Voltage Drop & Wire Size Calculator
Calculate single-phase, three-phase, and DC circuit voltage drop, terminal load voltage, power dissipation, and compliant AWG wire sizes according to National Electrical Code (NEC) guidelines.
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Electromagnetic Principles & Voltage Drop Equations
Electrical conductors possess intrinsic resistance determined by material atomic resistivity, cross-sectional circular mil area, operating temperature, and distance. When an electric current flows through a wire, Ohm’s Law dictates that an inevitable potential difference—termed voltage drop—develops across the conductor length, converting useful electrical energy into thermal heat dissipation.
Under the National Electrical Code (NEC), voltage drop calculations for alternating current (AC) and direct current (DC) circuits are calculated using the following mathematical formulas:
1. Single-Phase & 2-Wire DC Circuit Drop Equation:
VD = (2 * I * R * L) / 1000 = (2 * K * I * L) / CM
Where 2 represents both the supply and return conductor paths, I is current in Amperes, R is resistance per 1000 ft (from NEC Table 8), and L is one-way run length in feet.
2. Balanced Three-Phase Line-to-Line Drop Equation:
VD = (sqrt(3) * I * R * L) / 1000 = (1.732 * K * I * L) / CM
Where sqrt(3) ≈ 1.73205 accounts for the 120-degree phase angle displacement between line conductors in a balanced 3-phase wye or delta electrical system.
3. Percentage Voltage Drop & Heat Loss Equations:
%VD = (VD / V_source) * 100
V_load = V_source - VD
P_loss (Watts) = VD * I (Single Phase) or sqrt(3) * VD * I (Three Phase)
Resistivity Constant (K): At standard continuous conductor operating temperatures of 75°C, the resistivity factor K equals approximately 12.9 Ω·cmil/ft for solid uncoated copper and 21.2 Ω·cmil/ft for aluminum. Because aluminum has ~64% higher resistance than copper for an identical cross-section, aluminum wiring must be specified approximately two AWG gauges larger to maintain equal voltage drop.
Continuous Load Sizing (125% Rule) & Ambient Temperature Derating
Under NEC Section 210.20, branch circuits feeding continuous loads (where the maximum current is expected to persist for 3 hours or more, such as EV chargers, commercial lighting, and data centers) must be rated for at least 125% of the continuous load plus 100% of non-continuous loads.
- Ambient Temperature Correction: Standard NEC Table 8 resistances assume 75°C conductor temperatures in a 30°C (86°F) ambient environment. When conduits run through unconditioned attics or rooftop locations where temperatures reach 50°C (122°F), conductor resistance increases according to
R2 = R1 * [1 + 0.00393 * (T2 - T1)], escalating total voltage drop. - Conduit Bundling Derating (NEC 310.15(C)(1)): When more than 3 current-carrying conductors share a single conduit, mutual induction and restricted thermal dissipation require ampacity derating factors (80% for 4–6 wires, 70% for 7–9 wires). Sizing wire up for voltage drop concurrently resolves conduit ampacity derating challenges.
