# Wire Gauge - Ampacities - Ampacity

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## AWG

By definition, No. 36 AWG is 0.0050 inches in diameter, and No. 0000 is 0.4600 inches in diameter. The ratio of these diameters is 92, and there are 40 gauge sizes from No. 36 to No. 0000, or 39 steps. Using this common ratio, wire gauge sizes vary geometrically according to the following formulas.

• Where:

d = diameter
n = AWG gauge number
A = cross-sectional area

, $d_n = 0.005~\mathrm{inch} \times 92 ^ \frac{36-n}{39} = 0.127~\mathrm{mm} \times 92 ^ \frac{36-n}{39}$

or equivalently

, $d_n = e^ {-1.12436 - 0.11594n}\ \mathrm{inch} = e^ {2.1104 - 0.11594n}\ \mathrm{mm}$

The gauge can be calculated from the diameter using

, $n = -39\log_{92} \left( \frac{d_{n}}{0.005~\mathrm{inch}} \right)+36 = -39\log_{92} \left( \frac{d_{n}}{0.127~\mathrm{mm}} \right)+36$

(NB: if you are calculating AWG with a calculator that does not support logarithms to a definable base, then you can apply the Change of Base equivalent equation)

and the cross-section area is

, $A_n = \frac{\pi}{4} d_n^2 = 0.000019635~\mathrm{inch}^2 \times 92 ^ \frac{36-n}{19.5} = 0.012668~\mathrm{mm}^2 \times 92 ^ \frac{36-n}{19.5}$

Sizes with multiple zeros are successively larger than No. 0 and can be denoted using "number of zeros/0", for example 4/0 for 0000. For an m/0 AWG wire, use n = −(m−1) = 1−m in the above formulas. For instance, for No. 0000 or 4/0, use n = −3.

• We realize that the use of the legacy inch unit is not optimal - included here due to the historical nature of the wire gage (which should also be discontinued).

## Load Carrying Capacities or Ampacities

In part from Reference Data for Engineers: Radio, Electronics, Computer and Communications 7th Ed At 20 C

• De-rate with +0.00393 per °C - wire carrying current capacity sitting in the insulation and conduit will not be at 20 °C You will want to derate to at least the temperature rating of your insulation. Resistance listed here are not trade maxima - most wire that is soft or annealed will be slightly higher. Resistance of hard-drawn copper is slightly greater - 2 - 3%. Stranded wire may also be higher.

AWG Dia Inch Cir Mil Dia mm Area Inch2 lb/kft ohms
/kft
Ohms
/km
CU Max
free-air
Amps
CU Max
enclosed
Amps
32 0.008 63.2 0.20 4.964E-05 0.19 164.1 538.4 .53 0.32
30 0.010 100.5 0.25 7.894E-05 0.30 103.2 338.6 .86 0.52
28 0.013 159.8 0.32 1.255E-04 0.48 64.9 212.9 1.4 0.83
26 0.016 254.1 0.40 1.996E-04 0.77 40.81 133.9 2.2 1.3
24 0.020 404.0 0.51 3.173E-04 1.22 25.67 84.22 3.5 2.1
22 0.025 642.4 0.64 5.046E-04 1.94 16.14 52.95 7.0 5.0
20 0.032 1,021.5 0.81 8.023E-04 3.09 10.15 33.30 11.0 7.5
18 0.040 1,624.3 1.02 1.276E-03 4.92 6.385 20.95 16 10
16 0.051 2,582.7 1.29 2.028E-03 7.82 4.016 13.18 22 13
14 0.064 4,106.7 1.63 3.225E-03 12.43 2.525 8.284 32 17
12 0.081 6,529.9 2.05 5.129E-03 19.77 1.588 5.210 41 23
10 0.102 10,383.0 2.59 8.155E-03 31.43 0.999 3.985 55 33
8 0.128 16,509.7 3.26 1.297E-02 49.98 0.628 3.274 73 46
6 0.162 26,251.4 4.12 2.062E-02 79.46 0.395 1.296 101 60
4 0.204 41,741.3 5.19 3.278E-02 126.35 0.248 0.8136 135 80
2 0.258 66,371.3 6.54 5.213E-02 200.91 0.156 0.5118 181 100
1 0.289 83,692.7 7.35 6.573E-02 253.34 0.123 0.4035 211 125
0 0.325 105,534.5 8.25 8.289E-02 319.46 0.0983 0.3225 245 150
00 0.365 133,076.5 9.27 1.045E-01 402.83 0.0779 0.2556 283 175
000 0.410 167,806.4 10.40 1.318E-01 507.96 0.0618 0.2028 328 200
0000 0.460 211,600.0 11.68 1.662E-01 640.53 0.04901 0.1608 380 225

• A second version of the above table with 60°C trade derating - (affects ohms/kft and ohms/km.)

