AC Single-Phase V-Drop

Calculate conductor voltage drop for single-phase AC circuits using standard NEC Circular-Mil formulas (K=12.9 Copper / 21.2 Aluminum) and verify the 3% branch circuit guideline.

Circuit Architecture

Source Voltage

Volts

Load Current (Peak)

Amps

One-Way Length

Material

Target Wire Gauge

AWG Viability Sweep15.0A @ 150ft

14 AWG

11.8%

✗

12 AWG

7.4%

10 AWG

4.7%

8 AWG

2.9%

●

6 AWG

1.8%

●

4 AWG

1.2%

●

2 AWG

0.7%

●

1/0 AWG

0.5%

●

2/0 AWG

0.4%

●

3/0 AWG

0.3%

●

4/0 AWG

0.2%

●

Vd = (2 * K * I * L) / CMFormula

Vd = (2 * 12.9 * 15.0 * 150.0) / 411014.124V

Drop% = (14.12V / 120V) * 10011.77%

Diagnostic Telemetry

⚠ 11.8% voltage drop exceeds NEC 3% branch circuit design recommendation. Upgrade to at least 8 AWG to restore voltage within 3%.

Absolute System Drop

11.8%

Critical (> 10%)

Voltage Drop

14.12V

Conductor Loss

Voltage Delivered

105.9V

Terminal Voltage

Email Link Text/SMS WhatsApp

Step-by-Step Worked Example

Governing methodology applied to an authentic engineering scenario

NEC 210.19(A) Informational Note 4 / NEC Ch 9 Table 8

Design Scenario

An electrician plans a 120V, 15A branch circuit run spanning 150 feet to supply an outbuilding workshop using 14 AWG solid uncoated copper conductor. Baseline operating conditions assume 75°C conductor ratings and unity power factor. Calculate the absolute voltage drop across both conductors, the percentage drop, the arrival voltage at the receptacle, and assess compliance with the NEC 3% branch circuit guideline.

Design Parameters

Nominal Source Voltage120 V AC

Continuous Circuit Current15 Amps

One-Way Distance150 Feet

Conductor Size & Material14 AWG Copper (4,110 cmil, K=12.9)

Mathematical Solution

1Calculate Absolute Voltage Drop (Vd)

The 2x multiplier accounts for both hot and neutral conductor loop paths over the 150-foot run.

\frac{2 \times 12.9 \times 15 \times 150}{4,110} = \frac{58,050}{4,110} = 14.12 \text{ V}

14.12 V lost

2Calculate Drop Percentage

An 11.77% drop substantially exceeds the NEC 210.19(A) Informational Note 4 recommended branch threshold of 3.0%.

\frac{14.12}{120} \times 100 = 11.77\%

11.77% Drop

3Determine Operating Voltage at Equipment Terminal

Terminal voltage is depressed to ~106V, risking motor stalling and increased running temperatures for inductive equipment.

120 - 14.12 = 105.88 \text{ V}

105.9 V Delivered

4Upsize Conductor for NEC 3% Target (≤ 3.60V Drop)

Upsizing to 8 AWG brings line loss down to 3.52V (2.93%), fully within the NEC 3% branch circuit guideline.

\frac{58,050}{3.60} = 16,125 \text{ cmil} \rightarrow \text{Upsize to 8 AWG (16,510 cmil)}

8 AWG Copper (2.93% Drop)

What is NEC Chapter 9 Table 8 and Conductor Resistance?

Voltage drop is the physical loss of electrical potential as current flows through conductor resistance. In long AC branch runs, this resistance causes line losses, converting electrical energy into thermal heat along the run. The National Electrical Code (NEC) provides formulas using Circular Mils to calculate conductor voltage drop before installation.

Mathematical Foundation

Standard Circular-Mil Voltage Drop

V_d = \frac{2 \times K \times Amps \times Length}{CM}

K

= The Specific Resistivity Constant. Copper: K = 12.9 (Ω·cmil/ft). Aluminum: K = 21.2. This defines the thermal friction of the core material.

Amps

= The total running amperage of the connected branch load.

Length

= The physical one-way conductor routing distance in feet.

CM

= Circular Mil area of the conductor. 1 cmil = (diameter in mils)². Defined by NEC Chapter 9, Table 8.

