How to Calculate Voltage Drop
Voltage drop is the decrease in electrical potential along a conductor carrying current. Understanding and calculating voltage drop is crucial for electrical system design, ensuring equipment operates efficiently and safely within specified voltage ranges.
Understanding Voltage Drop
When current flows through a wire, the wire's resistance causes a voltage loss. This phenomenon follows Ohm's Law (V = I × R), where the voltage drop equals current times resistance. Longer wires, smaller wire gauges, and higher currents all increase voltage drop.
DC and Single-Phase AC Formula
For DC circuits and single-phase AC circuits, use the following formula:
Voltage Drop (VD) = (2 × K × I × L) ÷ 1000- 2 = Multiplier for both supply and return conductors
- K = Wire resistance in ohms per 1000 feet (at 75°C)
- I = Load current in amperes
- L = One-way length of wire run in feet
Example: 12 AWG copper wire (K = 1.98 Ω), 100 feet, 20 amps:
VD = (2 × 1.98 × 20 × 100) ÷ 1000 = 7.92 volts
Three-Phase AC Formula
For three-phase AC circuits, the formula accounts for the phase relationship:
Voltage Drop (VD) = (√3 × K × I × L) ÷ 1000- √3 = 1.732, the three-phase factor
- K = Wire resistance in ohms per 1000 feet
- I = Load current per phase in amperes
- L = One-way length of wire run in feet
Example: 6 AWG copper wire (K = 0.491 Ω), 200 feet, 50 amps, 480V:
VD = (1.732 × 0.491 × 50 × 200) ÷ 1000 = 8.50 volts
Calculating Voltage Drop Percentage
Voltage drop is often expressed as a percentage of the source voltage:
Percentage Drop = (Voltage Drop ÷ Source Voltage) × 100Example: 7.92V drop on a 120V circuit:
% Drop = (7.92 ÷ 120) × 100 = 6.6%
Professional Tip: Always use one-way length in calculations. The formula's multiplier (2 for single-phase, √3 for three-phase) accounts for current flow through both conductors. Measuring round-trip length and using it in the formula will double your calculated voltage drop.
Wire Sizing Table
This comprehensive table shows wire resistance values for copper and aluminum conductors at 75°C. Use these resistance values to calculate voltage drop or select appropriate wire sizes for your electrical installation.
Copper Wire Resistance (75°C)
| Wire Size | Resistance (Ω/1000 ft) | Ampacity (75°C) | Typical Use |
|---|---|---|---|
| 14 AWG | 3.14 | 20A | Lighting circuits, receptacles |
| 12 AWG | 1.98 | 25A | General purpose circuits, appliances |
| 10 AWG | 1.24 | 35A | Water heaters, dryers, air conditioners |
| 8 AWG | 0.778 | 50A | Electric ranges, sub-panels |
| 6 AWG | 0.491 | 65A | Large appliances, feeders |
| 4 AWG | 0.308 | 85A | Service entrance, sub-panels |
| 2 AWG | 0.194 | 115A | Service entrance, large feeders |
| 1/0 AWG | 0.122 | 150A | Service entrance, main feeders |
| 2/0 AWG | 0.0967 | 175A | Service entrance, main feeders |
| 4/0 AWG | 0.0608 | 230A | Large service entrance |
| 250 kcmil | 0.0515 | 255A | Commercial service entrance |
| 350 kcmil | 0.0367 | 310A | Commercial/industrial feeders |
| 500 kcmil | 0.0258 | 380A | Large commercial feeders |
Aluminum vs. Copper Comparison
Aluminum conductors have higher resistance than copper and require larger wire sizes for equivalent performance:
| Copper Size | Copper Ω/1000ft | Aluminum Equivalent | Aluminum Ω/1000ft |
|---|---|---|---|
| 12 AWG | 1.98 | 10 AWG | 2.04 |
| 10 AWG | 1.24 | 8 AWG | 1.28 |
| 8 AWG | 0.778 | 6 AWG | 0.808 |
| 6 AWG | 0.491 | 4 AWG | 0.508 |
Note on Aluminum: When using aluminum conductors, select a wire size two gauges larger than the copper equivalent to achieve similar voltage drop characteristics. Aluminum is lighter and less expensive but requires special connectors and installation techniques to prevent oxidation issues.
