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3-Phase Voltage Drop

Calculate voltage drop for three-phase electrical circuits using copper conductors per NEC standards.
Trades & Construction
Standard: NEC 210.19(A) Informational Note No. 4
Volts
Amps
feet

NEC 210.19(A) Notice: Calculated voltage drop exceeds the recommended 3% threshold. Upsize conductors to prevent equipment torque reduction and overheating.

The Square Root of 3 ⚡

In 3-phase power calculations, the multiplier 1.732 ($\sqrt3$) accounts for the 120° phase shift between the alternating current vectors. For a single-phase circuit, the multiplier is 2 (complete round-trip loop). For balanced 3-phase, the phase cancellation reduces line-to-line drop to $\sqrt3 \times L \times R \times I$.

Copper Conductor Resistance Reference (NEC Ch. 9 Table 8)

AWG / kcmil ConductorNEC Table 8 Resistance (Ω / 1000ft)75°C Copper Ampacity
10 AWG1.2135 A
8 AWG0.77850 A
6 AWG0.49165 A
4 AWG0.30885 A
2 AWG0.194115 A
1/0 AWG0.122150 A
2/0 AWG0.0967175 A
3/0 AWG0.0766200 A
4/0 AWG0.0608230 A
250 kcmil0.0515255 A
300 kcmil0.0429285 A
350 kcmil0.0367310 A
500 kcmil0.0258380 A
Calculated result for Voltage Drop:

Voltage Drop

16.80 Volts
3.50% drop
Calculated result for Volts at Load:

Volts at Load

463.2 Volts
Estimated delivered voltage
SOURCELOADLOSS OVER DISTANCE
For estimation purposes only. Always consult a licensed professional before beginning work. Full Trade Safety Notice →
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Worked Engineering Scenario: 480V 100A Feeder Over 500 Feet

NEC 210.19(A) 3-Phase Conductor Voltage Drop Verification

Design Parameters
Nominal Line-to-Line Voltage480 V (3-Phase Wye)
Continuous Feeder Load100 A
One-Way Conductor Run500 ft
Conductor Size & Material2 AWG Copper (R = 0.194 Ω / 1000 ft per NEC Ch. 9 Tbl. 8)
Mathematical Solution
1Step 1: Identify 3-Phase Line Vector Multiplier

In balanced 3-phase circuits, phase voltage cancellation results in a multiplier of √3 (1.732) rather than 2 (single-phase loop).

\sqrt{3} \approx 1.732
2Step 2: Calculate Absolute Line-to-Line Voltage Drop

Evaluating total resistance loss across the 500 ft run under full 100A load using standard NEC Chapter 9 Table 8 uncoated copper DC resistance.

V_d = \frac{1.732 \times L \times R \times I}{1000} = \frac{1.732 \times 500 \times 0.194 \times 100}{1000} = \frac{16799.7}{1000} = 16.80\text{ Volts}
3Step 3: Calculate Percentage Voltage Drop

Comparing line drop to nominal line-to-line 480V system voltage.

\% V_d = \left(\frac{16.80\text{ V}}{480\text{ V}}\right) \times 100 = 3.50\%
4Step 4: Determine Operating Terminal Voltage

Equipment terminals receive 463.2V, indicating a 3.50% drop.

V_{load} = 480\text{ V} - 16.80\text{ V} = 463.20\text{ V}
Engineering Conclusion: At 3.50% line-to-line voltage drop, 2 AWG exceeds the NEC Informational Note 210.19(A) recommended 3% branch/feeder limit. Upsizing to 1/0 AWG (R = 0.122 Ω / 1000 ft) reduces drop to 10.57V (2.20%), bringing the feeder into full code compliance.

What is 3-Phase Voltage Drop Engineering?

Excessive voltage drop in 3-phase systems can cause motors to run hot, equipment to trip, and overall power inefficiency. Sizing conductors for distance is as critical as sizing them for load.

Mathematical Foundation

3-Phase Drop Formula
Vd=1.732×L×R×I1000V_d = \frac{1.732 \times L \times R \times I}{1000}
VdV_d= Voltage Drop (Volts)
LL= One-Way Length (feet)
RR= Resistance in Ohms per 1000ft (NEC Ch. 9 Table 8)
II= Current (Amps)

Laws & Principles

  • NEC 210.19(A) Information Note: A voltage drop exceeding 3% at the farthest outlet leads to inefficient operation.
  • The 1.732 multiplier accounts for the 120-degree phase shift in 3-phase power (sqrt(3)).
  • Resistance (R) is based on standard NEC Chapter 9 Table 8 uncoated copper at 75°C.
  • Voltage at Load = System Voltage - Calculated Drop.
  • UPSIZE conductors if the percentage drop exceeds the equipment's tolerance (typically 3-5%).

