# Voltage drop and AWG wire gauge calculator

> Voltage drop over a DC, single-phase or three-phase cable run, plus AWG wire size to diameter, mm², kcmil and resistance per km, and back.

Versão interativa: https://www.calcopenly.com/pt/science/wire-gauge-voltage-drop-calculator
Tema: Calculadoras científicas

Voltage drop is the voltage lost along a cable because the conductor has resistance. The calculator takes the resistance per metre from the cross-section (R′ = ρ/A, with ρ at 20 °C) and multiplies it by the current and the one-way length: twice for DC and single-phase, because the current goes out and back, and by √3 for a balanced three-phase run. It also converts any AWG size to diameter, mm², kcmil and ohms per km with the ASTM B258 formula, or finds the nearest AWG for a measured diameter.

The default, 15 A over 30 m of 12 AWG copper at 120 V, drops 4.69 V, or 3.91%. That is above the 3% branch-circuit figure in the NEC informational note; 10 AWG brings the same run down to 2.46%.

The result is a resistive estimate at 20 °C. Copper's resistance is about 22% higher at a 75 °C operating temperature, and long AC runs of large cables add reactance, so leave a margin when the result is close to a limit.

## Dados

- **Calculate** (opções: AWG → size, Diameter → AWG, Voltage drop)
- **Wire gauge (AWG)** (opções: 4/0 (0000), 3/0 (000), 2/0 (00), 1/0 (0), 1 AWG, 2 AWG, 3 AWG, 4 AWG, 5 AWG, 6 AWG, 7 AWG, 8 AWG, 9 AWG, 10 AWG, 11 AWG, 12 AWG, 13 AWG, 14 AWG, 15 AWG, 16 AWG, 17 AWG, 18 AWG, 19 AWG, 20 AWG, 21 AWG, 22 AWG, 23 AWG, 24 AWG, 25 AWG, 26 AWG, 27 AWG, 28 AWG, 29 AWG, 30 AWG, 31 AWG, 32 AWG, 33 AWG, 34 AWG, 35 AWG, 36 AWG, 37 AWG, 38 AWG, 39 AWG, 40 AWG)
- **Conductor diameter**
- **Conductor** (opções: Copper, Aluminium)
- **Circuit** (opções: DC, Single-phase AC, Three-phase AC)
- **One-way length of the run**
- **Load current**
- **Current unit** (opções: µA, mA, A, kA)
- **Supply voltage (line-to-line for three-phase)**

## Resultados

- Voltage drop — resultado principal
- Voltage drop (V)
- Voltage at the load (V)
- Power lost in the wire (W)
- Nearest AWG
- Exact gauge number
- Diâmetro (mm)
- Diâmetro (in)
- Cross-section area (mm²)
- Cross-section area (kcmil)
- Resistance at 20 °C (Ω/km)
- Resistance at 20 °C (Ω/kft)

## Fórmula

$$
d = 0.005\,\text{in}\times 92^{(36-n)/39},\quad R' = \frac{\rho}{A},\quad \Delta V = k\,I R' L,\ k = 2\ (\text{DC, 1-phase}),\ \sqrt3\ (\text{3-phase})
$$

## Exemplos resolvidos

### 12 AWG copper

- Calculate: AWG → size
- Wire gauge (AWG): 12 AWG
- Conductor: Copper
- **Diâmetro: 2.05253 mm**
- **Cross-section area: 3.30877 mm²**
- **Resistance at 20 °C: 5.211 Ω/km**
- Fonte de verificação: Python 3.8 math: 0.005 in × 92^(24/39) = 2.0525254 mm; ρ/A with ρ = 1.7241e-8 Ω·m (AWG table: 2.053 mm, 3.31 mm², 5.211 Ω/km)

### 4/0 AWG is exactly 0.46 in

- Calculate: AWG → size
- Wire gauge (AWG): 4/0 (0000)
- Conductor: Copper
- **Diâmetro: 0.46 in**
- **Cross-section area: 211.6 kcmil**
- Fonte de verificação: ASTM B258 definition: 4/0 = 0.4600 in = 211.6 kcmil

### 36 AWG is exactly 0.005 in

- Calculate: AWG → size
- Wire gauge (AWG): 36 AWG
- Conductor: Copper
- **Diâmetro: 0.127 mm**
- **Cross-section area: 0.025 kcmil**
- Fonte de verificação: ASTM B258 definition: 36 AWG = 0.0050 in

### 2.05 mm wire

- Calculate: Diameter → AWG
- Conductor diameter: 2.05 mm
- Conductor: Copper
- **Nearest AWG: 12 AWG**
- **Exact gauge number: 12.01**
- Fonte de verificação: Python 3.8 math: n = 36 − 39·log₉₂(2.05/0.127) = 12.0106