NEC Table 8 Conductor Resistance & Ampacity Matrix
Reference table showing DC conductor resistance per 1000 feet at 75°C, circular mil area, 75°C THHN copper ampacity (NEC Table 310.16), and the maximum single-phase current delivering less than 3% drop over a 100-foot run at 120V:
| Wire Size (AWG / kcmil) | Area (CM) | Copper Res (Ω/kft) | Aluminum Res (Ω/kft) | 75°C THHN Ampacity | Max 100ft 3% Drop (120V) |
|---|---|---|---|---|---|
| 14 AWG | 4,110 CM | 3.070 Ω | 5.060 Ω | 15 A* | 5.86 A |
| 12 AWG | 6,530 CM | 1.980 Ω | 3.250 Ω | 20 A* | 9.09 A |
| 10 AWG | 10,380 CM | 1.240 Ω | 2.040 Ω | 30 A* | 14.52 A |
| 8 AWG | 16,510 CM | 0.778 Ω | 1.280 Ω | 50 A | 23.14 A |
| 6 AWG | 26,240 CM | 0.491 Ω | 0.808 Ω | 65 A | 36.66 A |
| 4 AWG | 41,740 CM | 0.308 Ω | 0.508 Ω | 85 A | 58.44 A |
| 2 AWG | 66,360 CM | 0.194 Ω | 0.319 Ω | 115 A | 92.78 A |
| 1 AWG | 83,690 CM | 0.154 Ω | 0.253 Ω | 130 A | 116.88 A |
| 1/0 AWG | 105,600 CM | 0.122 Ω | 0.201 Ω | 150 A | 147.54 A |
| 2/0 AWG | 133,100 CM | 0.0967 Ω | 0.159 Ω | 175 A | 186.14 A |
| 3/0 AWG | 167,800 CM | 0.0766 Ω | 0.126 Ω | 200 A | 234.99 A |
| 4/0 AWG | 211,600 CM | 0.0608 Ω | 0.100 Ω | 230 A | 296.05 A |
| 250 kcmil | 250,000 CM | 0.0515 Ω | 0.0847 Ω | 255 A | 349.51 A |
| 350 kcmil | 350,000 CM | 0.0367 Ω | 0.0605 Ω | 310 A | 490.46 A |
| 500 kcmil | 500,000 CM | 0.0258 Ω | 0.0424 Ω | 380 A | 697.67 A |
* Note: NEC Section 240.4(D) limits standard overcurrent protective devices (breakers) to 15A for 14 AWG, 20A for 12 AWG, and 30A for 10 AWG copper conductors regardless of higher calculated terminal insulation ampacity.
Frequently Asked Questions
What mathematical formulas govern single-phase and three-phase voltage drop?
Single-phase (and two-wire DC) circuits use the round-trip formula VD = (2 * K * I * L) / CM or VD = (2 * I * R * L) / 1000, where 2 accounts for the supply and return paths. Balanced three-phase circuits use VD = (sqrt(3) * K * I * L) / CM or VD = (sqrt(3) * I * R * L) / 1000, where sqrt(3) is approximately 1.732 representing the line-to-line phase displacement.
What are the NEC code recommendations for maximum allowable voltage drop?
The National Electrical Code (NEC Article 210.19(A) Informational Note No. 4 and Article 215.2(A)(1) Informational Note No. 2) recommends that voltage drop should not exceed 3% on any individual branch circuit or feeder, and the total cumulative drop from the service entrance to the furthest outlet should not exceed 5% to ensure reasonable operating efficiency.
What are the resistivity constants (K) for copper and aluminum conductors?
At standard operating temperatures (75°C), the approximate DC resistivity constant K is 12.9 ohms-circular mil per foot for uncoated copper conductors, and 21.2 ohms-circular mil per foot for aluminum conductors. Because aluminum has ~64% higher resistance than copper, aluminum conductors must typically be sized two AWG gauges larger to carry equivalent current with equal voltage drop.
How do power factor and conductor temperature impact alternating current (AC) voltage drop?
In AC circuits with inductive loads (e.g., motors and transformers), the effective impedance equation is VD = I * (R * cos(theta) + X * sin(theta)), where cos(theta) is the load power factor and X is the inductive reactance. Furthermore, conductor resistance increases with operating temperature according to R2 = R1 * [1 + alpha * (T2 - T1)], where alpha = 0.00393 for copper.
When is it mandatory to upsize conductor gauge due to circuit run distance?
When the calculated voltage drop exceeds the NEC 3% branch circuit threshold, the conductor must be upsized to the next standard AWG or kcmil rating until the voltage drop falls within permissible limits. Under NEC 250.122(B), whenever ungrounded circuit conductors are increased in size for voltage drop, the equipment grounding conductor (EGC) must also be proportionally increased in circular mil area.