Best for: facility engineers and planners applying this topic on real industrial sites.
Not ideal for: exam-only problems with fixed textbook rates and no site constraints.

Introduction #

How to calculate voltage drop (3-phase AC feeder): start from VD = √3 × I × (R × cos θ + X × sin θ) × L (I in amperes, R/X per unit length, L one-way length). Single-phase uses the factor 2 instead of √3; DC simplifies to VD = I × R. Instant check: Voltage Drop Formula & Calculator · conductor sizing: Cable Size Calculator.

Voltage drop is the reduction in voltage that occurs when electrical current flows through conductors due to conductor resistance. Excessive voltage drop causes equipment to operate inefficiently, can prevent motors from starting, reduces lighting output, and wastes energy. Understanding how to calculate voltage drop, apply NEC requirements, and properly size conductors is essential for designing reliable and efficient electrical systems.

This guide focuses on 3-phase feeder VD % with NEC 3% branch / 5% total limits—not transformer regulation (see Transformer Voltage Regulation Formula).

What is Voltage Drop? #

Voltage drop is the difference between the voltage at the source and the voltage at the load, caused by conductor resistance. When current flows through a conductor, the conductor's resistance creates a voltage drop proportional to the current and resistance. Transformer voltage regulation (the change in secondary voltage from no-load to full-load) is separate from conductor drop. For how transformer regulation works, see Transformer Voltage Regulation Explained.

Voltage Drop Formula #

DC Circuits:

VD = I × R

Where:

  • VD = Voltage drop (volts)
  • I = Current (amperes)
  • R = Resistance (ohms)

AC Single-Phase Circuits:

VD = 2 × I × (R × cos θ + X × sin θ) × L_kft

Where:

  • VD = Voltage drop (volts)
  • I = Current (amperes)
  • R = Resistance per unit length (ohms/1000 ft)
  • X = Reactance per unit length (ohms/1000 ft)
  • L_kft = One-way length in thousands of feet when R and X are in ohms/1000 ft
  • cos θ = Power factor
  • sin θ = Reactive factor

AC Three-Phase Circuits:

VD = √3 × I × (R × cos θ + X × sin θ) × L_kft

Where:

  • √3 = 1.732 (three-phase factor)
  • Other variables same as single-phase

Simplified Formulas #

For a resistive K-method screen (reactance omitted):

Single-Phase:

VD (%) = (2 × K × I × L × 100) / (CM × V)

Three-Phase:

VD (%) = (√3 × K × I × L × 100) / (CM × V)

Where:

  • K = 12.9 for copper, 21.2 for aluminum (at 75°C)
  • I = Current (amperes)
  • L = One-way length (feet)
  • CM = Circular mils (conductor size)
  • V = Voltage (volts)

NEC Voltage Drop Requirements #

NEC Recommendations #

NEC Article 210.19(A)(1) Informational Note:

  • Branch circuits: 3% maximum voltage drop
  • Combined feeder and branch: 5% maximum

NEC Article 215.2(A)(1) Informational Note:

  • Feeders: 3% maximum voltage drop recommended

Note: These are recommendations, not requirements, but should be followed for proper system operation.

Practical Limits #

Recommended Maximum Voltage Drop:

  • Feeders: 3% maximum
  • Branch Circuits: 3% maximum
  • Total (Feeder + Branch): 5% maximum

Critical Applications:

  • Motor starting: use the motor/load torque-speed requirement and manufacturer minimum terminal voltage; no single percentage fits every start
  • Motor running: < 3% at full load
  • Lighting: < 3% for proper operation
  • Control circuits: < 5% for reliable operation

Voltage Drop Calculation Methods #

Method 1: Using Conductor Resistance Tables #

Step 1: Determine Conductor Resistance

  • Use NEC Chapter 9, Table 8 or Table 9
  • Find resistance per 1000 ft for conductor size
  • Adjust for temperature if necessary

Step 2: Calculate Voltage Drop

  • Apply appropriate formula (single-phase or three-phase)
  • Include power factor
  • Convert one-way feet to thousands of feet when R/X are listed per 1000 ft