Max ambient 60°C

AWG Dia Inch Cir Mil Dia mm Area Inch2 lb/kft ohms
/kft
Ohms
/km
CU Max
free-air
Amps
CU Max
enclosed
Amps
32 0.008 63.2 0.20 4.964E-05 0.19 199.587 654.613 .53 0.32
30 0.010 100.5 0.25 7.894E-05 0.30 125.521 411.690 .86 0.52
28 0.013 159.8 0.32 1.255E-04 0.48 78.941 258.915 1.4 0.83
26 0.016 254.1 0.40 1.996E-04 0.77 49.647 162.833 2.2 1.3
24 0.020 404.0 0.51 3.173E-04 1.22 31.223 102.407 3.5 2.1
22 0.025 642.4 0.64 5.046E-04 1.94 19.636 64.404 7.0 5.0
20 0.032 1,021.5 0.81 8.023E-04 3.09 12.349 40.504 11.0 7.5
18 0.040 1,624.3 1.02 1.276E-03 4.92 7.767 25.473 16 10
16 0.051 2,582.7 1,29 2.028E-03 7.82 4.884 16.020 22 13
14 0.064 4,106.7 1.63 3.225E-03 12.43 3.072 10.075 32 17
12 0.081 6,529.9 2.05 5.129E-03 19.77 1.932 6.336 41 23
10 0.102 10,383.0 2.59 8.155E-03 31.43 1.215 3.985 55 33
8 0.128 16,509.7 3.26 1.297E-02 49.98 0.764 2.506 73 46
6 0.162 26,251.4 4.12 2.062E-02 79.46 0.481 1.576 101 60
4 0.204 41,741.3 5.19 3.278E-02 126.35 0.302 0.991 135 80
2 0.258 66,371.3 6.54 5.213E-02 200.91 0.190 0.623 181 100
1 0.289 83,692.7 7.35 6.573E-02 253.34 0.151 0.494 211 125
0 0.325 105,534.5 8.25 8.289E-02 319.46 0.120 0.392 245 150
00 0.365 133,076.5 9.27 1.045E-01 402.83 0.095 0.311 283 175
000 0.410 167,806.4 10.40 1.318E-01 507.96 0.075 0.247 328 200
0000 0.460 211,600.0 11.68 1.662E-01 640.53 0.060 0.196 380 225

## House Wiring

First, avoid the most common error in house wiring - hanging a 120Vac outlet off of a 3 conductor (L1,L2,N) 220Vac cable. It is dangerous! To do something like that you need a 4 conductor cable - (L1,L2,N,G) to provide a safety ground that is _NOT_ carrying any current.

The table below will not support any reduced ground cables and is for _Copper_wire_only_!. If you run aluminum wire you need to consult the manufacturer's data sheets and be sure to understand terminal block treatments! This table also in no way compensates for length of run! This table is not for wires packed in conduit - wires need to dissipate heat!

Normal COPPER House Wiring Gauge
will have a specific building code!
Circuit
Maximum
Amperage
Minimum COPPER
wire gage
15A 14AWG
20A 12AWG
30A 10AWG
40A (45A*) 8AWG
55A (60*) 6AWG
70A (80*) 4AWG
95A (100*) 2AWG
Alternate marked * is NOT to NEC code

for 60 degree wiring (inside romex).

If you are running more than 100A
you probably will run Aluminum and
need a different table.

Do not use copper ratings
for aluminum!

## PCB Trace Width vs Current

This chart can diverge from what you see for many reasons.

### Fusing Point of Wire

H. W. Preece’s Investigation way back in 1884 provided a way to calculate the fusing current of a wire based on its diameter.

$I = kd^{\frac {3}{2}}$

or

$d = \left ( \frac{I}{k} \right ) ^{\frac{2}{3}}$

Where:

I is the current in Amps
d is the diameter in cm
k is the fusing constant
Material k for d in cm Melting point°C Resistivity (Ω-m) at 20 °C Coefficient*
Silver 1900 961.78 1.59×10-8 .0038
Copper 2530 1084.62 1.72×10-8 .0039
Aluminum 1870 660.32 2.82×10-8 .0039
Iron 777.4 1538 1.0×10-7 .005
Tin 405.5 231.93 1.09×10-7 .0045
Platinum 1277 1768.3 1.1×10-7 .00392
Tin/lead solder 325.5 183 1.44x10-7 .0035

There should be a relationship between resistivity, melting temperature and k. Remember that the electrical resistivity ρ (Rho (letter)) of a material is given by:

, ${\rho={R \left. \frac{A}{\ell} \right.}}$

where

ρ is the static resistivity (measured in ohm meters, Ω-m);
R is the electrical resistance of a uniform specimen of the material (measured in ohms, Ω);
, $\ell$ is the length of the piece of material (measured in meters, m);
A is the cross-sectional area of the specimen (measured in square meters, m²).

