There is a specific formula you can use to calculate the resistance of copper wire based on its area and length. To save time, a calculator comes in handy to crunch the numbers. The area of electrical wire is measured in a unit called "circular mils.'' You need this number to calculate a wire's resistance. To get this information for your particular project, you can look it up in the "National Electrical Code Handbook NFPA 70," Chapter 9, Table 8. An electrical code pocket reference, electrical or instrumentation textbook may also have the same information.
Look up the cross sectional area for the gauge wire you are seeking to calculate from a reliable source, such as a code reference book. If the wire size is followed by "mcm" or "kc mil," just add three zeros after the number. For example, the circular mils areas for #10-gauge and 500-mcm size wire may read as follows:
10-gauge = 10,380 circular mils 500-mcm = 500,000 circular mils
Measure the length of the wire in feet, rounding to the nearest foot. If the wire is 110 feet, 8 inches long, round it up to 111 feet. If it is 110 feet, 5 inches long, round it down to 110 feet.
Insert the values from Step 1 and Step 2 into the formula below and solve.
Formula: L * K / A = R of conductor
L = length in feet
K = 10.4 (a constant, ohms per mil foot for copper) A = cross-sectional area in circular mils
R = resistance of conductor in ohms
For example, to calculate the resistance of a 250-foot #10-gauge copper wire, multiply length by the constant 10.4, then divide by the cross-sectional area for #10-gauge wire as the following steps show:
250 * 10.4 / 10,380 = R 2,600 / 10,380 = R .2505 ohms = R
Things You'll Need
- Table 8 of NFPA 70 or equivalent information
- Calculator, optional
Very small resistances, such as a fraction of an ohm, are common for wires having diameters greater than #2 gauge.
Before applying this information to an electrical installation, check with local building codes for specific requirements.
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