# What is the voltage drop?

Computes the voltage drop, the percent drop and the voltage at the load for a copper or aluminium circuit, from the AWG wire size, the one-way length, the current, the supply voltage and the conductor temperature.

- Page: https://www.acalculator.org/physics/voltage-drop-calculator
- JSON spec: https://www.acalculator.org/physics/voltage-drop-calculator.json
- Version: 12403d362f8b

## Default answer

Example with the default inputs (Conductor Copper, Wire size (AWG) 12 AWG, Circuit DC or single-phase, Supply voltage 120 V, Load current 20 A, One-way length 100 ft, Conductors in parallel 1, Conductor temperature 75 °C): Over 100 ft of 12 AWG wire at 20 A, the voltage drop is 7.73 V (6.44% of 120 V), leaving 112.27 V at the load.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| mat | Conductor | The metal of the wire: copper or aluminium. |
| awg | Wire size (AWG) | The American Wire Gauge size of each conductor. |
| phase | Circuit | DC or single-phase AC (the current goes out and back), or three-phase AC. |
| v | Supply voltage | The voltage at the source: line to line for three-phase. |
| i | Load current | The current the load draws, in amperes. |
| l | One-way length | The length of the circuit from the source to the load, one way. |
| sets | Conductors in parallel | How many conductors of this size share the current in each leg or phase; usually 1. |
| t | Conductor temperature | The temperature of the wire in use; 75 °C is a common rating for building wire. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| drop | Voltage drop | The voltage lost in the wires between the source and the load. |
| percent | Voltage drop, percent | The voltage drop as a percent of the supply voltage. |
| atLoad | Voltage at the load | The supply voltage less the voltage drop. |
| ohmsPerKft | Resistance, Ω per 1,000 ft | The resistance of one conductor per 1,000 feet at the temperature. |
| ohmsPerKm | Resistance, Ω per km | The resistance of one conductor per kilometre at the temperature. |
| diameterIn | Diameter, inches | The diameter of the bare wire: 0.005 in × 92^((36 − n) ÷ 39). |
| areaMm2 | Area, mm² | The cross-section of the bare wire in square millimetres: π × d² ÷ 4. |

## Method

d = 0.005 in × 92^((36 − n) ÷ 39); R = ρ₂₀ × (1 + α × (T − 20 °C)) ÷ (π d² ÷ 4); drop = k × L × I × R ÷ conductors in parallel, with k = 2 (DC or single-phase) or √3 (three-phase).

## Assumptions

- Solid round wire at the AWG diameter; stranded wire of the same gauge has a little more resistance.
- Copper is annealed copper of 100% IACS, 1/58 Ω·mm²/m at 20 °C with α = 0.00393; aluminium is 61% IACS, 0.028264 Ω·mm²/m with α = 0.00403.
- AC circuits count resistance only: no inductive reactance, skin effect or power factor, which add a little drop in large wires.
- The load draws the typed current whatever the voltage at its end.

## Worked examples

1. mat = copper, awg = 12, phase = single, v = 120, i = 20, l = 30.48, sets = 1, t = 293.15 gives ohmsPerKft = 1.588, diameterIn = 0.0808. Source: NBS Handbook 100, Copper Wire Tables (1966), Table 1: 12 AWG, 80.8 mils, 1.588 Ω per 1,000 ft at 20 °C.
2. mat = copper, awg = 10, phase = single, v = 120, i = 20, l = 30.48, sets = 1, t = 293.15 gives ohmsPerKft = 0.9989. Source: NBS Handbook 100, Copper Wire Tables (1966), Table 1: 10 AWG, 0.9989 Ω per 1,000 ft at 20 °C (rounded table value).
3. mat = copper, awg = 12, phase = single, v = 120, i = 20, l = 30.48, sets = 1, t = 348.15 gives ohmsPerKft = 1.931555, drop = 7.726221, percent = 6.438518%, atLoad = 112.273779. Source: ASTM B258 diameter formula.
4. mat = aluminum, awg = 4-0, phase = three, v = 480, i = 200, l = 76.2, sets = 1, t = 348.15 gives diameterIn = 0.46, drop = 8.500668, percent = 1.770972%. Source: ASTM B258 (4/0 AWG = 0.4600 in).
5. mat = copper, awg = 6, phase = single, v = 230, i = 32, l = 30, sets = 1, t = 348.15 gives ohmsPerKm = 1.57634, drop = 3.026572, percent = 1.315901%. Source: ASTM B258.