Total Drop Percentage

Drop\% = \left(\frac{V_d}{V_{\text{sys}}}\right) \times 100

V_d

= The absolute volts lost directly to heat inside the wall.

V_{sys}

= The nominal starting voltage measured at the load center (e.g. 120V / 240V).

Laws & Principles

The NEC 3% / 5% Guideline: NEC Article 210.19(A) Informational Note 4 recommends that branch circuits maintain a voltage drop of 3% or less, and combined feeder/branch circuits stay within 5% overall to provide reasonable efficiency of operation.
Motor Voltage Sensitivity: Inductive loads (compressors, table saws) are sensitive to input voltage. Significant voltage drop can prevent starting capacitors from engaging or cause motors to stall under load.
The 2X Multiplier: In single-phase formulas, one-way distance is multiplied by 2 to account for both the ungrounded (hot) conductor and the grounded (neutral) return path.
Conductor Resistivity Comparison: Aluminum (K=21.2) has higher electrical resistance than Copper (K=12.9). Conductor sizing must account for aluminum's higher resistivity to achieve equivalent voltage drop performance.

Step-by-Step Example Walkthrough

" A homeowner builds a detached workshop 150 feet away from their main 120V residential panel. They want to run a standard 15 Amp table saw out there using basic 14 AWG copper wire (4,110 CM). "

1. Identify the Constants: Volts = 120, Length = 150 ft, Amps = 15, Copper K-Factor = 12.9, 14 AWG CM = 4,110.
2. Calculate Absolute Volts Lost (Vd): (2 × 12.9 × 15 Amps × 150 ft) ÷ 4,110 CM = 58,050 ÷ 4,110 = 14.12 Volts lost to heat.
3. Calculate Drop Percentage: (14.12V ÷ 120V) × 100% = 11.77% Total Loss.
4. Evaluate System Delivery: 120V starting - 14.12V lost = The load is only receiving 105.9 Volts.

Final Result: Excessive voltage drop. The 11.77% drop significantly exceeds the NEC 3% recommended branch threshold. When operating the 15 Amp saw, the reduced voltage (105.9V) may cause the motor to lug and overheat. To bring voltage drop within the 3% guideline (maximum 3.60V drop), the conductor should be upsized to 8 AWG copper (16,510 CM), which brings line loss down to 3.52V (2.93%).

Quick Answer: How do you calculate Single-Phase AC Voltage Drop?

To calculate AC single-phase voltage drop, multiply your one-way distance by 2 to account for the neutral return leg, and then multiply by the specific resistance (K-factor) of your wire material (12.9 for Copper, 21.2 for Aluminum). Multiply that result by your Load Amps, and divide by the wire's Circular Mils (CM). Use this AC Single-Phase Voltage Drop Calculator to diagnose voltage drop, terminal voltage remaining, and verify compliance with the NEC 3% recommended branch circuit guideline for any residential or commercial branch circuit run.

The Standard NEC Tolerances

Drop < 3.0% → Within 3% NEC Recommended Guideline

Drop = 3.0% to 5.0% → Within 5% Combined Feeder / Branch Guideline

Drop = 5.0% to 10.0% → Exceeds Recommended Limit / Motor Stall / Dimming Risk

Drop > 10.0% → Critical Voltage Drop / Severe Voltage Depression & Conductor Loss

Heuristic: Never assume the utility company delivers 120V nominal at the service entrance. Under ANSI C84.1 Range A service voltage standards, utility supply may vary by ±5%. This means your service entrance may start at 114V before factoring in branch circuit drop. Maximizing Circular Mils and minimizing conductor length provides essential operating margin.

Typical 120V AC Distances for 3% Maximum Drop

Wire Size (Copper) AWG	15 Amps MAX DISTANCE	20 Amps MAX DISTANCE	30 Amps MAX DISTANCE
14 AWG	38 ft	Overloaded	Overloaded
12 AWG	60 ft	45 ft	Overloaded
10 AWG	96 ft	72 ft	48 ft
8 AWG	152 ft	114 ft	76 ft
6 AWG	244 ft	183 ft	122 ft
Distances represent ONE-WAY physical wire run. The X2 neutral return loop is automatically factored into these geometric limits. Data applies strictly to 120V AC systems targeted for 3% maximum loss using 12.9 K-factor copper.

