# Wire Gauge Calculator

Created by Steven Wooding
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Jun 05, 2023

The wire gauge calculator lets you know the diameter and cross-sectional area of your chosen wire, as well as the electrical resistance per unit length. This is all very useful if you are wiring up speakers to your home theater system, and you were looking for a speaker wire gauge calculator.

Use this wire gauge size calculator instead of wading through those tedious wire gauge charts. It supports both the American Wire Gauge (AWG) standard and the Standard Wire Gauge (SWG) system. Read on to understand more about these ways of measuring wire sizes

## The American Wire Gauge (AWG) standard

American wire gauge is a logarithmically stepped wire gauge system used mainly in North America since 1857. It applies to a solid, round, nonferrous, electrical wire. AWG is also commonly used to specify the size of jewelry, namely body piercing. However, if you check the ring size converter, you'll notice that sometimes this similarity may be misleading, so always double-check.

For increasing AWG numbers, the diameter and cross-sectional area of the wire gets smaller. The scale is defined at two points, in terms of wire diameter. Number 36 AWG wire has a diameter of 0.005 inches, while 0000 (4/0) AWG wire has a diameter of 0.46 inches. The ratio of these two diameters is 1:92 and there are 40 gauge sizes between them, giving 39 steps. The difference in diameter of each successive gauge is a constant ratio of 921/39. Between two steps of gauge number, the ratio difference is 922/39, and so on. The formula for the diameter for any AWG number, $n$, is:

\ \scriptsize \begin{align*} \text{diameter (in)} &= 0.005\ \text{inch} \times 92^{(36-n)/39}\\ \text{diameter (mm)} &= 0.127\ \text{mm} \times 92^{(36-n)/39} \end{align*}

For AWG gauge numbers 00, 000, and 0000, a negative number must be used for $n$. So, for gauge 00, use $n=-1$; 000, use $n=-2$; and for 0000, use $n=-3$.

As a rule of thumb, if you decrease the AWG by six, the diameter of the wire will double. Test this out in the wire gauge calculator if you like.

The cross-sectional area in terms of the AWG number $n$ can be found using the area of a circle:

\!\scriptsize \begin{align*} \text{area} &= \frac{\pi}{4} \times \text{diameter}^2 \\ \text{area (in}^2\text{)} &= 0.000019635\ \text{inch}^2 \times 92^{(36-n)/19.5}\\ \text{area (mm}^2\text{)} &= 0.012668\ \text{mm}^2 \times 92^{(36-n/19.5)} \end{align*}

The resistance per unit length calculation (discussed later on) requires the cross-sectional area of the wire to be computed.

## The Standard Wire Gauge (SWG)

This wire gauge calculator also supports the British Standard Wire Gauge (SWG), also known as the Imperial Wire Gauge or the British Standard Gauge. SWG is not so popular these days, but it is still used to define the thickness of guitar strings, as well as some types of electrical wiring.

SWG is built on the base unit of the mil, which is 0.001 inch, or a thousandth of an inch. The gauge number defines the diameter of the wire and ranges from the largest, number 7/0 at 500 mil (0.5 inch), to the smallest, number 50 at 1 mil (0.001 inch). Each step of the scale reduces the weight per unit length by approximately 20 percent. The weight per unit length of a wire is proportional to its cross-sectional area, which in turn is related to the square root of the diameter:

$\ \scriptsize \text{diameter reduction per step} = \\\quad \left(1 - \sqrt{(1-0.2)}\right) \times 100 = 10.6\%$

Unfortunately, the SWG scale doesn't follow this relationship precisely. The steps between the gauges are held constant over a range of gauges, before changing to a new constant for the next range. These changes in steps approximately follow an exponential curve. This system means that to learn the diameter of a particular gauge, you need to look it up in a gauge chart (shown below).

Wire Gauge Chart for the Standard Wire Gauge system.

SWG Gauge

Diameter (in)

Diameter (mm)

Step (in)