## FAQ

### How do I calculate voltage drop?

Multiply the wire’s resistance per foot by the length the current travels and by the current: VD = 2 × L × I × R for DC or single-phase AC, where L is the one-way length (the current goes out and back), and VD = √3 × L × I × R for three-phase. A 20 A load 100 ft away on 12 AWG copper at 75 °C (1.9316 Ω per 1,000 ft) loses 2 × 100 × 20 × 0.0019316 = 7.73 V.

### What is an acceptable voltage drop?

The US National Electrical Code has a note, not a rule, that suggests at most 3% on a branch circuit and 5% in total from the service to the farthest outlet. On a 120 V circuit, 3% is 3.6 V. If the calculator shows more, try the next larger wire size.

### How is the resistance of a wire found from its AWG size?

The AWG diameter is d = 0.005 in × 92^((36 − n) ÷ 39), where n is the gauge (1/0 is 0, 4/0 is −3). The cross-section is π × d² ÷ 4, and the resistance per length is the metal’s resistivity divided by that area. 12 AWG copper is 0.0808 in across and has 1.588 Ω per 1,000 ft at 20 °C, as the classic copper wire tables list.

### Why does temperature matter?

Metals conduct worse when hot. Copper’s resistance rises by 0.393% for each °C above 20 °C, aluminium’s by 0.403%. Building wire rated 75 °C, used at that temperature, has about 22% more resistance than at 20 °C, so the calculator starts at 75 °C.

### Does aluminium wire have more voltage drop than copper?

Yes, for the same size. Aluminium conducts about 61% as well as copper, so its resistance is about 1.64 times as high. That is why an aluminium conductor is usually one or two sizes larger than a copper one for the same load.

### Why does this answer differ a little from the NEC tables?

The calculator uses the AWG formula for solid round wire and the resistivity of the metal, not the NEC Chapter 9 tables. Stranded conductors and coated wire in the tables have slightly more resistance, and AC tables add reactance. For solid 12 AWG copper at 75 °C the formula gives 1.93 Ω per 1,000 ft, the same as the table’s solid value.

## Sources

- ASTM B258-18, Standard Specification for Standard Nominal Diameters and Cross-Sectional Areas of AWG Sizes of Solid Round Wires Used as Electrical Conductors (d = 0.005 in × 92^((36 − n)/39)). https://www.astm.org/b0258-18.html
- National Bureau of Standards, Copper Wire Tables, Handbook 100 (1966): annealed copper 100% IACS, 12 AWG = 1.588 Ω and 10 AWG = 0.9989 Ω per 1,000 ft at 20 °C. https://nvlpubs.nist.gov/nistpubs/Legacy/hb/nbshandbook100.pdf
- IEC 60028:1925, International standard of resistance for copper: 1/58 Ω·mm²/m at 20 °C, temperature coefficient 0.00393 per °C. https://webstore.iec.ch/publication/1
- IEC 60889:1987, Hard-drawn aluminium wire for overhead line conductors: resistivity 0.028264 Ω·mm²/m at 20 °C (61% IACS), temperature coefficient 0.00403 per °C. https://webstore.iec.ch/publication/2011
- NFPA 70, National Electrical Code (2020), 210.19(A)(1) Informational Note No. 4: branch-circuit voltage drop of not more than 3%, and 5% overall to the farthest outlet. https://www.nfpa.org/codes-and-standards/nfpa-70-standard-development/70