Step 3: Convert to Percentage

VD (%) = (VD / V) × 100

Example:

  • Circuit: 480V, 3-phase
  • Load: 100 A
  • Conductor: 3/0 AWG copper
  • Length: 200 ft one-way
  • Power factor: 0.85

Calculation:

  • Resistance (3/0 AWG, 75°C): 0.076 ohms/1000 ft
  • Reactance (3/0 AWG): 0.051 ohms/1000 ft
  • VD = √3 × 100 × (0.076 × 0.85 + 0.051 × 0.527) × 0.2
  • VD = 1.732 × 100 × (0.0646 + 0.0269) × 0.2
  • VD = 1.732 × 100 × 0.0915 × 0.2
  • VD = 3.17 volts
  • VD (%) = (3.17 / 480) × 100 = 0.66%

Method 2: Using Simplified Formula #

For Quick Calculations:

Three-Phase:

VD (%) = (√3 × K × I × L × 100) / (CM × V)

Where K = 12.9 for copper at 75°C

Example:

  • Circuit: 480V, 3-phase
  • Load: 100 A
  • Conductor: 3/0 AWG (167,800 CM)
  • Length: 200 ft

Calculation:

  • VD (%) = (1.732 × 12.9 × 100 × 200 × 100) / (167,800 × 480)
  • VD (%) = 44,687,000 / 80,544,000
  • VD (%) = 0.55%

Note: This K-method screen omits reactance. It is not equivalent to the R/X calculation above and should not be adjusted by inserting an arbitrary PF into K.

Method 3: Using Voltage Drop Tables #

NEC Chapter 9, Table 8:

  • Provides voltage drop per 1000 ft
  • For specific conductor sizes
  • At various power factors

Usage:

  • Find voltage drop per 1000 ft from table
  • Multiply by actual length (in thousands of feet)
  • Adjust for power factor if necessary

Conductor Sizing for Voltage Drop #

Sizing Process #

Step 1: Calculate Maximum Allowable Voltage Drop

VD_max = V × (VD% / 100)

Step 2: Calculate Required Conductor Size
Rearrange voltage drop formula to solve for CM:

CM = (√3 × K × I × L) / VD_max

For single-phase, replace √3 with 2. System voltage is used once to convert the allowed percentage to VD_max; do not divide by voltage again.

Step 3: Select Standard Conductor Size

  • Find conductor with CM ≥ calculated value
  • Use NEC Chapter 9, Table 8

Example:

  • Circuit: 480V, 3-phase
  • Load: 100 A
  • Length: 500 ft
  • Maximum VD: 3% (14.4 volts)

Calculation:

  • CM = (1.732 × 12.9 × 100 × 500) / 14.4
  • CM ≈ 77,600

Select:

  • 1/0 AWG (105,600 CM) clears this resistive voltage-drop screen
  • Ampacity, temperature, installation method, parallel-conductor rules and AC impedance still require separate checks

Real-World Case Study #

Problem: Motor Won't Start Due to Voltage Drop #

Background:
A 75 HP motor at 480V was installed 800 feet from the distribution panel. The motor would not start reliably, and when it did start, it ran hot and drew excessive current. The installation used 3 AWG copper conductors.

Initial Analysis:

  • Motor: 75 HP, 480V, 3-phase
  • FLC: 93 A (from NEC Table 430.250)
  • Starting current: 558 A (6× FLC)
  • Conductor: 3 AWG copper
  • Length: 800 ft one-way
  • Power factor: 0.85

Voltage Drop Calculation:

During Starting:

  • Resistance (3 AWG, 75°C): 0.245 ohms/1000 ft
  • Reactance (3 AWG): 0.041 ohms/1000 ft
  • VD = √3 × 558 × (0.245 × 0.85 + 0.041 × 0.527) × 0.8
  • VD = 1.732 × 558 × (0.208 + 0.022) × 0.8
  • VD = 1.732 × 558 × 0.230 × 0.8
  • VD = 178.5 volts
  • VD (%) = (178.5 / 480) × 100 = 37.2%

