To calculate cable voltage drop on a standard single-phase or DC circuit, use the formula: Vd = (2 × K × I × L) / CM. This calculation tells you exactly how many volts are lost as heat across the wire resistance before reaching the load. For most residential 120V branch circuits, a realistic voltage drop magnitude is between 1% and 3% (1.2V to 3.6V). If your calculation yields a drop of 15V or more, you have either undersized the wire, exceeded the maximum run length, or made a unit conversion error.
The Core Formula to Calculate Cable Voltage Drop
The formula below applies to single-phase AC circuits (where wire reactance is negligible for conductors 2 AWG and smaller) and DC circuits. It assumes a unity power factor (PF ≈ 1.0), which is standard for resistive loads like heaters and incandescent lighting. For inductive loads like large motors, the exact impedance (Z) rather than just DC resistance (K) should be used, but this simplified formula is the industry standard for general branch circuit sizing per NEC Article 210.19(A) Informational Notes.
Vd = (2 × K × I × L) / CM
| Symbol | Definition | Standard Units & Values |
|---|---|---|
| Vd | Voltage Drop | Volts (V) |
| 2 | Multiplier for the out-and-back current path (Line and Neutral) | Dimensionless constant |
| K | Specific resistance of the conductor material | 12.9 Ω·cmil/ft for Copper (at 75°C) 21.2 Ω·cmil/ft for Aluminum (at 75°C) |
| I | Current drawn by the load | Amperes (A) |
| L | One-way length of the cable run | Feet (ft) |
| CM | Cross-sectional area of the wire in Circular Mils | Circular Mils (cmil) — found in NEC Chapter 9, Table 8 |
Rearranged Forms for Wire Sizing and Distance
On the jobsite, you rarely just solve for Vd. Usually, you know your maximum allowable drop and need to find the required wire size or the maximum distance you can run a specific cable. Here are the algebraic rearrangements of the core formula:
- Solve for Wire Size (CM):
CM = (2 × K × I × L) / Vd
Use this to find the minimum circular mils required, then look up the corresponding AWG size in NEC Chapter 9, Table 8. - Solve for Maximum Distance (L):
L = (CM × Vd) / (2 × K × I)
Use this to determine how far you can run a specific wire gauge before exceeding your voltage drop limit. - Solve for Maximum Current (I):
I = (CM × Vd) / (2 × K × L)
Use this to find the maximum load an existing buried cable can handle without excessive voltage sag.
Worked Examples with Unit Tracking
Let's run through two real-world scenarios. Tracking your units through the calculation is the best way to catch errors before you pull the wrong wire.
Problem 1: 120V Receptacle Branch Circuit
Scenario: You are running a 120V, 15A dedicated circuit for a workshop heater. The one-way distance from the panel to the outlet is 60 feet. You plan to use 12 AWG copper THHN wire. What is the voltage drop?
- Identify the variables:
- K = 12.9 Ω·cmil/ft (Copper at 75°C)
- I = 15 A
- L = 60 ft
- CM = 6,530 cmil (12 AWG from NEC Chapter 9, Table 8)
- Substitute into the formula with units:
Vd = (2 × 12.9 Ω·cmil/ft × 15 A × 60 ft) / 6,530 cmil - Cancel units and calculate the numerator:
The 'ft' and 'cmil' units cancel out appropriately, leaving Volts.
Vd = 23,220 / 6,530 - Final Result:
Vd = 3.55 Volts - Calculate Percentage:
(3.55V / 120V) × 100 = 2.96%
Verdict: A 2.96% drop is just under the 3% NEC recommendation for branch circuits. 12 AWG is acceptable, though 10 AWG would be better if the run gets any longer.
Problem 2: 240V Electric Water Heater
Scenario: A 240V, 40A water heater is located 120 feet from the main panel. The installer used 6 AWG copper wire. Is the voltage drop within acceptable limits?
- Identify the variables:
- K = 12.9 Ω·cmil/ft
- I = 40 A
- L = 120 ft
- CM = 26,240 cmil (6 AWG)
- Substitute into the formula:
Vd = (2 × 12.9 Ω·cmil/ft × 40 A × 120 ft) / 26,240 cmil - Calculate numerator and divide:
Vd = 123,840 / 26,240 - Final Result:
Vd = 4.72 Volts - Calculate Percentage:
(4.72V / 240V) × 100 = 1.96%
Verdict: Excellent. A 1.96% drop on a 240V circuit is well within the 3% guideline. The 6 AWG wire is perfectly sized for this distance and load.
Unit Mistakes That Break the Calculation
When you calculate cable voltage drop, a math error usually manifests as an absurdly high or low result. Here are the most common unit traps:
The '2' in the formula accounts for the round-trip path of the current (out on the hot wire, back on the neutral). Therefore, L must be the one-way distance. If you measure the total wire length pulled from the spool (which includes both the hot and neutral) and plug that into 'L', you will accidentally double your voltage drop result.
- Mixing mm² and Circular Mils: The standard US formula requires CM. If you are using metric wire (e.g., 4 mm²), you cannot plug '4' into the CM variable. You must either convert mm² to CM (1 mm² ≈ 1,973.5 cmil) or use the metric resistivity formula (see FAQ below).
- Wrong K Value for Temperature: The K value changes with temperature. At 20°C (68°F), copper K is 10.8. At 75°C (167°F), which is the standard termination rating for most modern breakers and devices, K is 12.9. Using 10.8 for a loaded circuit will underestimate your voltage drop by nearly 20%.
- Forgetting to Convert Inches to Feet: If your tape measure reads 65 feet and 6 inches, you must use 65.5 for 'L'. Plugging in 656 will result in a calculated drop ten times higher than reality.
Frequently Asked Questions
How do I calculate cable voltage drop for a 3-phase system?
For a balanced 3-phase system, the current returns through the other phase conductors rather than a dedicated neutral, and the phase angles reduce the effective line-to-line resistance path. To calculate cable voltage drop for 3-phase, replace the '2' in the standard formula with the square root of 3 (approximately 1.732). The formula becomes: Vd = (1.732 × K × I × L) / CM. This assumes a balanced load and a wye or delta configuration where line-to-line voltage is being evaluated.
What is the acceptable limit when I calculate cable voltage drop for branch circuits?
The National Electrical Code (NEC) does not strictly enforce voltage drop as a hard violation for most standard residential branch circuits, but it provides strong guidance in Informational Notes. The industry standard benchmark is a maximum of 3% voltage drop on the furthest branch circuit, and a maximum combined voltage drop of 5% for the feeder and branch circuit combined. For a 120V circuit, a 3% drop is 3.6 Volts. For sensitive electronics or long motor runs, aiming for 1.5% to 2% is best practice to prevent dimming lights and motor overheating.
How do I calculate cable voltage drop using metric wire sizes (mm²)?
If you are working in a region that uses IEC standards and metric wire sizes, you will use the resistivity (ρ) of the material and the cross-sectional area (A) in square millimeters. The metric formula for single-phase is: Vd = (2 × ρ × I × L) / A. In this formula, ρ (rho) for copper is approximately 0.0172 Ω·mm²/m at 20°C (or 0.021 Ω·mm²/m at 75°C), L is the one-way length in meters, and A is the wire area in mm². You can find exact metric voltage drop tables in resources like the Electrical Technology voltage drop guides or IEC 60364-5-52.
