG is 80.81 mils across and 6530 circular mils. One kcmil is 0.5067 mm². The resistance of a conductor per unit length is its resistivity divided by that area, R = ρ / A, the relation the wire resistance calculator solves for any material and length.

Copper and aluminum at 20 °C and 75 °C

Copper wire tables use the International Annealed Copper Standard: 1.7241 µΩ·cm at 20 °C, with resistance rising 0.393 percent per °C (NBS Handbook 100). The aluminum here is the electrical grade at 61 percent of that standard’s conductivity, 2.8264 µΩ·cm at 20 °C and rising 0.403 percent per °C (NBS Handbook 109, Aluminum Wire Tables, 1972). Corrected linearly to 75 °C, the temperature NEC Chapter 9 Table 8 lists conductor resistance at, copper reaches 2.097 µΩ·cm and aluminum 3.453. The table below is worked from those.

For solid copper these match NEC Chapter 9 Table 8 to the figures it prints: 3.07, 1.93 and 1.21 Ω per 1,000 ft for 14, 12 and 10 AWG. Stranded wire has slightly more resistance than a solid rod of the same area, because each strand spirals and is longer than the cable; ASTM allows 2 percent for it, the figure used here. In US units the drop is often written VD = 2 × K × I × L ÷ CM, with the area CM in circular mils and K the resistivity in ohm circular mils per foot: 10.37 for copper and 17 for aluminum at 20 °C, 12.61 and 20.77 at 75 °C.

Where the 3 and 5 percent figures come from

They come from an informational note to section 210.19 of the National Electrical Code, NFPA 70, which says that branch-circuit conductors “sized to prevent a voltage drop exceeding 3 percent at the farthest outlet of power, heating, and lighting loads, or combinations of such loads, and where the maximum total voltage drop on both feeders and branch circuits to the farthest outlet does not exceed 5 percent, provide reasonable efficiency of operation.” Section 90.5(C) says informational notes are not enforceable as requirements of the Code, so the 3 percent is a recommendation, not a requirement.

Voltage drop is also not what sizes a wire for safety. Ampacity does that: NEC Article 310 and the overcurrent rules of 240.4 set the smallest conductor a load and its breaker may use, and voltage drop can only call for a larger one. At the full rating of the largest breaker 240.4(D) allows on each, a 120 V run of solid copper at 75 °C reaches 3 percent at 39.1 ft for 14 AWG on 15 A, 46.6 ft for 12 AWG on 20 A and 49.4 ft for 10 AWG on 30 A. On 240 V each distance doubles, because 3 percent of the supply is twice as many volts.

Single-phase, DC and three-phase circuits

In a two-wire circuit, DC or single-phase AC, the current runs the length of the run out and the same length back, so the loop holds twice the wire. A 240 V water heater on a 120/240 V service is two-wire in this sense: its current goes out on one hot conductor and returns on the other.

A balanced three-phase load sends no current back at all, since the three line currents add to zero. Each line drops I × R × L, and because a line-to-line voltage is √3 times a line-to-neutral voltage, the drop between lines is √3 times that. The percent drop is then taken against the line-to-line voltage, such as 208 V or 480 V, with the line current. Using the single-phase 2 instead overstates a three-phase drop by 15.5 percent.

What the formula leaves out

• Reactance. The calculation uses DC resistance, which is the whole answer for DC and close to it for small conductors on AC. In a large conductor on AC, skin effect raises the resistance, and the inductance of the run adds a drop that grows as the power factor falls. NEC Chapter 9 Table 9 gives AC resistance and reactance for that case.
• The real conductor temperature. A copper conductor at 90 °C, the rating of common building wire insulation, has 4.8 percent more resistance than at 75 °C.
• A changing current. The formula takes the current as fixed. A resistive heater draws less current at a lower voltage and a loaded motor draws more, so a large drop changes the current it was worked from. The power the wire wastes is I²R; the electrical power calculator gives the load’s own.

The drop itself is Ohm’s law, V = IR, applied to the wire as a resistance in series with the load. For a two-wire circuit the Ohm’s law calculator gives the same volts from the current and the resistance of both conductors together.

Common mistakes

• Doubling the length and then using the 2. The 2 already counts the return conductor, so a 100 ft run is entered as 100 ft. Entering 200 ft doubles the answer.
• Using 20 °C resistance for a loaded circuit. Copper’s resistance at 75 °C is 21.6 percent higher than at 20 °C, so a drop worked at 20 °C reads low.
• Comparing a three-phase drop with 120 V or 277 V. The √3 formula gives the drop between lines, so it is a percentage of the line-to-line voltage.
• Swapping copper for aluminum at the same gauge. Aluminum at 75 °C has 1.65 times the resistivity of copper. Two gauge sizes larger adds 59 percent to the area, not quite enough to make up for it.

Converting units first? Use the length, electric current, voltage and resistivity conversion tables.