# Wire Resistance and Voltage Drop Calculator

by Jeff Lucius

These calculators determine the resistance along a length of stranded copper wire, and if a value for current is provided, voltage drop across that same length of wire.

NOTE: These calculators may not work correctly in Netscape, Opera, or another browser besides MS Internet Explorer.

For those of you with IE 7 (or beyond), you may get a warning about my web site using ActiveX controls. It does not. I do use JavaScript for my calculators. If you want the functionality of the calculators, allow "ActiveX" controls (see instructions by clicking on the IE bar above my web page, if it is there).

In a one-dimensional body, such as a wire, the relationship between current and potential can be described by Ohm's Law:

V = IR
where
V = difference of potential between two points on a wire,
I = current through a wire, and
R = resistance measured between the same two points as the potential difference.

The resistance values for the stranded copper wire sizes shown in the tables below (ones that are typically found in an automobile) are from http://www.mogami.com/e/cad/wire-gauge.html, a 2% lay factor is assumed and diameters are approximate. AWG is the American Wire Gauge (formerly Brown and Sharp) size. Also shown is the corresponding millimeter wire gauge size, which is the cross-sectional area of circular wire. Circular mils (CM) is the diameter of a solid wire in 1/1000th inch diameter circle (a 1 inch diameter wire would be 1 million circular mils). Note: Before August 6, 2005, all CM values, as well as many values in the lower table including resistance, were incorrect (my thanks go to Bill Coffel for contacting me about this). For a solid wire of the same gauge or CM the resistance will be slightly less. For example, a 12 AWG solid copper wire has a resistance of about 5.21 ohm/km compared to 5.32 ohm/km for a 12 AWG stranded wire.

Enter the wire length in either feet or meters and click on "Calculate" to display the resistance for that length of wire in the sizes shown. In addition, if you enter a value for the current draw in amps, the voltage drop along that section of wire is also displayed (volts = amps times ohms). Please remember that by using your browser to "View Source" and saving the HTML file to your local disk drive, you can have this page available offline.

For a very complete, interesting, and handy software package that includes voltage drop calculation and much, much more for Palm OS handheld computers, see the Electrist for Palm OS .

The National Electric Code (NEC) specifies the following formular to determine the wires size in circular mils (CM) for a constant load of I amps, wire length L in feet, and voltage drop V.
CM = (25 x I x L) / V
The CM size can be converted to AWG using the tables below or the link above. This standard is a practical limit determined by NEC. NEC has established that a 2% maximum voltage drop is acceptable. Here are two example uses of this formula in our cars.

Example - Battery move to trunk: CM = (25 x 400A x 12')/0.24v = 500,000 circular mils. This would be a 8/0 AWG wire (diameter of about 0.816"). This is an overestimation of the actual wire size that can be used. A 0 AWG wire (105,535 CM) is adequate but would have a 0.48 voltage drop, or about 4 % with a nominal 12 v potential on the wire and a 400 A draw, which may only occur very briefly when the starter turns a cold engine. Using a 200 A max draw and the same setup would require a 250,000 CM wire or a 5/0 AWG wire. A 0 AWG wire would have a voltage drop of 0.24 volts, which is at the 2% NEC limit. The 150-A fuse (with a 0 AWG wire) I use in my rear-compartment battery setup has not blown, suggesting current draw is less than 200 to 400 A over 1 to 5 seconds. By re-arranging the equation above, we can estimate the voltage drop resulting from using a particular wire size.
V = (25 x I x L) / CM
For a constant current of 120 amps (the size of the main alternator fuse in my car), a wire CM of 105535 (0-ga wire), the voltage drop on a 12' wire would be about 0.144 volts.