NEC Voltage Drop Requirements
The National Electrical Code (NEC) provides recommendations for maximum voltage drop to ensure safe and efficient electrical system operation. While not mandatory requirements, following these guidelines is considered best practice and may be required by local jurisdictions.
NEC Article 210.19(A) - Branch Circuits
The NEC recommends that voltage drop on branch circuits should not exceed:
- 3%Maximum recommended voltage drop for branch circuits from the panel to the furthest outlet
- Example: On a 120V circuit, 3% = 3.6V maximum drop
- Example: On a 240V circuit, 3% = 7.2V maximum drop
NEC Article 215.2(A) - Feeders
For feeder circuits (wires from service entrance to sub-panels):
- 5%Maximum total voltage drop for combined feeder and branch circuit
- If branch circuit has 3% drop, feeder should be limited to 2% drop
- This ensures total system drop remains at or below 5%
Practical Voltage Drop Targets
Excellent (≤ 2%)
- • Motor circuits and sensitive equipment
- • Long wire runs
- • Solar and renewable energy systems
- • Computer and data center circuits
Acceptable (2-3%)
- • General purpose branch circuits
- • Lighting circuits
- • Receptacle outlets
- • Typical residential applications
Marginal (3-5%)
- • May cause equipment issues
- • Reduced energy efficiency
- • Consider upsizing wire
- • Not recommended for motors
Unacceptable (> 5%)
- • Equipment malfunction likely
- • Code violation in most jurisdictions
- • Safety concerns
- • Must upsize wire or redesign circuit
Special Considerations
Motor Circuits
Motors are particularly sensitive to voltage drop. A 10% voltage reduction can decrease motor life by 50%. Keep motor circuit voltage drop to 2% or less for optimal performance and longevity. Use larger conductors for long motor feeder runs.
LED and Electronic Loads
LED drivers and electronic equipment may be sensitive to voltage variations. While 3% is generally acceptable, some sensitive electronics perform better with lower voltage drop. Check manufacturer specifications for critical equipment.
Utility Voltage Variation
Remember that utility-supplied voltage can vary ±5% from nominal. Combined with system voltage drop, equipment may see voltages significantly different from nameplate ratings. Design systems to accommodate these variations.
Practical Applications
Understanding voltage drop calculations is essential for various electrical installations. Here are common scenarios where voltage drop analysis is critical for system performance and code compliance.