During Running:

  • VD = √3 × 93 × (0.245 × 0.85 + 0.041 × 0.527) × 0.8
  • VD = 1.732 × 93 × 0.230 × 0.8
  • VD = 29.7 volts
  • VD (%) = (29.7 / 480) × 100 = 6.2%

Problem Identified:

  • Starting voltage drop: 37.2% (excessive, motor can't start)
  • Running voltage drop: 6.2% (excessive, causes problems)
  • Voltage at motor during starting: 301.5V (63% of rated)
  • Voltage at motor during running: 450.3V (94% of rated)

Solution:

  1. Increase Conductor Size:

    • Required CM for 3% running drop:
    • CM = (1.732 × 12.9 × 93 × 800) / 14.4
    • CM ≈ 115,400 (resistive three-phase screen)
    • 2/0 AWG (133,100 CM) clears that screen; this scenario evaluates a larger 4/0 AWG option

  2. Verify Starting Voltage Drop:

    • Resistance (4/0 AWG): 0.051 ohms/1000 ft
    • Using the same assumed PF only as a consistency check: VD starting = √3 × 558 × (0.051 × 0.85 + 0.041 × 0.527) × 0.8
    • VD starting ≈ 50.2 volts (10.5%), before transformer/source impedance
    • This does not establish acceptable starting voltage; use motor locked-rotor data, acceleration time, source impedance and the driven-load torque curve

  3. Verify Running Voltage Drop:

    • VD running = √3 × 93 × (0.051 × 0.85 + 0.041 × 0.527) × 0.8
    • VD running ≈ 8.37 volts (1.74%)
    • Voltage at motor ≈ 471.6 V under the stated conductor-only assumptions

Result boundary: The larger conductor resolves the running-drop screen but does not, by itself, close the starting study. A reduced-voltage starter/VFD, a different source/transformer arrangement, further conductor changes or a load-specific acceleration study may still be required.

Key Takeaway:
Voltage drop during motor starting can govern even when running drop is acceptable. Use manufacturer locked-rotor current/PF and start duration rather than a universal multiple, and include source/transformer impedance as well as conductor impedance.

Common Mistakes to Avoid #

1. Ignoring Voltage Drop Completely #

Mistake:
Sizing conductors only for ampacity, ignoring voltage drop.

Example:

  • Motor 500 ft from panel
  • Conductor sized for ampacity: 4 AWG
  • Voltage drop: 8%
  • Result: Motor won't start, low voltage problems

Why It's Wrong:

  • Causes equipment problems
  • Prevents proper operation
  • Wastes energy
  • Creates reliability issues

Correct Approach:

  • Always calculate voltage drop
  • Size for both ampacity and voltage drop
  • Limit to 3% for feeders and branch circuits

2. Using Total Loop Length in a One-Way-Length Formula #

Mistake:
Using total circuit length (out and back) in single-phase calculations.

Example:

  • Circuit length: 200 ft (100 ft out, 100 ft back)
  • Using 200 ft in formula
  • Result: Incorrect voltage drop calculation

Why It's Wrong:

  • Formulas use one-way length
  • Using total length doubles the result
  • Leads to oversized conductors
  • Wastes money

Correct Approach:

  • Use one-way length in formulas
  • For single-phase: 2× accounts for return path
  • For three-phase: √3 accounts for phase relationship

3. Not Considering Power Factor #

Mistake:
Using simplified formulas that assume power factor = 1.0.

Example:

  • Motor with 0.75 power factor
  • Using simplified formula (assumes PF = 1.0)
  • Calculated VD: 2%
  • Actual VD: 3.5%
  • Result: Conductor undersized

Why It's Wrong:

  • Low power factor increases voltage drop
  • Simplified formulas underestimate drop
  • Can cause conductor undersizing
  • Leads to voltage problems

Correct Approach:

  • Use actual power factor in calculations
  • For motors, use nameplate or typical PF (0.85)
  • For lighting, PF ≈ 1.0 is acceptable
  • Verify with actual measurements

4. Not Checking Motor Starting Voltage Drop #

Mistake:
Only calculating running voltage drop, ignoring starting.

