Calculating the resistance of copper wires
(If you're not interested in all the number theory, skip to the chart below)
resistance = resistivity × length / area
Resistivity for Cu is 0.00000001678 ohm.m
Circular mils
The easiest measure of a wire's cross section is its diameter. For many years this measure has been expressed as Circular Mils (thousanths of an inch). To use that in resistance calculations, we need to convert to area: Area
Area = pi * r^2 (a mnemonic: circles are round, but pie are squared)
where pi is 3.14159265 and r is the radius or 1/2 of the diameter
Convert mils to inches
Putting it all together
area in square inches = ((circ mils / 1000) / 2) ^ 2 * pi
Since our constant for resistivity is expressed in Ohmmeters, we'll need to convert the area to meters also.
meters˛ = inches˛ / 39.370079
For your convenience, the resistance of some standard wire sizes have been calculated and reproduced in the chart below. Remember that the resistance of copper increases with increasing temperature.
Standard wire resistance chart (copper at 77°F/25°C,
resistivity 0.00000001678 ohm.m)
AWG
|
diam (inch)
|
diam (mm) |
Ohms/ft
|
Ohms/m
|
000
|
0.4096
|
10.40384
|
0.000060163
|
0.000197385
|
00
|
0.3648
|
9.26592
|
0.000075847
|
0.000248843
|
0
|
0.3249
|
8.25246
|
0.000095620
|
0.000313715
|
1
|
0.2893
|
7.34822
|
0.000120602
|
0.000395675
|
2
|
0.2576
|
6.54304
|
0.000152110
|
0.000499049
|
3
|
0.2294
|
5.82676
|
0.000191806
|
0.000629286
|
4
|
0.2043
|
5.18922
|
0.000241832
|
0.000793411
|
6
|
0.162
|
4.1148
|
0.000384609
|
0.001261842
|
8
|
0.1285
|
3.2639
|
0.000611285
|
0.002005528
|
10
|
0.1019
|
2.58826
|
0.000972079
|
0.003189236
|
12
|
0.0808
|
2.05232
|
0.001546063
|
0.005072386
|
14
|
0.0641
|
1.62814
|
0.002456597
|
0.008059701
|
16
|
0.0508
|
1.29032
|
0.003911313
|
0.012832391
|
18
|
0.0403
|
1.02362
|
0.006214982
|
0.020390361
|
20
|
0.032
|
0.8128
|
0.009857119
|
0.03233963
|
22
|
0.0254
|
0.64516
|
0.015645251
|
0.051329564
|
24
|
0.0201
|
0.51054
|
0.024983763
|
0.081967727
|
26
|
0.0159
|
0.40386
|
0.039925993
|
0.13099079 |
28
|
0.0126
|
0.32004
|
0.063578296
|
0.208590209 |
30
|
0.01
|
0.254
|
0.100936902
|
0.331157815
|
32
|
0.008
|
0.2032
|
0.157713909
|
0.517434086
|
34
|
0.0063
|
0.16002
|
0.254313182
|
0.834360835
|
36
|
0.005
|
0.127
|
0.403747608
|
1.324631261
|
|
