How to Calculate the Size of a Cable

Cables carry electricity over long distances.
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Thicker cables offer less resistance to electric flow. They offer more electrons to carry a charge and a greater number of paths through which the electrons can travel. As a result, given the same voltage, a thicker cable carries more current. Choose a cable's exact thickness to meet a target level of resistance. The other relevant factors are the length of the cable, which external needs usually dictate and the resistivity of the cable's material.

    Divide the voltage running through the cable by your target current. If, for instance, 120 volts will act on the cable, and you want 30 amps to run through it: 120 / 30 = 4. This is your target resistance, measured in ohms.

    Multiply the cable's length by its material's resistivity. Copper, for instance, has a resistivity of 1.724 x 10^-8 ohm meters at room temperature. If your cable must measure 30,000 meters in length:

    30,000 x 1.724 x 10^-8 = 0.0005172 ohm sq. m.

    Divide the answer by your target resistance:

    0.0005172 / 4 = 0.0001293.

    This is the cable's necessary cross-sectional area.

    Divide the cable's area by pi: (0.0001293) / 3.142 = 4.1152 x 10^-5.

    Find the square root of this answer: (4.1152 x 10^-5) ^ 0.5 = 0.006415. This is the cable's radius, measured in meters.

    Multiply your answer by 39.37 to convert it to inches: 0.006415 x 39.37 = 0.2526.

    Multiply the answer by 2: 0.2526 x 2 = 0.5052 inches. This is the cable's necessary thickness. It approximately corresponds with the standard 16-gauge cable.