How Do I Calculate Voltage Drop?
January 1, 2006
Q: I have a barn on my property that I would like to get power to. This barn is 377 feet from the nearest power. I would like to have 50 amps @240 volts and I’m going to run my power in conduit. What size wire do I need to run?
A: The formula for voltage drop is: Vd = 2K x L x I / Cm
Vd = Voltage Drop
I = Current in Conductor (Amperes)
L = One way Length of Circuit
Cm = Cross Section Area of Conductor (Circular Mils)
K = Resistance in ohms of one circular mil foot of conductor
K = 12.9 for Copper Conductors @ 75 degrees C
K = 21.2 for Aluminum Conductors @ 75 degree C
/ = Divided by
I will assume you are going to use copper conductors and your temperature is @ 75 degrees C.
Reasonable operating efficiency is achieved if the voltage drop of a feeder or a branch circuit is limited to 3 percent. However, the total voltage drop of a branch circuit plus a feeder can reach 5% and still achieve reasonable operating efficieny (210.19(A)(1)FPN No. 4 or 215.2(A)(4)FPN No. 2).
8 AWG = 50 amps @ 75 degrees C = 16510 Cm
Vd = 2 x 12.9 x 377 x 50 / 16510 = 30 volts
30 volts / 240 volts = 0.125 = 12.5% = Not Acceptable
6 AWG = 65 amps @ 75 degrees C = 26240 Cm
Vd = 2 x 12.9 x 377 x 50 / 26240 = 19 volts
19 volts / 240 volts = 0.079 = 7.9% = Not Acceptable
4 AWG = 85 amps @ 75 degrees C = 41740 Cm
Vd = 2 x 12.9 x 377 x 50 / 41740 = 12 volts
12 volts / 240 volts = 0.05 = 5% = Not Acceptable – This is not acceptable because the 5% voltage drop is at your sub panel. If you were to run any wire beyond the sub panel, your voltage drop would exceed 5%. I’m assuming you are going to install a light and some receptacles in your barn.
3 AWG = 100 amps @ 75 degrees C = 52620 Cm
Vd = 2 x 12.9 x 377 x 50 / 52620 = 9 volts
9 volts / 240 volts = 0.038 = 3.8% = Acceptable
Your equipment grounding conductor (ground wire) is sized off of table 250.122. You need to run a 10 AWG copper ground wire for this circuit.
To summarize; you need to run 3 – 3 AWG (2-hots and 1-neutral) branch circuit conductors and 1 – 10 AWG equipment grounding conductor (ground wire).
Tip: The rule of thumb is to plan for voltage drop at 100 feet and increase one wire size for every 100 feet thereafter.
Happy New Year!
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