Example:

  • Motor running VD: 2% (acceptable)
  • Motor starting current: 6× FLC
  • Starting VD: 12% (excessive)
  • Result: Motor won't start

Why It's Wrong:

  • Starting current much higher than running
  • Starting voltage drop much higher
  • Motor may not start with high drop
  • Causes starting problems

Correct Approach:

  • Calculate both starting and running VD
  • Verify motor-terminal voltage and acceleration torque against manufacturer/load data
  • Include source, transformer and conductor impedance in the start study
  • Consider reduced-voltage starting or a VFD where the application supports it

5. Using Wrong Temperature #

Mistake:
Using resistance values for wrong temperature.

Example:

  • Conductor operating at 90°C
  • Using 75°C resistance values
  • Result: Underestimated voltage drop

Why It's Wrong:

  • Resistance increases with temperature
  • Higher temperature = higher resistance = higher VD
  • Can cause conductor undersizing
  • Leads to voltage problems

Correct Approach:

  • Use resistance for operating temperature
  • Typically 75°C for most applications
  • 90°C for high-temperature applications
  • Adjust if necessary

6. Not Accounting for Future Expansion #

Mistake:
Sizing conductors for current load only.

Example:

  • Current load: 50 A
  • Conductor sized for 50 A
  • Future expansion: 25 A
  • Result: Conductor undersized, high voltage drop

Why It's Wrong:

  • No room for growth
  • Requires conductor replacement
  • Expensive to upgrade later
  • Creates voltage problems

Correct Approach:

  • Size for current + future load
  • Add 20-25% margin
  • Plan for expansion
  • Verify voltage drop with future load

7. Ignoring Voltage Drop in Long Feeders #

Mistake:
Focusing only on branch circuits, ignoring feeder voltage drop.

Example:

  • Feeder: 3% voltage drop
  • Branch: 2% voltage drop
  • Total: 5% voltage drop
  • Result: Excessive total drop, equipment problems

Why It's Wrong:

  • Total drop is sum of feeder + branch
  • Both contribute to total
  • Can exceed 5% limit
  • Causes equipment problems

Correct Approach:

  • Calculate feeder and branch separately
  • Limit each to 3% maximum
  • Verify total doesn't exceed 5%
  • Size both appropriately

Best Practices #

1. Always Calculate Voltage Drop #

Practice:
Calculate voltage drop for all circuits, especially long runs.

Reason:

  • Ensures proper operation
  • Prevents equipment problems
  • Meets NEC recommendations
  • Maintains efficiency

When to Calculate:

  • All circuits > 100 ft
  • Motor circuits
  • Lighting circuits
  • Critical loads

2. Use Actual Power Factor #

Practice:
Use actual power factor in calculations, not assumed values.

Reason:

  • More accurate results
  • Prevents undersizing
  • Accounts for reactive power
  • Ensures proper operation

Power Factor Values:

  • Motors: 0.80-0.90 (use nameplate or 0.85)
  • Lighting: 0.90-1.0 (LED: 0.95, fluorescent: 0.90)
  • General loads: 0.85-0.95

3. Check Both Starting and Running #

Practice:
Calculate voltage drop for both starting and running conditions.

Reason:

  • Starting drop often higher
  • Critical for motor operation
  • Ensures reliable starting
  • Prevents problems

Limits:

  • Starting: project/OEM motor-terminal-voltage and acceleration requirement
  • Running: 3% maximum

4. Size Conductors for Voltage Drop #

Practice:
Size conductors based on voltage drop, not just ampacity.

Reason:

  • Ensures adequate voltage
  • Prevents equipment problems
  • Meets NEC recommendations
  • Maintains efficiency

Process:

  • Calculate required size for voltage drop
  • Compare to ampacity requirement
  • Select larger of the two

5. Limit Total Voltage Drop #

Practice:
Limit total voltage drop (feeder + branch) to 5% maximum.