Step-by-Step Example Walkthrough

" 480V, 100A load at 500ft using 2 AWG Copper (R = 0.194 Ω/1000ft per NEC Ch. 9 Table 8). "

  1. 1. Find Resistance: 2 AWG = 0.194 Ohms per 1000ft per NEC Chapter 9 Table 8.
  2. 2. Apply 3-Phase Formula: (1.732 * 500 * 0.194 * 100) / 1000.
  3. 3. Calculation: 16,800 / 1000 = 16.80 Volts Drop.
  4. 4. Percentage: (16.80 / 480) * 100 = 3.50% (exceeds 3% limit; upsizing to 1/0 AWG yields 2.20%).
Final Result: 3.50% drop. Upsizing to 1/0 AWG recommended for < 3% threshold.

Quick Answer: What does the 3-Phase Voltage Drop Calculator do?

The 3-Phase Voltage Drop Calculator calculates line-to-line voltage loss in balanced three-phase AC circuits: V_drop = (√3 · I · L · R) / 1000. It verifies branch circuit and feeder compliance with NEC 210.19(A) 3% and 5% recommendations.

How to Use the Calculator

  1. 1.Enter your project parameters into the input fields above. All fields indicate expected measurement units.
  2. 2.Results calculate instantly as you adjust values — no submit button needed.
  3. 3.Use the Share button or export a PDF report to document your calculations.
  4. 4.Review the Knowledge Hub above for governing engineering standards, mathematical formulas, and worked examples.

Pro Tips

Best Practices

  • ✓Verify circuit parameters: Confirm nominal line voltage, one-way distance in feet, continuous load current, and conductor material before finalizing sizing.
  • ✓Factor in safety allowances: Always apply appropriate engineering service factors or code safety margins above theoretical minimums.

Common Mistakes

  • ✗Don't overlook local code amendments: Local municipal authority having jurisdiction (AHJ) codes may supersede national baseline standards.
  • ✗Don't ignore boundary conditions: Verify operating temperatures, pressures, and load limits do not exceed safe component thresholds.

Frequently Asked Questions

What are the recommended maximum voltage drop thresholds in the NEC?

NEC 210.19(A) Informational Note No. 4 recommends a maximum 3% voltage drop on branch circuits and a total combined drop of 5% across both feeders and branch circuits to maintain electrical equipment efficiency.

Why is the √3 factor used in three-phase voltage drop calculations?

The factor √3 (approximately 1.732) represents the phase-to-phase geometric vector relationship between the three 120-degree displaced sinusoidal voltages in a balanced wye or delta system.

How does operating temperature affect conductor resistance and voltage drop?

Conductor resistance increases with temperature. NEC Chapter 9 Table 8 provides DC resistance values at 75°C, which reflects standard operating temperatures under full continuous rated ampacity.

What happens to motors when operating at excessive voltage drop?

Electric motors experience reduced starting torque (proportional to V²), higher running current draw to produce required mechanical shaft power, and accelerated thermal winding breakdown.

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Calculation Provenance & Validation Record

Method

3-Phase AC Voltage Drop

Formula
Vd=3⋅K⋅I⋅DCMILV_d = \frac{\sqrt{3} \cdot K \cdot I \cdot D}{CMIL}
Assumptions
  • Balanced 3-phase load
  • K = 12.9 ohms-cmil/ft for copper at 75°C
  • Advisory 3% branch / 5% feeder + branch limit
References
  • National Electrical Code (NFPA 70) (2023 Edition) — NEC 210.19(A) Informational Note 4 & Chapter 9 Table 8
Last substantive review:
Method, assumptions & governing standards
Standard Sourced

Calculation Methodology

3-phase balanced AC circuit voltage drop and delivered terminal voltage calculation per NEC Informational Note 210.19(A) and 215.2(A)(1).

Governing Standard 2023 Edition

Standard:NFPA 70 National Electrical Code (NEC)

Statutory building, electrical, and mechanical codes vary by jurisdiction. Confirm local municipality amendments before installation.

Key Assumptions & Constraints

  • Balanced 3-phase sinusoidal load with sqrt(3) (1.732) line-to-line phase relationship
  • Conductor AC resistance per NEC Chapter 9 Table 8 at 75°C operating baseline
  • Advisory code thresholds: maximum 3% drop on branch circuits, 5% combined feeder + branch circuit
  • One-way routing distance from distribution source to utilization load
Regression Tests: 4 golden vectors
Last Verified:
Primary References: 3 documented
Field Trade Notice: For trade planning and engineering estimates. Final installations must conform to project blueprints, authority having jurisdiction (AHJ) code approvals, and site-specific inspections.