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AC and DC Voltage Drop Calculator with Formulas and Examples NEC

The Voltage Drop Calculator implements the USA NEC Code. It includes Voltage Drop Formulas and Examples of How To Calculate Voltage Drop.

Voltage (V)

Load rating (A, hp, kW or kVA)
  
Cable size (AWG)

Distance (m, ft)
 

See Also

Voltage Drop Calculator Parameters

What is Voltage Drop?

Voltage drop is the loss of voltage over a wire due to the wire's electrical resistance and reactance. The problem with voltage drop is:

For example, if you supply a 10 Ω heater from a 120 V supply. And the resistance of the wire is 1 Ω. Then the current will be I = 120 V / (10 Ω + 2 × 1 Ω) = 10 A.

The voltage drop will be Vdrop = 10 A × 2 × 2 Ω = 20 V. Therefore, only 100 V will be available for your appliance.

And P = 20 V × 10 A = 200 W will be wasted as heat in the wire.

How to Calculate Voltage Drop?

The voltage drop formulas for AC and DC are shown in the table below.

1-phase AC\(\Delta V_{1\phi-ac}=\dfrac{I L 2 Z_c}{1000}\)
3-phase AC\(\Delta V_{3\phi-ac}=\dfrac{I L \sqrt{3} Z_c}{1000}\)
DC\(\Delta V_{dc}=\dfrac{I L 2 R_c}{1000}\)

Where,

The impedance Zc in the voltage drop calculator is calculated as:

\(Z_c = \sqrt{R_c^2 + X_c^2}\)

Where,

The formula above for Zc is for the worse case. Which is when the cable and load power factor is the same.

Instead of the worse case impedance, you can work out the combined power factor of the cable and load. However, the difference is negligible. And it makes the calculation too complicated.

For example, the calculated worse case impedance for a number 10 conductor is 1.2Ω/1000ft. And the impedance for a load with a power factor of 0.85 is 1.1Ω/1000ft.

The voltage drop calculator uses the resistance Rc and reactance Xc values from Table 9 in chapter 9 of the NEC for both AC and DC calculations.

Theoretically, the values from Table 8 should be used for DC voltage drop calculations. However, the difference is negligible.

Here are two examples:

Example 1: The AC resistance in Table 9 for a number 10 conductor is 1.2Ω/1000ft. The DC resistance in Table 8 is 1.24Ω/1000ft. That is only a 3% difference in resistance. The actual voltage drop will be 3.09% instead of 3%. That is, slightly worse.

Example 2: The AC resistance in Table 9 for a number 12 conductor is 2.0 Ω/1000ft. The DC resistance Table 8 is 1.98 Ω/1000ft. That is only a 1% difference in resistance. The actual voltage drop will be 2.97% instead of 3%. That is, slightly better.

What is the Allowable Voltage Drop?

NFPA NEC 70 2020 in the USA recommends the following allowable voltage drop in the fine print notes of articles 210.19(A) and 215.2(A).

Branch circuit only3%
Branch circuit and feeder combined5%

In simple terms, the maximum total allowable voltage drop at a socket outlet is 5%.

Voltage Drop Calculation Examples

Example 1: Voltage drop calculation example for a residential 120 VAC, 1-phase load

Calculate the voltage drop for the following load:

Voltage120 VAC, 1-phase
Load15 A
Distance100 ft
Conductor size10 AWG

The resistance and reactance values from the NEC for a 10 AWG conductor is:

The impedance is calculated as:

\(Z_c = \sqrt{1.2^2 + 0.05^2}\)

\(Z_c = 1.2 \,\Omega/1000ft \)

The voltage drop is calculated as:

\(\Delta V_{1\phi-ac}=\dfrac{I L 2 Z_c}{1000}\)

\(\Delta V_{1\phi-ac}=\dfrac{15 \cdot 100 \cdot 2 \cdot 1.2}{1000}\)

\(\Delta V_{1\phi-ac}=3.6 \, V\)

The percentage voltage drop is calculated as:

\(\% V_{1\phi-ac}= \dfrac {3.6} {120} \cdot 100 \)

\(\% V_{1\phi-ac}= 3 \, \% \)

Example 2: Voltage drop calculation example for an industrial 480 VAC, 3-phase motor

Calculate the voltage drop for the following load:

Voltage380 VAC, 3-phase
Load25 hp motor, pf 0.86.
Full load current: 26 A
Efficiency ignored
Distance300 ft
Conductor size8 AWG

The resistance and reactance values from the NEC for a 8 AWG conductor is:

The impedance is calculated as:

\(Z_c = \sqrt{0.78^2 + 0.052^2}\)

\(Z_c = 0.78 \,\Omega/1000ft \)

The voltage drop is calculated as:

\(\Delta V_{3\phi-ac}=\dfrac{I L \sqrt{3} Z_c}{1000}\)

\(\Delta V_{3\phi-ac}=\dfrac{26 \cdot 300 \cdot \sqrt{3} \cdot 0.78}{1000}\)

\(\Delta V_{3\phi-ac}=10.6 V \, V\)

The percentage voltage drop is calculated as:

\(\% V_{3\phi-ac}= \dfrac {10.6} {480} \cdot 100 \)

\(\% V_{3\phi-ac}= 2.2 \, \% \)

Example 3: Voltage drop calculation example for a 12 VDC load

Calculate the voltage drop for the following load:

Voltage12 VDC
Load1 A
Distance80 ft
Conductor size12 AWG

The resistance values from the NEC for a 12 AWG conductor is:

Note that Reactance is not applicable in DC circuits.

The resistance values from Table 9 (AC) in the NEC is used, instead if the resistance values from Table 8 (DC). The difference is negligible.

The voltage drop is calculated as:

\(\Delta V_{dc}=\dfrac{I L 2 R_c}{1000}\)

\(\Delta V_{dc}=\dfrac{1 \cdot 80 \cdot 2 \cdot 2.0}{1000}\)

\(\Delta V_{dc}=0.32 \, V\)

The percentage voltage drop is calculated as:

\(\% V_{dc}= \dfrac {0.32} {12} \cdot 100 \)

\(\% V_{dc}= 2.7 \, \% \)

Thanks for using my calculator.

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