The voltage drop formula, explained

Every conductor has resistance, so every loaded circuit delivers less voltage at the far end than at the panel. Voltage drop is that loss. Too much of it dims lights, slows motor starts, overheats motors that compensate by drawing more current, and trips sensitive electronics. The standard screening formula for a single-phase or DC circuit is:

VD = 2 × K × I × L / CM

• VD — voltage drop, volts
• K — conductor constant: ≈ 12.9 Ω·cmil/ft for copper, ≈ 21.2 for aluminum (75°C values)
• I — load current, amps
• L — one-way circuit length, feet (the 2 supplies the return path)
• CM — conductor area in circular mils (12 AWG = 6,530; 10 AWG = 10,380; 8 AWG = 16,510)

For balanced three-phase circuits the multiplier drops from 2 to √3 ≈ 1.732, because the return currents partially cancel:

VD(3φ) = 1.732 × K × I × L / CM

The voltage drop calculator runs exactly this math for copper and aluminum, single- and three-phase, and can derive the current from a load kVA instead of amps.

What the NEC actually says about 3%

The widely quoted "3% rule" comes from Informational Notes to NEC 210.19(A) (branch circuits) and 215.2(A) (feeders): keep the drop to about 3% on the branch circuit or feeder, and 5% total from service to the farthest outlet, for "reasonable efficiency of operation." Informational Notes are advisory — they are not enforceable code text. Two caveats keep this from being a free pass:

• Some articles make voltage-drop limits mandatory — fire pumps (Art. 695) and sensitive-electronics circuits (Art. 647) among them — and some jurisdictions adopt the 3%/5% guidance as a local amendment.
• The load still has to work. Motors, EV chargers, and long LED runs have their own tolerance for low voltage regardless of what the inspector enforces.

Treat 3%/5% as the design target it was meant to be: cheap insurance that the load sees usable voltage on the worst day.

Worked example — 20 A at 120 V, 100 ft out

A 20 A load on a 120 V branch circuit, 100 ft one-way, on 12 AWG copper (CM = 6,530):

VD = 2 × 12.9 × 20 × 100 / 6,530 = 7.9 V → 6.6%

That fails the 3% target badly — the load would see about 112 V. Upsizing one gauge to 10 AWG (CM = 10,380):

VD = 2 × 12.9 × 20 × 100 / 10,380 = 5.0 V → 4.1%

Still above 3%. One more step to 8 AWG (CM = 16,510):

VD = 2 × 12.9 × 20 × 100 / 16,510 = 3.1 V → 2.6%

So this run wants 8 AWG copper even though 12 AWG satisfies ampacity for a 20 A circuit. That is the general pattern: ampacity sets the floor; distance sets the wire. At 240 V the same load and run would drop the same 3.1 V but only 1.3% — doubling the voltage halves the percentage, which is why long runs favor higher-voltage circuits.

Notes on accuracy

• The K·CM screen uses DC resistance at 75°C. For large conductors (≈ 4/0 and up), power factor and reactance matter; the effective-Z method of NEC Chapter 9 Table 9 is the better model there.
• Conductor temperature moves resistance about 0.4%/°C for copper — a cool basement run drops slightly less than the screen says, a hot attic slightly more.
• Use the actual circuit length including vertical runs, not the straight-line distance on the plan.

For the code-adjacent companions, see the NEC-style voltage drop calculator, the conduit fill calculator for raceway sizing of the upsized conductors, and the transformer kVA calculator when the feeder starts at a transformer instead of a panel.

Frequently asked questions

What is the voltage drop formula for single-phase circuits?

VD = 2 × K × I × L / CM, where K is the conductor constant (≈12.9 Ω·cmil/ft for copper, ≈21.2 for aluminum at 75°C), I is load current in amps, L is the one-way run length in feet, and CM is the wire size in circular mils. The 2 accounts for the out-and-back loop; balanced three-phase uses √3 instead of 2.

Is the NEC 3% voltage drop a requirement?

Generally no — it is guidance. NEC 210.19(A) and 215.2(A) carry Informational Notes recommending ≤3% on a branch circuit or feeder and ≤5% combined. Informational Notes are not enforceable rules, though specific articles (e.g., fire pumps, sensitive-electronics circuits) and some local amendments do make voltage-drop limits mandatory.

Does voltage drop change wire ampacity?

No. Ampacity (NEC 310.16 and adjustment factors) protects the insulation from heat and is a hard requirement. Voltage drop protects the load from low voltage and usually drives wire size only on long runs. Size for ampacity first, then upsize for voltage drop if the run is long.

How much does upsizing one wire gauge help?

Each AWG step changes the circular-mil area by about 26%, so voltage drop falls roughly 21% per single gauge upsize, and two steps cut it nearly in half. That is why the fix for a failing run is rarely more than one or two sizes.