Voltage drop formula [Step by Step Calculations and tables]

Voltage drop formula is used to calculate the voltage dropped across the conductor. Three equations are often used for doing calculations.

Voltage drop calculation formulas
Ohm's law (1 ϕ) V = IR
Single phase Vd =
2K * L * I / CM
Three phase Vd =
1.73K * L * I / CM

where

I = Current

R = Resistance

K = Resistance in ohms in one CM of conductors

L = Length of the circuit in feet

CM = Circular mills

Where at t = 75°
K = 12.9 for copper conductors
K = 21.2 for Aluminum Conductors
————————————-
For other temperatures use the equation
R2 = R1 [1 + α (T2 − 75)]
Where
αcu = 0.00323
αAL = 0.00330
Source: NEC Chapter 9 Table 8, Edition 2011.

Circular Mills table

The CM (circular mills) are calculated from the solid copper wire American wire gauge table:

Size

(AWG)

Diameter

(inches)

Area (CM)
4/0 0.46 211600
3/0 0.4096 167800
2/0 0.3648 133100
1/0 0.3249 105600
1 0.2893 83690
2 0.2576 66360
3 0.2294 52620
4 0.2043 41740
5 0.1819 33100
6 0.162 26240
7 0.1443 20820
8 0.1285 16510
9 0.1144 13090
10 0.1019 10380
11 0.09074 8234
12 0.08081 6530
13 0.07196 5178
14 0.06408 4110
15 0.05707 3257
16 0.05082 2583
17 0.04526 2048
18 0.0403 1624
19 0.03589 1288
20 0.03196 1022
21 0.02846 810.1
22 0.02535 642.5
23 0.02257 509.5
24 0.0201 404
25 0.0179 320.4
26 0.01594 254.1
27 0.0142 201.5
28 0.01264 159.8
29 0.01126 126.7
30 0.01003 100.5
31 0.008928 79.7
32 0.00795 63.21
33 0.00708 50.13
34 0.006305 39.75
35 0.005615 31.52
36 0.005 25
37 0.004453 19.83
38 0.003965 15.72
39 0.003531 12.47
40 0.003145 9.888
41 0.0028 7.842
42 0.002494 6.219
43 0.002221 4.932
44 0.001978 3.911

Single phase voltage drop formula calculations

The single-phase voltage drop is defined as the product of 2K into current into L divided by circular mills of wire.

Example: Find the voltage drop of a 180-volt single phase # 6 copper conductor which provides 20 amp current to load. The length of wire is 200 feet. Take K = 12.9 as for 75° temp.

Solution: Vd(single phase) = [2K * L * I]/CM

= [2 * 12.9 * 200 * 20 ]/26240

= 3.93 V

Percentage voltage drop = 3.93/200 = 1.96%

As per standards the recomend drop is less than 3% .

Three phase voltage drop calculations

The three-phase voltage drop calculations are similar to single phase with the difference of factor 1.73. Here the multiplication factor is 1.73 instead of 2. While all other calculations are same.

Example: Find the voltage drop of 1 kV three-phase system which uses #5 copper wire and delivers 30 amp load at a distance of 800 feet.  Take K = 12.9 as for 75° temp.

Solution: Vd(three phase) = [1.73K * L * I]/CM

= [1.73 * 12.9 * 1000 * 200]/33100 = 16.18 V

%age Vd(three phase) = 16.18/1000 = 1.6%.

Ohm’s law

Ohm’s law can also be used to calculate the voltage drop. Remember that Ohm’s law is only valid for single phase calculations.

Example: What is a voltage drop of two no 6 conductors when a current of 20 Amps flows through them. Use uncoated conductor at 75° for calculations.

Solution: R = 0.510/1000 feet. In our case:

R = 0.510/1000 * 400 = 0.204

V = IR

= 20  Amp * 0.102 = 4.08