Voltage Drop Formula with Examples

[Swartz09]

Voltage Drop Calculations

NEC 2017 – 210.19(A) information note #4, and 215.2(A)(1)(b) information note #2
NEC 2020 _ 210.19(A) information note # 3, and 215.2(A)(1), 215.2(A)(1)(b) information note #4

210.19(A) Informational Note No.3: Conductors for branch circuits as defined in Article 100, shall be sized to prevent a voltage drop exceeding 3 percent at the furthest outlet of power, heating, and lighting loads, or combinations of such loads.
Where the maximum total voltage drop on both feeders and branch circuits to the farthest outlet does not exceed 5 percent provided reasonable efficiency of operation.
See Informational Note No.2 of 215.2(A)(1) for voltage drop on a feeder conductor.

Formula Breakdown ( Definition ) of Voltage drop

VD = Volts dropped from the circuit

CM = Circular mills for the conductor from chapter 9, Table 8

R = Resistance of a conductor from chapter 9, Table 8
Note: That in chapter 9, Table 8, on the right hand side of the table for conductor resistance under the heading for “copper” there are two column one is (coated) and the other is (uncoated). Use the resistance from the (uncoated) column. The (coated) column is for tinned conductors.

I = Current or Amperage of the load

D = Distance from the source to the load in feet (one way)

Approximate K:
12.9 - Copper (constant for copper wire)
21.2 – Aluminum (constant for aluminum wire)

Exact K:
R x CM / 1000 (R = conductor resistance, CM = Circular Mills For the conductor / 1000)

2 = Multiplying factor for a single – phase circuits

1.732 = Multiplying factor for 3 phase circuits (The 1.732 represents the square root of 3)

VD Permitted = 3% of source voltage
EX:
120 x 3% = 3.6,
208 x 3% = 6.24
240 x 3% = 7.2
277 x 3% = 8.31
480 x 3% = 14.4

Voltage Drop Formulas:

VD = I x R (or) VD = 2 x R x D x I / 1000

Conductor Size = CM = 2 x K x D x I / VD Permitted

Distance: (From source to load) – D = CM x VD permitted / 2 x K x I

Load: I (current of load) I = CM x VD permitted / 2 x K x D

A common formula that can be used to determine the voltage drop in a single – phase circuit is:
VD = 2 x K x I x D / CM

Example – A 120 volt , single phase branch circuit, is using a AWG 10 copper conductor, and is supplying a 30 ampere load eighty (80) feet from the source. Determine the approximate voltage drop? (K = 12.9)

Answer – 5.9653 or 6 volts dropped
Cm = 10380 (chapter 9, Table 8)
K = 12.9 copper
I = 30 amperes
D = 80 feet
VD = 2 X 12.9 x 30 x 80 = 61920 =

Example: VD = I x R (or) VD = 2 x R x D x I / 1000

Using AWG 12 stranded copper conductors, the voltage drop on a single phase 120 volt branch circuit, supplying a 20 amp load located 150ft from the source is ___________ volts dropped?

Answer – 11.88 volts dropped.
Go to chapter 9, Table 8, and find the resistance for a AWG 12 stranded copper conductor 1.98 ohm/KFT (1.98 ohms per 1000ft of conductor length), now that we have all are values wright the formula,

VD: volts dropped from a circuit.
2: Multiplying factor for a single – phase circuits
R: Resistance of a conductor from chapter 9, Table 8 D: Distance from the source to the load in feet (one way)
I = Current or Amperage of the load

VD = 2 x 1.98 x 150ft x 20 amps / 1000 = 11880/1000= 11.88 volts dropped


Example: Conductor Size = CM = 2 x K x D x I / VD Permitted

What size THWN copper conductor is required for a 240-volt single phase branch circuit that has a 30-amp load 200ft from the source?

Answer – AWG 6

2: Multiplying factor for a single – phase circuits
K: 12.9 - Copper (constant for copper wire)
D: Distance from the source to the load in feet (one way)
I = Current or Amperage of the load
VD Permitted = 3% of source voltage 240 x 3% = 7.2

2 x 12.9 x 200ft x 30 amps / 7.2 VD permitted = 154800 / 7.2 = 21500 or a AWG 6 (26240 is the closet to our answer) from chapter 9, Table 8, go to column (Area Circular mils)


Example: Distance: (From source to load) – D = CM x VD permitted / 2 x K x I

How far from a 208 3 phase source can a 24-amp load be located if AWG 10 copper stranded conductors are to be installed?

Answer – 120.79 ft (from source)

D: Distance from the source to the load in feet (one way)
CM = Circular mills for the conductor from chapter 9, Table 8
VD Permitted = 3% of source voltage 208 x 3% = 6.24
1.732 = Multiplying factor for 3 phase circuits (The 1.732 represents the square root of 3)
K: 12.9 - Copper (constant for copper wire)
I = Current or Amperage of the load

Chapter 9, Table 8, go to column (Area Circular mils), AWG 10 stranded is (10380 CM), VD permitted for this 208 volts is 6.24 (208 x 3% = 6.24 volts) and this is a 3 phase circuit.

D = 10380 x 6.24 / 1.732 x 12.9 x 24 amp = 64771.2 / 536.2272 = 120.79ft

Example: Load: I (current of load) I = CM x VD permitted / 2 x K x D

A 240-volt single phase feeder with size 4/0 THWN copper conductors is to supply an existing panelboard located 290ft from the main switchboard. What is the maximum load that can be placed on the panelboard so that voltage drop is limited to 3%?

Answer – 128 amperes

I = Current or Amperage of the load
CM = Circular mills for the conductor from chapter 9, Table 8
VD Permitted = 3% of source voltage 240 x 3% = 7.2
2: Multiplying factor for a single – phase circuits
K: = 12.9 copper
D: Distance from the source to the load in feet (one way)

Chapter 9, Table 8, go to column (Area Circular mils), AWG 2/0 stranded is (133,100 CM), VD permitted for this 240 volts is 7.2 (240 x 3% = 7.2 volts) and this is a single phase circuit. With a distance of 290ft.

I = 133100 x 7.2 / 2 x 12.9 x 290 = 958320 / 7482 = 128 amperes