# 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.

## See Also

## Voltage Drop Calculator Parameters

**Rated voltage (V):**Specify the voltage in volt (V). And select the phase arrangement:**1 Phase AC**,**3 Phase AC**or**DC**.**Load (kW, kVA, A, hp):**Specify the load in A, hp, kW or kVA. Specify cosΦ (power factor) when the electrical load is specified in kW or hp.**Cable size (AWG):**Select a standard electrical wire size in AWG (American Wire Gauge) as defined in the NPFA 70 NEC (National Electrical Code) in the USA.**Distance (m, ft):**Specify the estimated cable length in meters or feet.

## 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:

- It may cause equipment to malfunction.
- It reduces the potential energy.
- It results in an energy loss.

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 V_{drop} = 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,

**I**is the load current in ampere (A).**L**is the wire distance on meters (m) or feet (ft).**Z**is the wire impedance in Ω/km or Ω/1000ft._{c}**R**is the wire resistance in Ω/km or Ω/1000ft._{c}

**Z**in the voltage drop calculator is calculated as:

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

Where,**R**is the wire resistance in Ω/km or Ω/1000ft._{c}**X**is the wire reactance in Ω/km or Ω/1000ft._{c}

The formula above for **Z _{c}** 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 **R _{c}** and reactance

**X**values from Table 9 in chapter 9 of the NEC for both AC and DC calculations.

_{c}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 only | 3% |

Branch circuit and feeder combined | 5% |

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:

Voltage | 120 VAC, 1-phase |

Load | 15 A |

Distance | 100 ft |

Conductor size | 10 AWG |

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

**R**= 3.9 Ω/km or 1.2 Ω/1000ft_{c}**X**= 0.164 Ω/km or 0.05 Ω/1000ft_{c}

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:

Voltage | 380 VAC, 3-phase |

Load | 25 hp motor, pf 0.86. Full load current: 26 A Efficiency ignored |

Distance | 300 ft |

Conductor size | 8 AWG |

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

**R**= 2.56 Ω/km or 0.78 Ω/1000ft_{c}**X**= 0.171 Ω/km or 0.052 Ω/1000ft_{c}

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:

Voltage | 12 VDC |

Load | 1 A |

Distance | 80 ft |

Conductor size | 12 AWG |

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

**R**= 6.6 Ω/km or 2.0 Ω/1000ft_{c}

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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