### 15 A over 30 m of 12 AWG copper at 120 V

- Calculate: Voltage drop
- Wire gauge (AWG): 12 AWG
- Conductor: Copper
- Circuit: Single-phase AC
- One-way length of the run: 30 m
- Load current: 15
- Current unit: A
- Supply voltage (line-to-line for three-phase): 120 V
- **Voltage drop: 4.68962 V**
- **Voltage drop: 3.91%**
- **Voltage at the load: 115.31 V**
- **Power lost in the wire: 70.3444 W**
- Fonte de verificação: Python 3.8 math: ΔV = 2 × 30 × 15 × 1.7241e-8/3.308773e-6 = 4.6896238 V

### Three-phase 60 A over 50 m of 4 AWG aluminium at 400 V

- Calculate: Voltage drop
- Wire gauge (AWG): 4 AWG
- Conductor: Aluminium
- Circuit: Three-phase AC
- One-way length of the run: 50 m
- Load current: 60
- Current unit: A
- Supply voltage (line-to-line for three-phase): 400 V
- **Voltage drop: 6.94372 V**
- **Voltage drop: 1.74%**
- Fonte de verificação: Python 3.8 math: ΔV = √3 × 50 × 60 × 2.8264e-8/A(4 AWG) = 6.9437169 V

## Perguntas

### What is the maximum allowed voltage drop?

In the US, an informational note to NEC 210.19 recommends at most 3% on a branch circuit and 5% in total for feeder plus branch circuit. The note is advice, not an enforceable rule, although some jurisdictions adopt it. IEC 60364-5-52 and BS 7671 give 3% for lighting and 5% for other loads when the installation is fed from a public low-voltage network, and 6% and 8% from a private supply.

### How do you calculate voltage drop in a wire?

Multiply the current by the resistance of the wire that carries it. For DC or single-phase, ΔV = 2 × I × R′ × L, where R′ is the resistance per metre and L the one-way length; the 2 counts the outgoing and return conductors. For balanced three-phase, use √3 (1.732) instead of 2 and compare the result with the line-to-line voltage. 15 A over 30 m of 12 AWG copper (5.21 Ω/km) drops 4.69 V.

### How does the AWG number relate to wire diameter?

ASTM B258 defines AWG by a formula: 36 AWG is 0.005 in and 4/0 (0000) is 0.46 in, with 39 equal ratio steps between them, so each gauge number changes the diameter by a factor of 1.1229. Three gauge numbers double or halve the cross-sectional area, and six double or halve the diameter. 12 AWG is 2.053 mm across with 3.31 mm² of metal.

### Why is this resistance lower than in NEC Chapter 9 Table 8?

Table 8 lists DC resistance at 75 °C, while this calculator uses solid conductors at 20 °C with copper's resistivity from IEC 60028 (0.017241 Ω·mm²/m). For solid 12 AWG copper, Table 8 gives 1.93 Ω per 1000 ft against 1.59 here; the whole difference is the 55 °C of extra temperature. Stranded 12 AWG is listed slightly higher, at 1.98 Ω per 1000 ft.

### How much bigger does an aluminium wire need to be than copper?

About 1.6 times the cross-section, or roughly two AWG sizes larger, for the same resistance and voltage drop. Electrical-grade aluminium conducts 61% as well as copper (IEC 60889), with a resistivity of 0.028264 Ω·mm²/m against copper's 0.017241. The final size must also meet the ampacity tables, and aluminium terminations need connectors rated for it.

### Qual é a precisão de “Voltage drop and AWG wire gauge calculator”?

A precisão depende dos dados inseridos e das hipóteses do método. O cálculo decimal usa 50 algarismos significativos, mas estimativas, métodos numéricos e dados de origem podem ter menor precisão; o arredondamento exibido não elimina essas limitações. Exemplos resolvidos verificados com fontes independentes: 6. Por exemplo, “12 AWG copper” é verificado com Python 3.8 math: 0.005 in × 92^(24/39) = 2.0525254 mm; ρ/A with ρ = 1.7241e-8 Ω·m (AWG table: 2.053 mm, 3.31 mm², 5.211 Ω/km).

### De onde vem o método?

ASTM B258 — Standard specification for standard nominal diameters and cross-sectional areas of AWG sizes; IEC 60028 — International standard of resistance for copper (0.017241 Ω·mm²/m at 20 °C); NFPA 70 (NEC) 210.19(A) Informational Note — 3% branch / 5% total voltage drop guidance; Wikipedia — American wire gauge (table of diameters, areas and copper resistance).

## Fontes

- ASTM B258 — Standard specification for standard nominal diameters and cross-sectional areas of AWG sizes
- IEC 60028 — International standard of resistance for copper (0.017241 Ω·mm²/m at 20 °C)
- NFPA 70 (NEC) 210.19(A) Informational Note — 3% branch / 5% total voltage drop guidance
- [Wikipedia — American wire gauge (table of diameters, areas and copper resistance)](https://en.wikipedia.org/wiki/American_wire_gauge)