# Copper wire figures

NOTE: This information and the circuits are provided as is without any express or implied warranties. While effort has been taken to ensure the accuracy of the information contained in this text, the authors/maintainers/contributors assume no responsibility for errors or omissions, or for damages resulting from the use of the information contained herein. The contents of the articles below might be totally inaccurate, inappropriate, or misguided. There is no guarantee as to the suitability of said circuits and information for any purpose.

## AWG Table

``` 1 AWG is 289.3 thousandths of an inch
2 AWG is 257.6 thousandths of an inch
5 AWG is 181.9 thousandths of an inch
10 AWG is 101.9 thousandths of an inch
20 AWG is  32.0 thousandths of an inch
30 AWG is  10.0 thousandths of an inch
40 AWG is   3.1 thousandths of an inch
```
The table in ARRL handbook warns that the figures are approximate and may vary dependent on the manufacturing tolerances. If you don't have a chart handy, you don't really need a formula. There's several handy tricks:

```Solid wire diameters increases/decreases by a factor of  2 every  6 gages,
"    "      "          "          "                    3 every 10 gages,
"    "      "          "          "                    4 every 12 gages,
"    "      "          "          "                    5 every 14 gages,
"    "      "          "          "                   10 every 20 gages,
"    "      "          "          "                  100 every 40 gages,
```
With these, you can get around alot of different AWGs and they cross check against one another. Start with solid 50 AWG having a 1 mil diameter.
```So, 30 AWG should have a diameter of ~  10 mils. Right on with my chart.
36 AWG should have a diameter of ~   5 mils. Right on with my chart.
24 AWG should have a diameter of ~  20 mils. Actually ~ 20.1
16 AWG should have a diameter of ~  50 mils. Actually ~ 50.8
10 AWG should have a diameter of ~ 100 mils. Actually ~ 101.9
```
If you are more interested in current carrying ability than physical size, then also remember that a change of 3 AWG numbers equals a doubling or halving of the circular mills (the cross sectional area). Thus, if 10 AWG is safe for 30 amps, then 13 AWG (yeah, hard to find) is ok for 15 amps and 16 AWG is good for 7.5 amps.

The wire gauge is a logarithmic scale base on the cross sectional area of the wire. Each 3-gauge step in size corresponds to a doubling or halving of the cross sectional area. For example, going from 20 gauge to 17 gauge doubles the cross sectional area (which, by the way, halves the DC resistance).

So, one simple result of this is that if you take two strands the same gauge, it's the equivalent of a single wire that's 3 gauges lower. So two 20 gauge strands is equivaent to 1 17 gauge.

### Wire Gauge Resistance per foot

```4   .000292
6   .000465
8   .000739
10  .00118
12  .00187
14  .00297
16  .00473
18  .00751
20  .0119
22  .0190
24  .0302
26  .0480
28  .0764
```

## Current ratings

Most current ratings for wires (except magnet wires) are based on permissible voltage drop, not temperature rise. For example, 0.5 mm^2 wire is rated at 3A in some applications but will carry over 8 A in free air without overheating. You will find tables of permitted maximum current in national electrical codes, but these are based on voltage drop (not the heating which is no problem in the current rating those codes give).

Here is a small current and AWG table taken from the Amateur Radio Relay Handbook, 1985.

```AWG  dia    circ  open   cable  ft/lb   ohms/
mils   mils  air A  Amp    bare    1000'

10   101.9 10380    55    33    31.82   1.018
12    80.8  6530    41    23    50.59   1.619
14    64.1  4107    32    17    80.44   2.575
```

Mils are .001". "open air A" is a continuous rating for a single conductor with insulation in open air. "cable amp" is for in multiple conductor cables. Disregard the amperage ratings for household use.

To calculate voltage drop, plug in the values: V = DIR/1000
Where I is the amperage, R is from the ohms/1000' column above, and D is the total distance the current travels (don't forget to add the length of the neutral and hot together - ie: usually double cable length). Design rules in the CEC call for a maximum voltage drop of 6% (7V on 120V circuit).

## Resistivities at room temp:

```Element     Electrical resistivity (microohm-cm)

Aluminum    2.655
Copper      1.678
Gold        2.24
Silver      1.586
Platinum    10.5
```

This clearly puts silver as the number one conductor and gold has higher resistance than silver or copper. It's desireable in connectors because it does not combine well with other materials so remains relatively pure at the surface. It also has the capability to adhere to itself (touch pure gold to pure gold and it sticks together) which makes for very reliable connections.

