What this lesson covers
Voltage drop is one of the most common calculations on state journeyman exams, and one of the easiest to get wrong by a single factor of 2. Theory and calculations are the largest area on our 100-question practice exam, about 14 questions. This lesson gives you one formula in two forms, a habit for checking it, and the code status of the 3% and 5% figures.
We cite the 2023 NEC by article in our own words. Keep your own copy open beside this page.
Step 1: pick the formula
Use the circular mil method:
- Single-phase: VD = 2 × K × I × L ÷ CM
- Three-phase: VD = 1.732 × K × I × L ÷ CM
Where:
- K is about 12.9 for copper and 21.2 for aluminum (ohm-circular mils per foot, a trade approximation).
- I is the load current in amperes.
- L is the one-way length in feet, from source to load.
- CM is the conductor's area in circular mils, from the conductor properties table in Chapter 9.
The 2 in the single-phase formula is there because current goes out on one conductor and back on the other. The 1.732 in the three-phase formula replaces it, because the return current is shared among the phases.
Step 2: check it with the resistance method
Chapter 9 also lists each conductor's resistance in ohms per 1,000 ft. Then:
- R = ohms per 1,000 ft × total conductor length ÷ 1,000 (for single-phase, the total length is out and back, 2 × L)
- VD = I × R
The two methods agree within a few tenths of a volt. Working both is the habit that catches a missing 2.
Step 3: compare it with the target
Divide the drop by the source voltage for a percentage. The NEC's informational notes in Articles 210 and 215 suggest no more than 3% on a branch circuit or feeder and 5% total from the service to the farthest outlet. These are recommendations, not general requirements. A few articles do set mandatory limits for specific equipment; if a question names that equipment, read its article.
Worked examples
Example 1: single-phase drop. A 120 V circuit feeds a 16 A load 75 ft away on 12 AWG copper. Take 12 AWG as 6,530 cmil and 1.98 Ω per 1,000 ft.
The working (2 steps)
- CM method: 2 × 12.9 × 16 × 75 ÷ 6,530 = 30,960 ÷ 6,530 = 4.74 V, or 4.74 ÷ 120 = 3.95%.
- Resistance check: 150 ft × 1.98 ÷ 1,000 = 0.297 Ω, and 16 × 0.297 = 4.75 V. Agrees.
Example 2: sizing up to meet 3%. Same circuit. 3% of 120 V is 3.6 V. Solve the formula for CM: CM = 2 × K × I × L ÷ VD = 30,960 ÷ 3.6 = 8,600 cmil. Take 10 AWG as 10,380 cmil: it is the smallest that meets 8,600.
- Check: 30,960 ÷ 10,380 = 2.98 V, or 2.49%. Under 3%.
Example 3: three-phase. A 480 V, three-phase load draws 65 A at 250 ft on 6 AWG copper. Take 6 AWG as 26,240 cmil and 0.491 Ω per 1,000 ft.
- CM method: 1.732 × 12.9 × 65 × 250 ÷ 26,240 = 363,071 ÷ 26,240 = 13.84 V, or 13.84 ÷ 480 = 2.88%.
- Resistance check: one conductor is 250 × 0.491 ÷ 1,000 = 0.1228 Ω, and 65 × 0.1228 = 7.98 V per conductor. Times 1.732 for three-phase line to line: 13.82 V. Agrees.
Example 4: the longest run that meets 3%. A 240 V, single-phase, 40 A load on 8 AWG copper (16,510 cmil). 3% is 7.2 V. Solve for L: L = VD × CM ÷ (2 × K × I) = 7.2 × 16,510 ÷ (2 × 12.9 × 40) = 118,872 ÷ 1,032 = 115 ft.
- Check: at 115 ft, 2 × 12.9 × 40 × 115 ÷ 16,510 = 7.19 V. Just under 7.2.
Example 5: aluminum. Repeat Example 1 with aluminum of the same area: use K = 21.2. 2 × 21.2 × 16 × 75 ÷ 6,530 = 50,880 ÷ 6,530 = 7.79 V. Check by ratio: 4.74 × (21.2 ÷ 12.9) = 7.79 V. Aluminum drops about 64% more than copper of the same size.
What a drop does to the load
A resistive load's power changes with the square of its voltage. A 240 V, 4,800 W heater has R = 240² ÷ 4,800 = 12 Ω. At 228 V (a 5% drop), P = 228² ÷ 12 = 4,332 W. Check by ratio: 0.95² × 4,800 = 4,332 W. Motors respond differently: lower voltage makes them draw more current and run hotter.
Common traps
- Doubling the length and keeping the 2. L is one way. The formula's 2 covers the return.
- Using 2 on three-phase. Use 1.732. Using 2 overstates the drop by about 15%.
- Using the wrong voltage for the percentage. Divide by the circuit's source voltage: 120 V for a 120 V circuit, 480 V for a 480 V three-phase circuit.
- Calling 3% a requirement. It is an informational note unless a specific article requires a limit.
- Rounding the conductor down. If the CM you need falls between sizes, take the larger.
- Forgetting the EGC. If you upsize the phase conductors for voltage drop, the equipment grounding conductor grows in proportion (Article 250; see Module 6).
Check yourself
Try the ten questions in the free practice set for this lesson. Work each one twice, once each way.
Where to look in the NEC
- Chapter 9: conductor properties (circular mils and resistance per 1,000 ft)
- Articles 210 and 215: voltage drop informational notes
- Article 250: proportional increase of the equipment grounding conductor