The complete formula reference — resistance method, K-factor method, three-phase, and metric — each with a worked example.
Single-phase & DC: Vd = 2 × I × L × R / 1000 · Three-phase: Vd = √3 × I × L × R / 1000
where I is amps, L is one-way feet, and R is Ω per 1000 ft from NEC Chapter 9 Table 8. Example: 12 AWG copper (1.93 Ω/kft), 20 A, 100 ft, 120 V: Vd = 2 × 20 × 100 × 1.93 / 1000 = 7.72 V = 6.4% — a fail that 10 AWG (1.21 Ω/kft → 4.84 V, 4.0%) only partially fixes; this circuit wants 8 AWG or a shorter run.
Vd = 2 × K × I × L / CM · CM is the conductor's circular-mil area; K is the resistance of a 1-foot, 1000-cmil conductor: 12.9 for copper, 21.2 for aluminum (75 °C). Same example: Vd = 2 × 12.9 × 20 × 100 / 6530 = 7.90 V — the small difference versus Table 8 comes from K's rounding. Rearranged for sizing: CM = 2 × K × I × L / Vd, then pick the next larger size from the AWG chart.
Vd = 2 × I × L × R / 1000 with L in meters and R in Ω/km (multiply Ω/kft by 3.281). The gauge converter handles the size translation.
Vd% = Vd / Vsource × 100 · Vload = Vsource − Vd · Power lost as heat: P = Vd × I — see what that costs with the energy loss calculator.
K = 12.9 is a rounded constant; Table 8 lists measured resistance per size. Differences are within a few percent — both are accepted for design, and the next-size-up decision almost never changes.
For AC circuits with reactive loads, effective impedance replaces plain resistance. A practical approximation multiplies R by the power factor, which this site's calculator applies; precise feeder work at large sizes in steel conduit should use NEC Table 9 impedance values.