### Thermal conductivity at room temp:

```               W/cm C

silver          4.08
copper          3.94
gold            2.96
platinum        0.69

diamond         0.24
bismuth         0.084
iodine          43.5E-4
```
This explains why diamonds are being used for high power substrates now. That's man-made diamonds. Natural diamonds contain sufficient flaws in the lattice that the phonons (heat conductors) get scattered and substantially reduce the ability to transport the heat.

## Copper wire resistance table

```AWG   Feet/Ohm  Ohms/100ft  Ampacity*   mm^2   Meters/Ohm  Ohms/100M

10    490.2       .204        30      2.588    149.5       .669
12    308.7       .324        20      2.053     94.1       1.06
14    193.8       .516        15      1.628     59.1       1.69
16    122.3       .818        10      1.291     37.3       2.68
18     76.8       1.30         5      1.024     23.4       4.27
20     48.1       2.08        3.3     0.812     14.7       6.82
22     30.3       3.30        2.1     0.644     9.24       10.8
24     19.1       5.24        1.3     0.511     5.82       17.2
26     12.0       8.32        0.8     0.405     3.66       27.3
28     7.55       13.2        0.5     0.321     2.30       43.4
```
These Ohms / Distance figures are for a round trip circuit. Specifications are for copper wire at 77 degrees Fahrenheit or 25 degrees Celsius.

## Wire current handling capacity values

```A/mm2    R/mohm/m        I/A
6         3.0             55
10        1.8             76
16        1.1             105
25        0.73            140
35        0.52            173
50        0.38            205
70        0.27            265
```

## Information about 35 mm2 Cu wire

According Str�berg TTT 35mm2 copper wire can take continuous current of 170A on free air and 200 A on ground. The wire can handle 5 kA short circuit current for 1s. DC resistance of the wiure is 0.52mohm/m.

## Mains wiring current ratings

In mains wiring there are two considerations, voltage drop and heat buildup. The smaller the wire is, the higher the resistance is. When the resistance is higher, the wire heats up more, and there is more voltage drop in the wiring. The former is why you need higher-temperature insulation and/or bigger wires for use in conduit; the latter is why you should use larger wire for long runs.

Neither effect is very significant over very short distances. There are some very specific exceptions, where use of smaller wire is allowed. The obvious one is the line cord on most lamps. Don't try this unless you're certain that your use fits one of those exceptions; you can never go wrong by using larger wire.

This is a table apparently from BS6500 which is reproduced in the IEE Wiring Regs which describes the maximum fuse sizes for different conductor sizes:

```Cross-     Overload
sectional   current
area         rating

0.5mm�           3A
0.75mm�          6A
1mm�            10A
1.25mm�         13A
1.5mm�          16A
```

## Typical current ratings for mains wiring

### Inside wall

```mm^2  A
1.5   10
2.5   16
```

### Equipment wires

```mm^2   A
0.5    3
0.75   6
1.0   10
1.5   16
2.5   25
```

### We sizes used in USA inside wall

For a 20 amp circuit, use 12 gauge wire. For a 15 amp circuit, you can use 14 gauge wire (in most locales). For a long run, though, you should use the next larger size wire, to avoid voltage drops.

Here's a quick table for normal situations. Go up a size for more than 100 foot runs, when the cable is in conduit, or ganged with other wires in a place where they can't dissipate heat easily:

```                Gauge           Amps
14              15
12              20
10              30
8               40
6               65
```

## PCB track widths

For a 10 degree C temp rise, minimum track widths are:

```Current  width in inches
0.5A      .008"
0.75A     .012"
1.25A     .020"
2.5A      .050"
4.0A      .100"
7.0A      .200"
10.0A     .325"
```

## Equipment wires in Europe

### 3 core equipment mains cable

```Current               3A      6A      10A     13A     16A
Condictor size(mm)   16*0.2  24*0.2  32*0.2  40*0.2  48*0.2
Copper area (mm^2)    0.5     0.75    1.0     1.25    1.5
Overall diameter(mm)  5.6     6.9             7.5
```
Calbe ratings for 3A, 6A and 13A are based on BS6500 1995 specifications and are for stranded thick PVC insulated cables.

