---
title: Voltage Drop Calculations
tags:
  - authorship/other
  - topic/construction/electrical
  - type/media/article
authors:
  - David A. Snyder, PE
year: 2020
up: "[[electrical-construction]]"
---
# Voltage Drop Calculations

%%
[E426_Voltage_Drop_Tables.pdf](https://pdhonline.com/courses/e426/E426_Voltage_Drop_Tables.pdf)
retrieved from [pdhonline.com "Voltage Drop Calculations"](https://pdhonline.com/courses/e426/e426_new.htm)

PDHonline Course E426 (3 PDH)

Local copy saved as [[snyder_2020_voltage-drop-calculations.pdf]]
%%

## Introduction

#### Table 1 --- Quick Guide to Voltage Drop Formulas

## Voltage Drop and the National Electrical Code

### Branch Circuits

### Feeders

### Sensitive Electronic Equipment

### Other Considerations

## Common Formulas for Voltage Drop Calculations

### Single-Phase Approximate Voltage Drop Formulas

#### Figure 1 --- Single-Phase, Two-Wire Voltage-Drop Circuit Diagram

#### Figure 2 --- Distributed Resistance in Conductors

#### Table 2 --- Derivation of the Value of K for Copper Conductors

#### Figure 3 --- Single-Phase, Three-Wire Voltage-Drop Circuit Diagram

### Three-Phase Approximate Voltage Drop Formulas

#### Figure 4 --- Three-Phase Wye-Connected with Neutral Voltage-Drop Circuit Diagram

### No Neutral Current in a Balanced Three-Phase System?

#### Figure 5 --- Balanced, Wye-Connected, Three-Phase, Resistance Load, with Neutral Connection

#### Figure 6 --- Balanced, Wye-Connected, Three-Phase 10 KW Load at 480 V

### √3 Relationship of Three-Phase Voltages

#### Figure 7 --- 480Y/277V Wye-Delta Voltage Relationship

#### Figure 8 --Wye-Delta Voltage Relationship --- Right Triangle Geometry

#### Figure 9 --- 208Y/120V Wye-Delta Voltage Relationship

### Why the √3 Is Used in Balanced, Three-Phase Voltage Drop Calculations

#### Figure 10 --- The Square Root of Three in Three-Phase Voltage-Drop Calculations

## Table 9 in the NEC

### Which Columns Are Applicable?

### XL (Reactance)

### Alternating-Current Resistance

### Effective Z at 0.85 PF

#### Table 3 --- Selected Effective Z Calculations at 0.85 PF (Ohms-to-Neutral per 1,000 feet) . 21

### Effective Z at Any Power Factor: Note 2 to Table 9 in the NEC

#### Table 4 --- Effective Z Calculations for Selected Wire Sizes at Various Power Factors (Ohms-to-Neutral per 1,000 feet)

## Note 2 to Table 8 in the NEC

### Phasor Diagrams of Resistance, Reactance, and Impedance for Conductors

#### Figure 11 --- Phasor Diagram of Resistance, Reactance, and Impedance for 12 AWG Copper Conductors in Steel Conduit at 0.85 PF

#### Figure 12 --- Phasor Diagram of Resistance, Reactance, and Impedance for 12 AWG Copper Conductors in Steel Conduit at Selected Power Factor Values

#### Figure 13 --- Phasor Diagram of Resistance, Reactance, and Impedance for 250 KCMIL Copper Conductors in Steel Conduit at 0.85 PF

#### Figure 14 --- Phasor Diagram of Resistance, Reactance, and Impedance for 500 KCMIL Copper Conductors in Steel Conduit at 0.85 PF

#### Figure 15 --- Phasor Diagram of Resistance, Reactance, and Impedance for 500 KCMIL Copper Conductors in Steel Conduit at Selected Power Factor Values

### Estimated Vdrop Derived from Impedance Phasor Diagrams

#### Figure 16 --- Applying 300 Amps to the Impedance Phasor Diagram for 500 KCMIL Copper Conductors in Steel Conduit at Selected Power Factor Values

### Estimated Vdrop, Single-Phase:

### Estimated Vdrop, Three-Phase:

## Voltage Drop Phasor Diagram in IEEE Standard 141 (Red Book)

#### Figure 17 --- IEEE Phasor Diagram of Voltage Drop

#### Figure 18 --- Vertical Components of Phasor Diagram of Voltage Drop

#### Figure 19 --- Triangle Formed by Vs, Vr + Estimated Vdrop, and IXcosΦ-IRsinΦ

#### Figure 20 --- When the Vector I * Z Really Is the Actual Vdrop

#### Figure 21 --- If Conductor X > R, the Error Increases as Power Factor Increases

## Calculating the Error Shown in the IEEE Phasor Diagram

#### Figure 22 --- Finding the Height h of a Circular Segment

### Single-Phase Formulas for Error and Actual Vdrop:

### Three-Phase Formulas for Error and Actual Vdrop:

#### Table 5 --- Error Voltage Drop Calculations for Real-World Examples in Next Section

## Real-World Examples

#### Table 6 --- Real-World Examples

### 10 Hp Motor at 480V/3Φ with 12 AWG Conductors

#### Figure 23 --- Line-to-Neutral Voltage Drop for 10 Hp Motor at 480V/3Φ with 200' of 12 AWG Conductors

#### Table 7 --- Line-to-Line Voltage Drop for 10 Hp Motor at 480V/3Φ with 200' of 12 AWG Conductors

### 15 KW Heater at 480V/3Φ with 10 AWG Conductors

#### Figure 24 --- Line-to-Neutral Voltage Drop for 15 KW Load at 480V/3Φ with 200' of 10 AWG Conductors

#### Table 8 --- Line-to-Line Voltage Drop for 15 KW Load at 480V/3Φ with 200' of 10 AWG Conductors

### 250 Hp Motor at 480V/3Φ with 500 KCMIL Conductors

#### Figure 25 --- Line-to-Neutral Voltage Drop for 250 Hp Motor at 480V/3Φ with 200' of 500 KCMIL Conductors

#### Table 9 --- Line-to-Line Voltage Drop for 250 Hp Motor at 480V/3Φ with 200' of 500 KCMIL Conductors

## Rearranging the Formulas Used for Approximate Vdrop

### Single-Phase Voltage Drop Formulas --- Rearranged

#### Table 10 --- Voltage Drop for 10 A Load at 120V/1Φ with 100' of 10 AWG Conductors

### Three-Phase Voltage Drop Formulas --- Rearranged

## Other Considerations

### Increase Equipment Grounding Conductor Size

### Increase Grounded (Neutral) Conductor Size

### Verify Wire Size and Quantity Capacity of Terminations at Both Ends

### Verify Conduit Size

### Rule-of-Thumb

### Converting Formulas from Single-Phase to Three-Phase

#### Table 11 --- Voltage Drop for 10 A Load at 120V/1Φ with 120' of 12 AWG Conductors

#### Table 12 --- Voltage Drop for 10 A Load at 208V/3Φ with 208' of 12 AWG Conductors

#### Table 13 --- Voltage Drop for 10 A Load at 277V/1Φ with 277' of 12 AWG Conductors

#### Table 14 --- Voltage Drop for 10 A Load at 480V/3Φ with 480' of 12 AWG Conductors

## In Closing

## Abbreviations

## Additional Reading