Wire Size Selection Formula

Choosing the right wire gauge means satisfying two independent constraints at the same time: NEC branch-circuit ampacity (so the wire does not overheat) and voltage drop (so the load actually sees its rated voltage after a long run). At short distances ampacity usually decides the gauge; at long distances voltage drop forces an upsize. This page walks through the four-step process and shows worked examples for copper, aluminum, 120V, and 240V circuits.

Formulas

Step 1: NEC branch-circuit OCP ≥ circuit amps (from NEC 310.16 with the 240.4(D) small-conductor cap)

Step 2: V_drop = (2 × L × I × R) ÷ 1000 (single-phase / DC); use √3 instead of 2 for three-phase

Step 3: %VD = V_drop ÷ V_source × 100 ≤ maximum allowable drop (default 3% for branch circuits)

Step 4: If a gauge fails Step 1 or Step 3, move to the next larger gauge and retry

Wire sizing means finding the smallest gauge that satisfies two independent constraints: NEC branch-circuit ampacity AND voltage drop. Neither one alone is sufficient. The inputs are current (amps), one-way run length (feet), source voltage, conductor material (copper or aluminum), and the allowable drop percentage (NEC recommends 3% for branch circuits, 5% for feeder plus branch combined). Short runs are usually limited by ampacity; long runs are usually limited by voltage drop. Higher source voltage does not change the drop in volts, but it raises the allowable drop in volts for a given percentage, so the same gauge often works on 240V where it fails on 120V. Aluminum has roughly 1.6× the resistance per foot of copper and a lower ampacity per gauge, so aluminum always ends up one to two gauge sizes larger than copper for the same load. The calculator on the hub page runs this four-step process against real NEC 310.16 values and the 240.4(D) small-conductor caps for both copper and aluminum.

Worked Examples

Example 1: 30A copper at 50ft on 120V, 3% max

Step 1: 10 AWG Cu branch OCP = 30A ≥ 30A ✓ (240.4(D) cap, not the 35A 75°C table value). Step 2: VD = (2 × 50 × 30 × 0.999) ÷ 1000 = 3.00V. Step 3: 3.00 ÷ 120 = 2.5% ≤ 3% ✓. 10 AWG copper works.

Example 2: 30A copper at 150ft on 120V, 3% max

Step 1: 10 AWG OCP 30A ≥ 30A ✓. Step 2: VD = (2 × 150 × 30 × 0.999) ÷ 1000 = 8.99V. Step 3: 8.99 ÷ 120 = 7.5% > 3% ✗. 8 AWG: 5.65V = 4.7% ✗. 6 AWG copper: 3.56V = 2.96% ✓. Voltage drop, not ampacity, drove the upsize.

Example 3: 20A copper at 100ft on 240V, 3% max

Step 1: 12 AWG Cu branch OCP = 20A ≥ 20A ✓ (the ampacity check passes before voltage drop is even considered). Step 2: VD = (2 × 100 × 20 × 1.588) ÷ 1000 = 6.35V. Step 3: 6.35 ÷ 240 = 2.65% ≤ 3% ✓. 12 AWG works on 240V. On 120V the same run would fail Step 3 at 5.29%, forcing an upsize to 10 AWG.

Example 4: 30A aluminum at 100ft on 120V, 3% max

Step 1: 10 AWG Al branch OCP = 25A < 30A ✗ (plus small Al conductors are not recommended for residential branches). 8 AWG Al OCP = 40A ≥ 30A ✓. Step 2: VD = (2 × 100 × 30 × 1.02) ÷ 1000 = 6.12V. Step 3: 6.12 ÷ 120 = 5.1% > 3% ✗. Step through: 6 AWG Al = 3.85V (3.2%) ✗. 4 AWG aluminum: 2.42V = 2.02% ✓. Aluminum lands two gauge sizes larger than the 6 AWG copper that would solve the same run.

Common Mistakes

Sizing for ampacity only and ignoring voltage drop. This is the number-one mistake on long runs.
Using the raw 75°C ampacity column (14 AWG = 20A, 12 AWG = 25A, 10 AWG = 35A) for branch-circuit OCP. NEC 240.4(D) caps those at 15A, 20A, and 30A for copper regardless of the table value.
Picking the wrong ampacity column for the installation context. The correct column is set by the lowest-rated component in the circuit (terminal lug, splice, or wire insulation), not the wire insulation alone. NM-B cable is further limited to the 60°C column under NEC 334.80 even though its conductors are 90°C rated.
Applying the copper resistance and ampacity values to aluminum conductors. Aluminum uses its own NEC 310.16 column and resistance table; a 10 AWG aluminum conductor is not equivalent to a 10 AWG copper conductor.
Forgetting the factor of 2 in the single-phase voltage-drop formula (it accounts for the round trip), or using that factor on a three-phase circuit. Three-phase uses √3 instead of 2.

Try the Calculator

Use the interactive Wire Size 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 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 →
NEC 240.4(D). Small conductor rule: overcurrent protection shall not exceed 15A for 14 AWG, 20A for 12 AWG, and 30A for 10 AWG copper, regardless of ampacity table values.
National Electrical Code (NFPA 70), Article 240, Overcurrent Protection. Reference →
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 →
IEC 60364. Low-voltage electrical installations. The international counterpart to the NEC, covering voltages up to 1000V AC / 1500V DC in residential, commercial, and industrial installations.
International Electrotechnical Commission. Reference →
UL 83. Underwriters Laboratories standard for thermoplastic-insulated wires and cables (THHN, THWN, MTW). Defines insulation temperature ratings, voltage ratings, and the safety testing that justifies the NEC ampacity tables.
Underwriters Laboratories. Reference →
ASTM B3. Standard specification for soft or annealed copper wire. Defines the physical properties (resistivity, tensile strength, elongation) that set the resistance-per-1000ft values used in voltage drop and ampacity calculations.
ASTM International. 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.