Field Case Studies

The '240V Receptacle' Assumption

An amateur runs a 240V NEMA 14-50 plug 150 feet to power an RV. They correctly calculate a 50 Amp load and use 6 AWG wire. They ignored that while the main AC units use 240V, the RV's internal subpanel splits that into two 120V legs for the TV and microwave. While 6 AWG provides an acceptable 240V drop, when parsed as a 120V sub-leg, the voltage drops 6.7%. The microwave barely spins, and the TV keeps restarting. When sizing 4-wire 240V systems, you must mathematically verify the drop on the 120V individual legs to ensure reliable operation.

The 'Aluminum is Cheaper' Illusion

A pool contractor buries a 100-foot run of 10 AWG to power a 20 Amp pool pump. Because copper is more costly, they consider 10 AWG Aluminum. 10 AWG Copper has a 12.9 K-Factor and yields a 2.5% drop (within the 3% branch guideline). But 10 AWG Aluminum has a 21.2 K-Factor, resulting in a 4.1% drop that exceeds recommended design limits. In addition, aluminum conductors require compatible dual-rated (AL/CU) termination lugs torqued to manufacturer specifications to avoid loose connections over thermal expansion cycles.

Architectural Directives

Do This

✓Calculate against LRA (Locked Rotor Amps). Almost all standard branch circuit calculations are run against 'Running Load Amps'. This is a significant oversight for electric motors (air conditioners, well pumps). An AC compressor that runs at 15 Amps will surge to 70 Amps (LRA) for half a second when it starts. If your wire shrinks the voltage too far during that 70-Amp surge, the compressor cannot break static inertia and will mechanically stall.
✓Embrace 240V for Long Runs. If you need to push a massive load out to a detached garage 200 feet away, avoid running a 120V 30-Amp circuit. Reconfigure the equipment (if possible) to run natively at 240V. Doubling the voltage instantly halves the amperage, significantly reducing percentage voltage drop and allowing you to use dramatically thinner, cheaper wire.

Avoid This

✗Do not assume Ampacity equals Drop safety. This is a common pitfall in branch circuit design. A 12 AWG wire can safely handle 20 Amps of heat without melting according to the NEC Ampacity chart. But if that 12 AWG wire is 150 feet long, it severely exceeds recommended Voltage Drop limits. Just because it won't catch fire directly does NOT mean it has the required volume to push power that far safely.

Frequently Asked Questions

Are Circular Mils measured differently for stranded vs solid wire?

No. NEC Chapter 9 Table 8 standardizes the circular mil area for both solid and stranded variants. A 10 AWG solid core wire and a 10 AWG 19-strand wire both contain identically 10,380 Circular Mils of copper volume. The math does not care about the geometry of the strands.

Why don't 3-phase systems use the 'Multiply by 2' rule?

Single phase power has one 'hot' pushing out, and one 'neutral' returning, literally making a 2-part physical loop. In a balanced 3-phase AC system, the three hot legs organically cancel out each other's return path. The neutral carries 0 amps, thus generating zero heat and zero voltage drop on the return. 3-Phase uses a 1.732 (square root of 3) multiplier instead.

Does PVC vs Metal Conduit change voltage drop?

For standard Single-Phase calculations under 4/0, no. However, in hyperscale massive-feed systems running parallel 500 kcmil cables, routing through Metallic Conduit adds 'inductive reactance' (AC magnetic field friction) that routing through plastic PVC does not. Basic calculators ignore this, but engineers factor it constantly.

If my voltage drops 5%, what happens to the missing power?

It is dissipated as resistive heat along the conductor length (P = I²R). For example, a 6V drop at 20A dissipates 120W of heat across the wiring run, reducing system efficiency and depressing equipment terminal voltage.

Related Electrical Calculators

Calculation Provenance & Validation Record

Method

AC Single-Phase Exact Conductor Voltage Drop

Formula

V_d = \frac{2 \times K \times I \times L}{CM}

Assumptions

Copper resistivity K = 12.9 ohms-cmil/ft at 75°C, Aluminum K = 21.2
Two-wire single-phase loop distance 2L
NEC recommended 3% branch circuit limit

References

National Electrical Code (NFPA 70) (2023 Edition) — NEC Article 210.19(A) Informational Note 4 & Chapter 9 Table 8

Last substantive review: 2026-10-03