Reason:

  • Ensures adequate voltage at load
  • Prevents equipment problems
  • Meets NEC recommendations
  • Maintains system performance

Distribution:

  • Feeder: 3% maximum
  • Branch: 3% maximum
  • Total: 5% maximum

6. Consider Future Expansion #

Practice:
Size conductors with future load in mind.

Reason:

  • Prevents need for replacement
  • Maintains voltage with growth
  • Reduces future costs
  • Supports expansion

Guideline:

  • Add 20-25% to current load
  • Verify voltage drop with future load
  • Plan for growth

7. Verify with Measurements #

Practice:
Measure actual voltage drop after installation.

Reason:

  • Verifies calculations
  • Identifies problems
  • Confirms proper operation
  • Supports troubleshooting

Measurements:

  • Voltage at source
  • Voltage at load
  • Calculate actual drop
  • Compare to calculated

Standards & References #

NEC/NFPA Standards #

  • NEC Article 210.19(A)(1): Branch-Circuit Conductors

  • NEC Article 215.2(A)(1): Feeder Conductors

    • Feeder voltage drop recommendations

  • NEC Chapter 9, Table 8: Conductor Properties

    • Resistance and reactance values
    • Used for voltage drop calculations

IEEE Standards #

  • IEEE 141: Recommended Practice for Electric Power Distribution for Industrial Plants

Industry Resources #

  • Southwire: Voltage Drop Calculator

Engineer's Practical Insight #

From 15+ years of electrical design experience: Voltage drop is the most overlooked factor in conductor sizing. I've seen more problems from voltage drop than from ampacity. A motor circuit sized correctly for ampacity but with 8% voltage drop won't start, while the same circuit with 2% drop works perfectly. Always calculate voltage drop, especially for circuits over 100 feet.

Motor starting reality: Starting drop can be much larger than running drop, but the ratio follows actual locked-rotor current, PF, source impedance and acceleration time—not a universal multiple. Check starting and running conditions separately and verify motor-terminal voltage against the motor/load acceleration requirement.

Long feeder problem: Voltage drop in long feeders is often ignored. In one facility, we had a 1,200-foot feeder with 6% voltage drop. All equipment at the end of the feeder had problems. Upgrading the feeder conductor from 500 MCM to 750 MCM reduced drop to 2% and solved all problems. The cost was $15,000, but it eliminated $50,000/year in equipment problems and downtime.

Power factor impact: In an AC impedance model, drop depends on both R cos θ and X sin θ; for a fixed kW load, PF also changes line current. Recalculate both current and impedance terms rather than applying a universal percentage benefit from power-factor correction.

Next step #

Use Breaker size calculator and Cable size calculator to apply the numbers from this guide, then browse the Protection calculators hub for related calculators.

Conclusion #

Voltage drop calculation is essential for proper electrical system design. Excessive voltage drop causes equipment problems, prevents proper operation, and wastes energy. Understanding calculation methods, NEC requirements, and proper conductor sizing ensures reliable and efficient electrical systems.

Key takeaways:

  1. Always calculate voltage drop for circuits, especially long runs
  2. Use actual power factor in calculations for accuracy
  3. Check both starting and running voltage drop for motors
  4. Size conductors for voltage drop, not just ampacity
  5. Limit total voltage drop to 5% maximum (3% feeder + 3% branch)
  6. Consider future expansion when sizing conductors
  7. Verify with measurements after installation

For voltage drop calculations, use our 3-Phase Power Calculator to determine circuit currents, and always consult NEC Chapter 9, Table 8 for conductor resistance values and follow NEC voltage drop recommendations.

About the Author: James Chen, P.E. is a licensed electrical engineer with 15+ years of experience in industrial power systems design. Former Schneider Electric application engineer specializing in 3-phase motor control and power distribution. Has designed electrical systems for manufacturing facilities, chemical plants, and water treatment facilities. All content in this guide has been reviewed and validated by licensed engineers.