### Watts of heat generated in a wire for a given current

First, an example using the formula in the above section to determine the wattage dissipated in a 1 meter length of 12 gage copper wire at 10A.

, ${\rho={R \left. \frac{A}{\ell} \right.}}$

Rearrange to solve for R

, $R = \frac{\rho\ell}{A}$

Remembering that P = I2R

, $P = \frac{I^2 \rho\ell}{A}$

Substituting in where:

I = 10
ρ = 1.72x10 − 8Ω − m
, $\ell = 1m$
d = 0.205cm = .00205m
, $r = .001025m \approx .001m$
, $A = \pi r^2 \approx 3.14 \mathrm{x} 10^{-6}m^2$

, $P \approx \frac{\left (10^2\right) 1.72\mathrm{x}10^{-8} \left ( 1 \right)}{3.14 \mathrm{x} 10^{-6}} \approx 0.55W$

### Temperature Rise in Wire, accounting only for radiative heat loss

Note, in practical terrestrial cases, convective and conductive heat losses will dominate radiative losses. The following are appropriate for only two situations. One, where you have to install cabling in regions with exceptionally thin atmospheres, such as in vacuum vessels or piping. The other, is where the current densities are sufficiently high for the wire to glow - radiative transfer may then dominate the other loss mechanisms and the following can be used.

Now, to figure the temperature rise per watt in steady-state conditions.

, $\dot{Q}_{12} = \epsilon A\left ( \sigma T_1^4 - \sigma T_2^4\right )$

Where :

, $\dot{Q}_{12} =$ Net radiant energy
ε = emissivity (sometimes called emittance) - the degree of similarity to a black body
ε = 1 a black body
ε = 0.35 a very shiny aluminum alloy
T = Absolute temperature in degrees Kelvin
, $\sigma = 5.67 \mathrm{x}10^{-8} \frac{W}{M^2 K^4}$ Stefan-Boltzmann constant

When T1 and T2 are not very different, it is convenient to linearize the equation by factoring the term , $\left( \sigma T_1^4 - \sigma T_2^4 \right )$ to obtain:

, $\dot{Q}_{12} = \epsilon A \sigma \left( T_1^2 + T_2^2 \right )\left(T_1 + T_2\right )\left(T_1 - T_2\right )$
, $\dot{Q}_{12} \approx \epsilon A \sigma \left( 4T_m^3\right)\left( T_1 - T_2 \right )$

When , $T_1 \approx T_2$ and Tm is the mean of T1 and T2

Written again as

, $\dot{Q}_{12} \approx A h_r \left( T_1 - T_2 \right)$

Where

, $h_r = 4 \epsilon \sigma T^3_m$ or Radiation heat transfer coefficient with the units , $\frac{W}{m^2K}$
, $h_r = 4 \epsilon \left(5.67 \mathrm{x} 10^{-8} \frac{W}{m^2K^4}\right)\left(298K\right)^3$
, $h_r \approx 6 \epsilon \frac{W}{m^2K}$

Emissivity is always a fuzzy number that depends on details like surface finish and for copper can vary from 0.7 to .88 but for electrical work 0.4 works most of the time. Give it large error bands!

The surface area of our wire is

, $A = \ell \pi d = \left(1m\right) .0205m \pi = .0644 m^2$

Our power is 0.55 Watts and , $\epsilon \approx 0.4$

, $T_2 = 30^\circ C = 303K$
, $\dot{Q}_{12} = \epsilon A\left ( \sigma T_1^4 - \sigma T_2^4\right )$

, $0.55W = \left ( 0.4 \right ) \left ( 0.0644m^2 \right ) \left [ \sigma T_1^4 - \left ( 5.67 \mathrm{x} 10^-8 \frac{W}{m^2 K^4} \right ) \left(303K\right)^4 \right ]$
, $\sigma T_1^4 = \left[ \frac {0.55}{ \left ( 0.4 \right ) \left ( 0.0644 \right )} + 478\right] \frac{W}{m^2}$
, $\sigma T_1^4 = \frac {0.55}{ \left ( 0.4 \right ) \left ( 0.0644 \right )} + 478 = 480.1\frac{W}{m^2}$
, $T_1 = \left [ \frac{480.1}{5.67 \mathrm{x}10^{-8}} \right]^{\frac{1}{4}} = 303.35K$

or a rise of 0.034 C

We can solve for T1 generally:

