Electrical Wire Gauge & Voltage Drop Calculator (NEC)
Calculate conductor voltage drop percentage, terminal voltage, and minimum copper/aluminum AWG wire size compliant with NEC 3% branch circuit limits.
Parameters & Inversions
Deterministic EngineCalculated Output Metrics
Analytical Proof & Invariants
Machine PrecisionVoltage Drop = (2 × K × I × L) / Circular Mils (Single Phase) | Max NEC Drop ≤ 3.0%
Step-by-Step Mathematical Derivation
Copper resistivity constant K = 12.9 ohms-cmil/ft at 75°C. Aluminum K = 21.2 ohms-cmil/ft.
NEC Informational Note 210.19(A) recommends max 3.0% voltage drop on branch circuits (7.20V on a 240V circuit).
Circular Mils = (2 × K × I × L) / V_drop_allowed. For 40A over 125 ft at 3% (7.2V): (2 × 12.9 × 40 × 125) / 7.2 = 17,916 cmil.
#8 AWG = 16,510 cmil (too small, yields 3.25% drop). #6 AWG = 26,240 cmil (compliant, yields 2.05% drop).
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