Voltage Drop Formula

Voltage drop is why long wire runs need thicker conductors than short ones. Every conductor has resistance, and when current flows through that resistance part of the source voltage is lost along the wire instead of reaching the load. The formula differs between single-phase (factor of 2 for the round trip) and three-phase (factor of √3 for the balanced line-to-line drop). This page shows both forms, the NEC 3% / 5% Informational Note guidance that sets the design target, and worked examples for 120V, 240V, and 480V circuits.

Formulas

DC and single-phase AC (two-wire): V_drop = (2 × L × I × R) ÷ 1000

Three-phase AC (balanced, line-to-line): V_drop = (√3 × L × I × R) ÷ 1000

%VD = V_drop ÷ V_source × 100

L is one-way run length in feet; R is conductor resistance in ohms per 1,000 feet (NEC Chapter 9 Table 8); I is circuit current in amps.

Every conductor has resistance, and when current flows through that resistance some of the source voltage is dropped across the wire rather than delivered to the load. The correct factor in front depends on the circuit type. For DC and single-phase AC, the factor is 2 because the current travels out to the load on one conductor and returns on another, so the effective resistance is twice the one-way length. For a balanced three-phase AC circuit, the factor is √3 (about 1.732) because the line-to-line voltage drop across balanced conductors is geometrically related to the per-phase I×R product through the three-phase vector diagram, not a simple round-trip doubling. Using the single-phase formula on a three-phase circuit overstates the drop by roughly 15% and is a common source of oversized wire. NEC Informational Notes in 210.19 (branch circuits) and 215.2 (feeders) suggest keeping branch-circuit voltage drop to no more than 3% and total feeder-plus-branch drop to no more than 5%; these are recommendations, not mandatory code requirements, but they are the practical design target for most installations and are commonly enforced by inspectors as good practice.

Worked Examples

Example 1: 12 AWG copper, 20A, 100ft, single-phase 120V

V_drop = (2 × 100 × 20 × 1.588) ÷ 1000 = 6.35V. %VD = 6.35 ÷ 120 × 100 = 5.29%. Above the 3% Informational Note target for branch circuits.

Example 2: 10 AWG copper, 30A, 75ft, single-phase 120V

V_drop = (2 × 75 × 30 × 0.999) ÷ 1000 = 4.50V. %VD = 4.50 ÷ 120 × 100 = 3.75%. Above the 3% target at 120V.

Example 3: Same 10 AWG, 30A, 75ft on 240V

%VD = 4.50 ÷ 240 × 100 = 1.87%. The drop in volts is unchanged, but 3% of 240V is 7.2V of headroom instead of 3.6V, so the same run fits inside the Informational Note target at the higher source voltage.

Example 4: 4 AWG copper, 60A, 150ft, three-phase 480V (line-to-line)

V_drop = (√3 × 150 × 60 × 0.249) ÷ 1000 = 3.88V. %VD = 3.88 ÷ 480 × 100 = 0.81%. Using the single-phase formula (factor of 2) on this same run would give 4.48V and about 0.93%, overstating the drop by ~15%.

Common Mistakes

Using the two-wire single-phase formula (factor of 2) on a three-phase circuit. Three-phase uses √3, not 2, and the error is ~15% oversized.
Comparing the percentage against 120V when the circuit is actually 240V or 480V. Always divide by the real source voltage.
Treating the 3% and 5% figures as hard NEC violations. They are NEC 210.19 and 215.2 Informational Notes, not enforceable code sections. They are the practical design target and the number most inspectors expect to see, but a 3.2% drop is not automatically a code failure.
Using the 5% feeder-plus-branch total as the branch-circuit target on its own. Branch circuits target 3%; the 5% figure is the combined feeder and branch.
Forgetting that R in the formula is resistance per 1,000 feet, not total resistance, which is why the formula divides by 1,000.

Try the Calculator

Use the interactive Voltage Drop Calculator for instant results with any values. Every result page shows the formula applied with your specific numbers.

All Formulas

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This is a formula reference page for educational use. Always consult a licensed electrician and verify compliance with the National Electrical Code (NEC) and local electrical codes before applying any of these formulas to real installations.

Standards & References

This page cites the following electrical codes and standards. Always consult the current edition of your local adopted standard for authoritative requirements.

NEC 210.19(A) Informational Note 4. Branch-circuit conductors sized to prevent a voltage drop exceeding 3% at the farthest outlet. Combined with feeders, total voltage drop should not exceed 5%.
National Electrical Code (NFPA 70), Article 210, Branch Circuits. Reference →
NEC 215.2(A)(1) Informational Note 2. Feeder conductors sized to prevent a voltage drop exceeding 3%. Total branch + feeder drop should not exceed 5%.
National Electrical Code (NFPA 70), Article 215, Feeders. Reference →
NEC Table 310.16. Allowable ampacities of insulated conductors rated up to 2000V, 60°C through 90°C, not more than three current-carrying conductors in raceway or cable.
National Electrical Code (NFPA 70), Article 310, Conductors for General Wiring. Reference →

Disclaimer: The information on this page is provided for reference. Always consult a licensed electrician and the current edition of your local adopted electrical code before performing electrical work.