Residential Applications
Example 1: Kitchen Appliance Circuit
Scenario: 20A kitchen circuit, 80 feet from panel, 12 AWG copper wire
Calculation:
VD = (2 × 1.98 × 20 × 80) ÷ 1000 = 6.34V% Drop = (6.34 ÷ 120) × 100 = 5.28%Solution: Upgrade to 10 AWG (K = 1.24):
VD = (2 × 1.24 × 20 × 80) ÷ 1000 = 3.97V (3.31% - acceptable)Example 2: Detached Garage Sub-Panel
Scenario: 60A sub-panel, 150 feet from main panel, 240V
Wire Selection: Try 6 AWG copper (K = 0.491)
VD = (2 × 0.491 × 60 × 150) ÷ 1000 = 8.84V% Drop = (8.84 ÷ 240) × 100 = 3.68%Result: Exceeds 3% recommendation. Upgrade to 4 AWG (K = 0.308):
VD = (2 × 0.308 × 60 × 150) ÷ 1000 = 5.54V (2.31% - excellent)Commercial and Industrial Applications
Example 3: Three-Phase Motor Circuit
Scenario: 50 HP motor (65A), 480V three-phase, 200 feet from panel
Wire Selection: Try 6 AWG copper (K = 0.491)
VD = (1.732 × 0.491 × 65 × 200) ÷ 1000 = 11.05V% Drop = (11.05 ÷ 480) × 100 = 2.30%Result: Acceptable for motor circuits (< 3%)
Solar and Renewable Energy
Example 4: Solar Panel DC Circuit
Scenario: Solar array 30A output, 48V DC, 75 feet to charge controller
Wire Selection: Try 10 AWG copper (K = 1.24)
VD = (2 × 1.24 × 30 × 75) ÷ 1000 = 5.58V% Drop = (5.58 ÷ 48) × 100 = 11.63%Solution: Unacceptable for solar. Upgrade to 6 AWG (K = 0.491):
VD = (2 × 0.491 × 30 × 75) ÷ 1000 = 2.21V (4.60%)Better, but solar systems target 2%. Use 4 AWG (K = 0.308):
VD = (2 × 0.308 × 30 × 75) ÷ 1000 = 1.39V (2.89% - still high)Optimal: 2 AWG (K = 0.194):
VD = (2 × 0.194 × 30 × 75) ÷ 1000 = 0.87V (1.81% - excellent for solar)Design Tip: When voltage drop calculations fall near the 3% threshold, consider upsizing the wire. The cost difference is minimal during installation but prevents future issues and provides capacity for additional loads. This is especially important for permanent installations and critical circuits.
How We Calculate Voltage Drop
Our voltage drop calculator uses industry-standard formulas based on conductor resistance, circuit length, and load current. The calculations follow NEC guidelines and electrical engineering principles to provide accurate results for system design and analysis.
Calculation Methodology
1. Wire Resistance Values
We use standard conductor resistance values from NEC Chapter 9, Table 8. These values are specified at 75°C operating temperature in ohms per 1000 feet:
- • Copper conductors: 14 AWG through 1000 kcmil
- • Aluminum conductors: 12 AWG through 1000 kcmil
- • Values account for DC resistance at 75°C
- • AC circuits: values approximate resistance (reactance ignored for most applications)
2. Single-Phase Calculation
For DC and single-phase AC circuits:
VD = (2 × K × I × L) ÷ 1000Where:
- • 2 = Round-trip multiplier (supply and return conductors)
- • K = Conductor resistance (Ω per 1000 feet)
- • I = Load current (amperes)
- • L = One-way conductor length (feet)
3. Three-Phase Calculation
For three-phase AC circuits:
VD = (√3 × K × I × L) ÷ 1000VD = (1.732 × K × I × L) ÷ 1000Where:
- • √3 = 1.732, three-phase factor
- • Voltage drop is line-to-line
- • Current is per-phase line current
- • Assumes balanced three-phase load
4. Percentage Calculation
Voltage drop is expressed as a percentage of source voltage:
% Drop = (Voltage Drop ÷ Source Voltage) × 100This percentage is compared against NEC recommendations (3% branch, 5% total) to determine circuit acceptability.
5. End Voltage
The voltage available at the load:
End Voltage = Source Voltage - Voltage DropThis is the actual voltage that will be delivered to the connected equipment.
Assumptions and Limitations
Our calculations make the following assumptions:
- Conductor temperature: 75°C (167°F) - standard for most THHN/THWN wire
- AC calculations use DC resistance (valid for power frequencies 50-60 Hz)
- Three-phase systems are balanced (equal current on all phases)
- Conduit effects and conductor spacing: minimal impact (typically < 5%)
- Power factor: not included (affects current magnitude, not voltage drop per amp)
- Harmonic distortion: not included (may increase effective resistance)
Engineering Note: For critical applications, long runs, or high-frequency loads, consult a licensed electrical engineer. AC circuits with significant reactance, high harmonic content, or skin effect considerations may require more detailed analysis beyond these simplified calculations.