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 were originally developed many years ago in Internet Explorer.
In a one-dimensional body, such as a wire, the relationship between current and potential can be described by Ohm's Law:
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 (sizes 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. The lay factor relates the diameter of the helical wire path and the length of braided strands (360º of rotation) and is but one factor used to determine the ratio of a wire braid to the equivalent tubular, or solid, conductor (please see http://www.fiskalloy.com/products/wire-facts/ for some additional information). 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). For a solid wire of the same gauge or CM, the resistance will be slightly less than that for a stranded wire. 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.
In the calculators below, 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 more, see Electrist software.
Also providing information regarding voltage drop is Schneider Electric in their Electrical Installation Guide.
The National Electric Code (NEC) specifies the following formula to determine acceptable wire 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. The formula is available at http://en.wikipedia.org/wiki/Circular_mil. 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 very 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.
NOTE May 5, 2013. I have removed the calculator because I was not correctly calculating voltage drop. The resistance was calculated correctly. I should have the calculator back up soon. - JL
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.
The resistance, R
, of a length of wire is described by the expression:
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; CRC Handbook of Chemistry and Physics, 90th Edition, 2009-2010, CRC Press, p. 12-14, p. 15-37) 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 and considering the relative difference in resistivity. For example, aluminum has about 1.58 times the resistivity of copper (2.709/1.712). 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 0.0256 ohms (1.58 x 0.0162) and voltage drop would be about 0.128 (1.64 x 0.081).
|Resistance and Resistivity for Selected Common Metals
||10-ga wire Resistance
10-8 ohm-m @ 25º C
I thank Bill Coffel for his helpful comments and corrections for this article. 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).
Page last updated may 5, 2013