, $T_1 = \left( \frac{\frac{\dot{Q}_{12}}{\epsilon A} + \sigma T_2^4}{\sigma}\right)^{\frac{1}{4}}$

### Why was 'hot' Black in House Wiring?

Black used to be the colour of the live wire in ordinary cables in Europe (as it still as it is in the USA). This is because the very first power wires were insulated by strips of linen soaked with guttappercha ( a good organic insulator) and natural rubber filled with soot. Hence: black colour for the dangerous one. The neutral wires weren't insulated at all, just bare copper wire. Later they got a grey coating (less soot in them), still later blue as artificial dyes came up in Europe.

#### Mains wire codes in Germany

In ordinary 230 V AC household cables, e.g. for kitchen devices, TV-sets, small machines etc.:

• black live 230 V AC labeled L or L1 or P (Phase, on older devices)
• blue neutral, 0 V labeled N
• green/yellow protective earth (PE) connected to ground

In three phase 400 V cables

• black L1
• grey L2
• brown L3
• blue neutral
• green/yellow protective earth (PE) connected to ground.

L1, L2, L3 were labeled formerly as R, S, T respectively. Motor inputs were U, S, V. The corresponding cold ends of the motor windings were called X, Y, Z, usually shorted together in a "star" or "Y" connection arrangement.

In older three phase cables the grey lead was also black so when installing cables, it was difficult to determine the direction of rotation. In cables older than, say, 60 years the PE lead was red, in Switzerland even more recently.

Blue may be (and is frequently) used for any purpose, especially for switched power, can't be sure that it's neutral. Other colours may be used for any purpose. Green/yellow may not be used for anything else but PE.

### Other older standards from Europe

In the UK and those areas adopting British standards, red was universally live and black was neutral (with green earth if sleeved)for both fixed wiring and flexes from before the war, until 1971. Then the green with yellow stripe earth was introduced. (mitigating risks of mistake with red green colour blindness) At the same time brown was introduced for live and blue for neutral in new flexes. (3 phase went from red-white-blue to red-yellow-blue, but very few were seriously affected by this. There was also agreement that the colours in this order represent the sequence of positive half cycles for correct rotation. This was a more useful change.) In the UK from late 2005 fixed-wiring also changed to to brown & blue ( this change is sometimes referred to as euro-harmonization). At the same time 3-phase colours went from red/blue/yellow with a black neutral to brown/black/grey with a blue neutral. So now both blue and black can either be live or neutral depending on the age of the installation, leading to some potentially expensive and dangerous errors when old and new systems co-exist.

Prior to Unification in 1989, much of East Germany had many appliances of the older German colour code, with gray and white or black as current carrying colours and red earth. Live and neutral polarity is not preserved in the Shcucko socket system, and it is important to be very careful with older equipment from this era of unknown provenance.

In DC (direct current) electronics applications, Black is most often ground and Red most often positive. More wire about see - telco color codes

### Stranded wire Terms

Tinned
Individual copper strands are coated with tin
Heavy Tinned
Similar to basic tinning, but a much thicker coating of tin. It is commonly used with high frequency induction heaters because it can bond on stripped areas while the rest of the cable remains flexible.
Tin Overcoat (TOC)
Tinned stranded wire twisted and then is coated with a second coat of pure tin

Top Coat, or Topcoat
Bare (untinned) copper stranded wire is twisted first then gets an overall coating of pure tin. Its advantages are similar to prefused or pre-bond tinning(below). It is accepted by the UL and the CSA, but not the Mil-Spec standards.
Prebonded, Prefused, or Pre-bond
Tinned-Over-Coat or Top Coat that is then fused - which makes it stiffer. They use Heavy tin coated individual wires stranded which are then bonded by resistance heat. (the entire conductor is bonded before other operations, such as insulating, are started.) Acts similar to a solid conductor, but is less likely to break or work-harden in flex applications. Note - some insulated wire manufacturers also use the term "Prebond" to mean any stranded wire which has been fused or overtinned. Prefused or pre-bond conductors are usually accepted under UL and CSA guidelines, but not by Mil-W-16878 cable specifications.
• Top Coat, Tinned Over Coat, and Prebonded are often used for wire that goes through a hole in a PCB or terminal block to prevent stray stands from causing shorts. These terms are often misused.

## Disclaimer

This information may have errors; It is not permissible to be read by anyone who has ever met a lawyer.
Use is confined to Engineers with more than 370 course hours of electronic engineering for theoretical studies.
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