### Insulted hook-up wire in circuits (DEF61-12)

```Max. current               1.4A    3A     6A
Max. working voltage (V)   1000   1000   1000
PVC sheat thickness (mm)    0.3    0.3   0.45
Conductor size (mm)        7*0.2 16*0.2 24*0.2
Conductor area (mm^2)       0.22   0.5   0.75
Overall diameter (mm)       1.2    1.6   2.05
```

## Car audio cable recommendations

This info in from rec.audio.car FAQ (orognally from IASCA handbook). To determine the correct wire size for your application, you should first determine the maximum current flow through the cable (looking at the amplifier's fuse is a relatively simple and conservative way to do this). Then determine the length of the cable that your will use, and consult the following chart:

```                              Length of run (in feet)
Current     0-4  4-7 7-10  10-13  13-16  16-19  19-22  22-28

0-20A     14   12   12     10     10      8      8      8
20-35A     12   10    8      8      6      6      6      4
35-50A     10    8    8      6      6      4      4      4
50-65A      8    8    6      4      4      4      4      2
65-85A      6    6    4      4      2      2      2      0
85-105A      6    6    4      2      2      2      2      0
105-125A      4    4    4      2      2      0      0      0
125-150A      2    2    2      2      0      0      0     00
```

## Skin effect

Skin effect is an effect that the electricity in high frequencies does not use the whole condictor area. High frequencies tend to use only the outer parts of the conductor. The higher the frequency, the less of the wire diameter is used and higher the losses. Sin effect must be taken care in high frequency coil designs.

The frequency dependency of the resistance of a cylindrical conductor can be calculated by the following formula, which is surely valid for high frequencies and radii of approx. 50 um:
R(f) = R(DC)* (1 + 1/3 * x^4) with x = Radius/2*sqrt(pi*frequency*permeability*conductivity)

The "formula" for skin effect is the same whether the conductor is rectangular or cyclindrical. That is why the same value of "radius" used in wire size in a switchmode transformer is used to determine half the thickness of a flat foil conductor in the case of foil-wound secondaries.

An approximate equation for the resistance ratio for rectangular conductors (from Terman) is:
rho = 1/(((8PI * f)/(Rdc * 10^9))^0.5)

Skin depth is not an absolute, but only the depth where current through the wire or foil has fallen to a specific proportion of the current at the surface. In fact, current falls off exponenially as you move inward fromm the surface. The depth of the "skin" is also influenced by proximity to nearby conductors (such as in a transformer) so is itself not absolute. Also the formula has to be modified if you use wire that is ferromagnetic (iron for example).

In addition to skin effect a lot of engineers doing their own magnetics design don't consider the 'proximity effect' which 'crowds' the current to one side of the conductor and increases losses. This condition is worst in thick multi-layer windings. Fortunately, many of the new transformer shapes have a long and skinny window - good for low leakage L and low proximity effect losses.

## Wire sizes used in fuses

The Standard Handbook for Electrical Engineers lists the following formula:

33 * (I/A)^2 * S = log( (Tm - Ta) / (234 + Ta) + 1 )

```I = current in Amperes
A = area of wire in circ. mils
S = time the current flows in seconds
Tm = melting point, C
Ta = ambient temp, C
```
The melting point of copper is 1083 C.
See pp. 4-74 .. 4-79 of the 13th edition of the Handbook for more info.

## Skin effect

At high frequencies there is one thing to consider on wire resistance besides the DC resistence: skin effect.

The current intensity falls off exponentially with depth. The depth of penetration (s=sigma) is the depth at which the current intensity has fallen to 1/e of its value at the surface, where e equals 2.718.

Where the diameter of the conductor is large compared to the depth of penetration, the total current is the same as if the surface current intensity were maintained to a depth of penetration.

For example, for copper the depth of penetration is as follows:

```   MHz        Depth of Penetration sigma (mm)
.1          .209
1           .066
10          .021
100        .0066
1000       .0021
```
For other materials the skin dpeth can be calculated using the formula:
```    s = 503.3sqrt(rho/(urf)) millimeters

rho = resistivity in ohm-meters
= 1.72x10e-8 for copper or 2.83x10e-8 for aluminum
ur  = mu r = relative magnetic permeability
= 1 for both copper and aluminum
f  = frequency in magahertz
```