7/0

0.5

12.7

0.036

6/0

0.464

11.786

0.032

5/0

0.432

10.973

4/0

0.4

10.16

0.028

3/0

0.372

9.449

0.024

2/0

0.348

8.839

0

0.324

8.23

1

0.3

7.62

2

0.276

7.01

3

0.252

6.401

0.02

4

0.232

5.893

5

0.212

5.385

6

0.192

4.877

0.016

7

0.176

4.47

8

0.16

4.064

9

0.144

3.658

10

0.128

3.251

0.012

11

0.116

2.946

12

0.104

2.642

13

0.092

2.337

14

0.08

2.032

0.008

15

0.072

1.829

16

0.064

1.626

17

0.056

1.422

18

0.048

1.219

19

0.04

1.016

0.004

20

0.036

0.914

21

0.032

0.813

22

0.028

0.711

23

0.024

0.61

0.002

24

0.022

0.559

25

0.02

0.508

26

0.018

0.4572

0.0016

27

0.0164

0.4166

28

0.0148

0.3759

0.0012

29

0.0136

0.3454

30

0.0124

0.315

0.0008

31

0.0116

0.2946

32

0.0108

0.2743

33

0.01

0.254

34

0.0092

0.2337

35

0.0084

0.2134

36

0.0076

0.193

37

0.0068

0.1727

38

0.006

0.1524

39

0.0052

0.1321

0.0004

40

0.0048

0.1219

41

0.0044

0.1118

42

0.004

0.1016

43

0.0036

0.0914

44

0.0032

0.0813

45

0.0028

0.0711

46

0.0024

0.061

47

0.002

0.0508

48

0.0016

0.0406

49

0.0012

0.0305

0.0002

50

0.001

0.0254

## Electrical resistance per unit length

This wire gauge calculator also calculates the electrical resistance per unit length of wire. To calculate that, we need to know a fundamental property of the electrical conductor material that forms the core of the wire - resistivity. Here is its equation:

$\quad \rho = R \times \frac{A}{l}$

where:

• $R$ – Electrical resistance;
• $A$ – Cross-sectional area of the wire; and
• $l$ – Length of the wire.

To find the resistance per unit length of wire, we can rearrange the resistivity equation in terms of $R/l$:

$\quad \frac{R}{l} = \frac{\rho}{A}$

So, it's merely a case of dividing the resistivity by the cross-sectional area. To get the total resistance of a particular wire, multiple the above result by the length of the wire, or use our wire resistance calculator. And if you are interested in knowing the voltage drop along your wire, the voltage drop calculator is just the ticket.

## How to use the wire gauge calculator

Let's now go through step-by-step how to use the wire gauge calculator. It's quite straightforward.

1. Select either the AWG and SWG wire gauge standards.
2. Select the wire gauge number you require.
3. Select the wire core material. For most wires, this will be copper. The resistance calculation assumes that the wire is at room temperature. Advanced mode: If your wire core material is not listed, enter the advanced mode, and you will be able to enter a custom value for the material's resistivity.
4. Results time! The diameter, cross-sectional area, and electrical resistance per length will then appear.
5. To change any of the units of these quantities, simply click on the current unit and select a new unit from the drop-down menu.

## Worked example using the American wire gauge calculator – 12 gauge wire

To finish up, here is a worked example of how to calculate the wire diameter, cross-sectional area, and electrical resistance per unit length of 12 gauge wire. First, let's calculate the diameter of the wire:

\footnotesize \begin{align*} \text{diameter} &= 0.005\ \text{inch} \times 92^{(36-12)/39}\\ &= 0.0808081\ \text{inch} \end{align*}

Followed by the cross-sectional area calculation:

\footnotesize \begin{align*} \text{area} &= \frac{\pi}{4} \times \text{diameter}^2\\ &= 0.785398 \times 0.08081^2\\ &= 0.0051286\ \text{inch}^2 \end{align*}

If the electrical conductor material of the wire is copper, we would use the resistivity value for copper at room temperature, which is $1.68\times10^{-8}\ \Omega\cdot\text{m}$ in metric units. Given there are 39.37 inches in a meter, that's:

$\footnotesize 1.68\times10^{-8} \times 39.37 = \\\quad6.6142\times10^{-7}\ \Omega\cdot\text{inch}$

Then the resistance per unit length can be calculated:

$\footnotesize \text{resistance per inch} = \frac{6.6142\times10^{-7}}{0.0051286}\\\ \\ \qquad \qquad \qquad = 0.00012896\ \Omega/\text{inch}$

It is more common to state the resistance per unit length in the imperial system as Ohms per 1,000 feet, or kilofeet (kft). Since there are 12 inches per foot, you multiple the above number by 12,000:

$\footnotesize \text{resistance per kft} =\\\quad\ 0.00012896\ \Omega/\text{inch} = 1.5476\ \Omega/\text{kft}$

Depending on your needs, sometimes it might be easier to use the wire size calculator to find the correct gauge for your project without delving into much detail.

Steven Wooding
Gauge type
American Wire Gauge (AWG)
American wire gauge
0 (1/0)
AWG
Wire material (@ 20 °C)
Copper
Diameter
in
Cross-sectional area
in²
Resistance per length
0.09576
Ω/
kft
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