Example - Power wire for 500 W (42 A @ 12 V) stereo amplifier: CM = (25 x 42A x 6')/0.24v = 26,250 circular mils. This would require a 6 AWG wire according to NEC standards. Using the "voltage drop" method, if the user wanted less than 1% voltage drop on this wire (assuming a nominal 12 v potential) in this setup then a 6 AWG wire is required. If the user can tolerate a 1.5% drop then an 8 AWG wire would suffice. A 10 AWG wire would have a 2.2% voltage drop, just over the NEC standard.
AWG 20 18 16 14 12 10 8 AWG Stranded Copper Wire Resistance and Voltage Drop Size Diameter Resistance @ 77ºF Resistancefor length(Ohms) VoltageDrop(Volts) Metricmm2 Circularmils inch mm ohm/1000' ohm/km 0.518 1,022 0.0369 0.938 10.3632 34.000 0.823 1,624 0.0465 1.182 6.5227 21.400 1.309 2,583 0.0587 1.491 4.0843 13.400 2.081 4,107 0.0740 1.880 2.5756 8.450 3.309 6,530 0.0933 2.371 1.6215 5.320 5.261 10,383 0.1177 2.989 1.0180 3.340 8.366 16,510 0.1484 3.770 0.6401 2.100 13.302 26,251 0.1871 4.753 0.4023 1.320 21.151 41,741 0.2360 5.994 0.2533 0.831 33.631 66,371 0.2976 7.558 0.1594 0.523 42.408 83,693 0.3341 8.487 0.1265 0.415 53.475 105,535 0.3752 9.530 0.1003 0.329 ENTER Length in feet or meters      Amps
The table and calculator below show the metric wire sizes, with the nearest corresponding AWG gauge, I found in the circuit diagrams for the Mitsubishi 3000GT and Dodge Stealth.
Metricmm2 0.50 0.85 1.25 2 3 5 8 Metric Stranded Copper Wire Resistance and Voltage Drop Size Diameter Resistance @ 77ºF Resistancefor length(Ohms) VoltageDrop(Volts) ClosestAWG Circularmils inch mm ohm/1000' ohm/km 21 986.8 0.0363 0.922 10.7290 35.200 18 1,677 0.0473 1.202 6.3094 20.700 17 2,467 0.0574 1.457 4.2977 14.100 15 3,947 0.0726 1.843 2.6792 8.790 13 5,921 0.0889 2.257 1.7861 5.860 11 9,868 0.1147 2.523 1.0729 3.520 9 15,788 0.1451 3.686 0.6706 2.200 5 39,471 0.2294 5.828 0.2679 0.879 ENTER Length in feet or meters      Amps
The resistance, R, of a length of wire is described by the expression:

R = ρL/A
where
ρ = resistivity of the material composing the wire,
L = length of the wire, and
A = area of the conducting cross section of the wire.

The table below (from the CRC Handbook of Chemistry and Physics, 57th Edition, 1976-1977, CRC Press, p. F167-168) shows values for resistance (of a 10-ga solid wire at 20ºC) and resistivity for selected common metals. The calculators above are for stranded copper wire. You can estimate resistance and voltage drop for the metals listed below using the calculators above using the relative difference in resistivity. For example, aluminum has about 1.64 times the resistivity of copper (2.828/1.724). For a 12-ga copper wire 10 feet long with a load of 5 amps, the calculator above indicates a resistance of 0.0162 ohms and voltage drop of 0.0810 volts. For a similar aluminum wire, the resistance would be about 0.02657 ohms (1.64 x 0.0162) and voltage drop would be about 0.1328 (1.64 x 0.081).

 Resistance and Resistivity for Selected Common Metals 10-ga wire ResistanceOhms/ft Resistivity 10-6 ohm-cm Silver 0.000944 1.629 Copper 0.000999 1.724 Gold 0.00114 2.44 Aluminum 0.00164 2.828 Iridium 0.00306 5.29 Brass 0.00406 7.00 Nickel 0.00452 7.8 Iron 0.00579 10.0 Platinum 0.00579 10.0 Steel 0.00684 11.8 Lead 0.0127 22

Acknowledgments