Voltage Drop Calculations

Voltage drop is the reduction in voltage as current flows through a conductor. The NEC recommends limits on voltage drop to ensure equipment operates properly and efficiently. This calculation determines whether your conductor size and run length will deliver adequate voltage to the load.

The Voltage Drop Formula

$VD = \frac{2 \times K \times I \times D}{CM}$

Where:

• $VD$ = Voltage drop in volts
• $K$ = Resistivity constant — 12.9 for copper, 21.2 for aluminum
• $I$ = Current in amperes
• $D$ = One-way distance in feet (panel to load)
• $CM$ = Circular mils — the cross-sectional area of the conductor (from NEC Chapter 9, Table 8)

The factor of 2 accounts for the round trip — current flows out on one conductor and returns on the other. For three-phase circuits, replace 2 with $\sqrt{3}$ (1.732).

NEC Voltage Drop Recommendations

NEC 210.19(A) Informational Note No. 4 and 215.2(A) Informational Note No. 2 recommend:

These are recommendations, not hard requirements — but inspectors expect compliance and the exam tests these values.

Calculating Percent Voltage Drop

$\%VD = \frac{VD}{V_{\text{source}}} \times 100$

Circular Mils by Wire Size (NEC Table 8)

Worked Examples

Example 1: #12 AWG Copper at 150 ft, 16A, 120V

Scenario: You are running a 120V, 20A branch circuit with #12 AWG copper to a workshop 150 feet from the panel. The continuous load is 16A. Will the voltage drop meet the NEC 3% recommendation?

Step 1 — Apply the formula:

$VD = \frac{2 \times 12.9 \times 16 \times 150}{6{,}530}$

$VD = \frac{61{,}920}{6{,}530} = 9.48 \text{ V}$

Step 2 — Calculate percent:

$\%VD = \frac{9.48}{120} \times 100 = 7.9\%$

Answer: The voltage drop is 9.48V (7.9%) — far above the 3% limit. You need a larger conductor. Trying #8 AWG (16,510 CM):

$VD = \frac{61{,}920}{16{,}510} = 3.75 \text{ V} \quad (3.1\%)$

Still slightly over 3%. Trying #6 AWG (26,240 CM):

$VD = \frac{61{,}920}{26{,}240} = 2.36 \text{ V} \quad (2.0\%)$

Solution: Use #6 AWG copper for this 150 ft run at 16A to stay within 3%.

Example 2: 240V Circuit, #10 AWG Copper, 80 ft, 24A

Scenario: A 240V, 30A circuit feeds a workshop sub-panel 80 feet away using #10 AWG copper. The load is 24A.

$VD = \frac{2 \times 12.9 \times 24 \times 80}{10{,}380} = \frac{49{,}536}{10{,}380} = 4.77 \text{ V}$

$\%VD = \frac{4.77}{240} \times 100 = 2.0\%$

Answer: The voltage drop is 4.77V (2.0%) — within the 3% recommendation.

Example 3: Finding Minimum Wire Size

Scenario: What is the minimum copper conductor size for a 120V, 20A circuit that runs 100 feet and must stay within 3% voltage drop?

Step 1 — Find maximum allowable VD:

$VD_{\text{max}} = 120 \times 0.03 = 3.6 \text{ V}$

Step 2 — Rearrange the formula to solve for CM:

$CM = \frac{2 \times K \times I \times D}{VD} = \frac{2 \times 12.9 \times 20 \times 100}{3.6} = \frac{51{,}600}{3.6} = 14{,}333 \text{ CM}$

Step 3 — Select the wire: From the CM table, #8 AWG (16,510 CM) is the first size that exceeds 14,333 CM.

Answer: Use #8 AWG minimum for this run.

Practice Problems

Test your understanding with these problems. Click to reveal each answer.

Common Mistakes to Avoid

1. Forgetting the factor of 2. The formula uses one-way distance ($D$), but the factor of 2 accounts for the complete circuit. If you use round-trip distance, do not also multiply by 2.
2. Using the wrong K-factor. Copper is 12.9, aluminum is 21.2. Aluminum requires larger wire for the same voltage drop.
3. Confusing 3% and 5%. The 3% limit applies to either the branch circuit or feeder alone. The 5% limit applies to the total from service entrance to the final outlet.
4. Using ampacity instead of actual load. The formula uses the actual current ($I$) the circuit will carry, not the wire’s ampacity rating.
5. Neglecting voltage drop on long runs. A #12 AWG circuit that works fine at 50 ft may fail at 150 ft. Always check VD on runs over 100 ft.

Key Takeaways

• The voltage drop formula $VD = \frac{2KID}{CM}$ is one of the most-tested formulas on the electrician exam
• Use $K = 12.9$ for copper and $K = 21.2$ for aluminum
• NEC recommends 3% maximum for branch circuits or feeders alone, 5% maximum total
• Rearrange the formula to find the minimum wire size: $CM = \frac{2KID}{VD}$
• Long runs are the most common cause of voltage drop problems — always check before pulling wire

Math for Electricians