What is the voltage drop formula?

For DC and single-phase AC, voltage drop = 2 × I × R × cosφ, where I is current, R is the one-way conductor resistance and cosφ is the power factor (1 for DC). The 2 accounts for the current travelling out and back. For three-phase, the factor is the square root of 3 instead of 2: voltage drop = √3 × I × R × cosφ.

How much voltage drop is acceptable?

A common rule of thumb is to keep voltage drop at or below 3% for the run that feeds a load, and up to 5% total once you include the path before it. Tighten to 1–2% for critical or high-current circuits, and you can allow more on non-critical loads like lighting. These are guidelines, not legal limits.

Why is the distance doubled in the calculation?

Current has to flow out to the load and back to the source, so it passes through twice the one-way length of conductor. That round trip is why the DC and single-phase formula multiplies by 2. Enter the one-way distance and the calculator doubles it for you — forgetting this is the most common voltage-drop mistake.

What is the voltage drop on 12-gauge wire?

12 AWG copper is about 1.59 Ω per 1000 ft, so a 50 ft one-way run carrying 15 A drops roughly 2 × 15 × (0.00159 × 50) = 2.4 V. On a 120 V circuit that is about 2%, comfortably under a 3% target; on a 12 V circuit the same 2.4 V is 20%, far too much — which is why low-voltage DC needs much thicker wire.

Does voltage drop differ for DC, single-phase and three-phase?

Yes. DC and single-phase AC use a factor of 2 for the round-trip conductors, while three-phase uses the square root of 3 (about 1.732) because the line-to-line relationship differs. For the same current and wire, a three-phase run drops less than a single-phase one. AC also applies the power factor.

Voltage Drop Calculator (DC, 1φ & 3φ, wire size)

Pre-calculated runs you can open and tweak — each loads this calculator with the scenario set.

Voltage drop formula

Voltage drop is simply the current multiplied by the conductor's resistance, with a factor for the circuit type. The equations the calculator uses:

DC & single-phase: Vdrop = 2 × I × R_one-way × cosφ
Three-phase: Vdrop = √3 × I × R_one-way × cosφ
% drop = Vdrop ÷ V_source × 100 · V_load = V_source − Vdrop · P_loss = I² × R_total

R_one-way is the resistance of the run in one direction, found from the wire's gauge and material. For DC the power factor cosφ is 1. The conductor resistance is temperature-corrected with R_T = R₂₀(1 + α(T − 20)), where α is 0.00393/°C for copper and 0.00403/°C for aluminum.

DC & 12 V voltage drop

Low-voltage DC is where voltage drop bites hardest, because the drop is measured as a share of a small voltage. Losing 0.36 V is only 0.3% on a 120 V circuit but a full 3% at 12 V. DC systems also pull high current for the same power, which increases the drop further, so 12 V and 24 V runs need surprisingly thick cable. Going from 12 V to 24 V halves the current and roughly quarters the drop — often cheaper than upsizing wire.

Single-phase and three-phase voltage drop

The only difference between the circuit types is the multiplier. DC and single-phase AC use 2, because current flows out and back through two conductors. Three-phase uses √3 (about 1.732) for the line-to-line voltage, so for the same current and wire a three-phase run drops less. AC circuits also include the power factor, which is 1 for purely resistive loads like heaters and lower for motors.

Voltage drop over distance

Resistance is proportional to length, so doubling the run length doubles the loss. That is why a fixed gauge that is fine at 10 ft can be hopeless at 100 ft. The calculator takes the one-way distance and doubles it for the round trip automatically — the step people most often forget when doing it by hand.

You can also work out a quick estimate straight from a small reference table. The figures below are the volts lost over a fixed copper run at a sample 10 A; the relationship is linear, so scale them for your own case — double the current or double the length and the drop doubles. To browse a full matrix by gauge and current, or the maximum run length for a target, see the voltage drop chart.

Volts dropped over a one-way copper run at 10 A (DC / single-phase, round trip, 20 °C).
Gauge	Ω / 1000 ft	Drop per 100 ft	Drop per 100 m
4 AWG	0.248	0.50 V	1.63 V
6 AWG	0.395	0.79 V	2.59 V
8 AWG	0.628	1.26 V	4.12 V
10 AWG	0.999	2.00 V	6.55 V
12 AWG	1.588	3.18 V	10.42 V
14 AWG	2.525	5.05 V	16.57 V

For aluminum, multiply the drop by about 1.6; for three-phase, by √3÷2 (about 0.87). The calculator above does the exact calculation for any current, length and material.

What wire size do I need? (3% / 5% rule of thumb)

Rather than guessing a gauge and checking, the reverse helper finds the smallest wire that keeps the drop within a target. A widely used rule of thumb is 3% for the circuit feeding a load and up to 5% overall; tighten to 1–2% on critical or high-current runs. These are planning guidelines, not legal limits, so adjust them to your application. For the full conductor specs behind the recommendation, see the AWG wire size chart.

Voltage drop across a resistor

“Voltage drop” has a second, component-level meaning too: the voltage developed across a resistor (or any component) as current flows through it. That one is pure Ohm's law — V = I × R — not a cable-length question. To determine the drop across a resistor, multiply the current through it by its resistance, so 20 mA through 150 Ω drops 0.02 × 150 = 3 V. To size a resistor for a target drop instead — a series resistor for an LED, say — rearrange to R = V ÷ I and calculate the resistance you need. The Ohm's Law Calculator works out either direction.

Voltage Drop Calculator

Worked examples