Calculation for Voltage Drop of Cable: Formulas, Tables, and Worked Examples

The fundamental calculation for voltage drop of cable in single-phase AC and DC systems relies on a direct application of Ohm’s Law, adapted for the physical geometry of the wire. When sizing branch circuits or feeders, you must ensure the voltage at the load remains within acceptable limits (typically a 3% maximum drop for branch circuits and 5% total for feeder plus branch, per NFPA National Electrical Code recommendations). Below is the exact formula, the reference data required to use it, and step-by-step worked examples to prove your wire size before you pull the first foot of cable.

The Core Voltage Drop Formula & Symbol Definitions

For single-phase AC (at or near unity power factor) and DC circuits, the standard approximate voltage drop formula used in North American NEC-style calculations is:

VD = (2 × K × I × D) / CM

This formula calculates the absolute voltage lost across the entire circuit loop. To use it correctly, every variable must be tracked in strict imperial/US customary units. Here is the exact definition of each symbol:

Reference Data: Wire Properties & Resistivity Constants

You cannot execute the calculation for voltage drop of cable without accurate constants. The Copper Development Association and NEC Chapter 9 Table 8 provide the baseline resistivity values. The 'K' value changes slightly with temperature; use the 75°C column for standard terminations and the 90°C column if calculating thermal limits for high-ambient environments.

Next, you need the Circular Mil (CM) area for your chosen wire gauge. Do not confuse CM with square mils or metric mm². The CM values below are exact for solid and stranded conductors per NEC Chapter 9:

Rearranged Forms for Sizing and Troubleshooting

On the bench or in the field, you rarely just solve for VD. Usually, you know your maximum allowable voltage drop (e.g., 3% of 120V = 3.6V) and need to find the right wire size or maximum run length. Here are the algebraically rearranged forms:

• Solve for Wire Size (CM): CM = (2 × K × I × D) / VD
  Use when: You have a fixed load and distance, and need to select the minimum AWG to stay under 3% drop.
• Solve for Max Distance (D): D = (CM × VD) / (2 × K × I)
  Use when: You are deploying a specific wire gauge (e.g., a spool of 10 AWG) and need to know how far you can run it before upsizing is required.
• Solve for Max Current (I): I = (CM × VD) / (2 × K × D)
  Use when: Troubleshooting an existing long run to determine the maximum safe continuous load it can support without excessive voltage sag.

Worked Examples with Strict Unit Tracking

Abstract formulas fail on the jobsite without rigorous unit tracking. Below are two real-world scenarios demonstrating the intermediate math steps.

Example 1: 120V Branch Circuit for a Workshop Receptacle

Scenario: You are running a dedicated 120V circuit to a table saw. The one-way distance from the subpanel to the outlet is 85 feet. The saw draws a continuous 16A under load. You plan to use 12 AWG copper THHN wire in conduit. Will this wire keep the voltage drop under the recommended 3%?

1. Identify Variables:
   K = 12.9 (Copper at 75°C)
   I = 16A
   D = 85 ft
   CM = 6,530 (for 12 AWG)
2. Substitute into Formula:
   VD = (2 × 12.9 × 16 × 85) / 6,530
3. Calculate Numerator (Round-trip resistance factor × current × distance):
   2 × 12.9 = 25.8
   25.8 × 16 = 412.8
   412.8 × 85 = 35,088
4. Divide by CM:
   VD = 35,088 / 6,530 = 5.37 Volts
5. Calculate Percentage:
   (5.37V / 120V) × 100 = 4.47%

Verdict: 4.47% exceeds the 3% NEC recommendation for branch circuits. The motor may run hot and trip its internal thermal overload. Action: Upsize to 10 AWG (CM = 10,380). Recalculating with 10 AWG yields a 3.38V drop (2.8%), which passes.

Example 2: 240V Feeder to a Detached Garage Subpanel

Scenario: You are feeding a 60A subpanel in a detached garage. The trench is 160 feet long (one-way). You are using 2 AWG aluminum XHHW-2 wire. Calculate the voltage drop at full 60A load.

1. Identify Variables:
   K = 21.2 (Aluminum at 75°C terminations)
   I = 60A
   D = 160 ft
   CM = 66,360 (for 2 AWG)
2. Substitute into Formula:
   VD = (2 × 21.2 × 60 × 160) / 66,360
3. Calculate Numerator:
   2 × 21.2 = 42.4
   42.4 × 60 = 2,544
   2,544 × 160 = 407,040
4. Divide by CM:
   VD = 407,040 / 66,360 = 6.13 Volts
5. Calculate Percentage:
   (6.13V / 240V) × 100 = 2.55%

Verdict: 2.55% is well under the 3% feeder recommendation. The 2 AWG aluminum wire is adequately sized for this distance and load.

Assumptions, Limits, and Fatal Unit Mistakes

The formula VD = (2 × K × I × D) / CM is an approximation. Understanding its boundaries prevents catastrophic sizing errors.

When the Formula Applies (and Its Assumptions)

• DC or Single-Phase AC: It assumes a two-wire loop (Line and Neutral, or Line-to-Line 240V).
• Near Unity Power Factor: It assumes the load is primarily resistive (heaters, incandescent lighting, standard electronics). For highly inductive loads like large uncorrected AC motors, the wire's reactance (X) matters. The true AC formula is VD = I × (R cosθ + X sinθ) × 2D. For residential and light commercial wiring under 100A, the reactance is negligible, and the K-constant approximation holds within 1-2% accuracy.
• Steady-State Temperature: The K values assume the wire is at its rated operating temperature (75°C). Cold wire has lower resistance; a wire sitting in a 120°F attic will have slightly higher resistance.

Fatal Unit Mistakes That Break the Math

1. The 'Total Length' Trap: The most common DIY error is measuring the total length of the Romex/NM-B cable (e.g., 170 ft) and plugging that into 'D' while keeping the '2' multiplier. This artificially doubles your calculated voltage drop. Rule: 'D' is strictly the physical one-way distance from source to load. The '2' accounts for the return path.
2. Mixing Metric and Imperial: If you are using European IEC standards, wire size is in mm² and distance in meters. You cannot plug mm² into the 'CM' slot. To convert mm² to CM, multiply by 1,973.5. Alternatively, use the metric formula: VD = (2 × ρ × I × D) / A, where ρ is resistivity in Ω·m and A is area in m².
3. Using Breaker Size for 'I': Voltage drop is based on the actual operating current of the load, not the breaker rating. Calculating drop using a 20A breaker for a circuit that only ever powers a 5A refrigerator results in massive, unnecessary wire upsizing.

What a Realistic Answer Magnitude Looks Like

When you measure voltage at a receptacle under load, what should you expect?

• 1.5V to 3.5V Drop (120V circuit): Normal and healthy. This is the expected I²R heating loss in standard 12 AWG or 14 AWG residential branch wiring.
• 4V to 6V Drop (120V circuit): Marginal. Acceptable for short-duration motor starts, but if continuous, the wire will run warm and sensitive electronics may brown out.
• >8V Drop (120V circuit): Danger/Fault. Unless you are at the absolute end of a 200-foot rural run with undersized wire, a drop this large under a 15A load indicates a high-resistance fault. Stop and check for loose backstabbed receptacle connections, corroded panel busbars, or a failing breaker terminal. Torque your lugs to manufacturer specs; a loose neutral connection will manifest as severe voltage drop on one leg of a multi-wire branch circuit.