Electrical Engineering

Voltage Drop Calculator

Calculate voltage drop across a conductor run from current, length, cross-sectional area and material.

Formula Vdrop = 2 × I × ρ × L / AReviewed Sep 8, 2026

Voltage drop is the reduction in voltage a conductor produces as current flows through its resistance. Long conductor runs, high currents, or an undersized wire can drop enough voltage to dim lights, overheat equipment, or trip protection needlessly. Enter the load current, one-way conductor length, cross-sectional area and material to calculate the voltage drop and see how it compares to the NEC's recommended limits.

Calculation Bench

Circuit Type

Conductor Material

01Current

I · Load current carried by the conductor.

02Length

L · One-way conductor run length, from source to load.

03Cross-Sectional Area

A · Cross-sectional area of the conductor.

04Supply Voltage

V · The circuit's nominal supply voltage, used to express the drop as a percentage.

Solution

Enter the required values to calculate voltage drop.

Vdrop = 2 × I × ρ × L / A

Formula Sheet

V_{drop} = \dfrac{2 I \rho L}{A}

V_{drop} = \dfrac{\sqrt{3}\, I \rho L}{A}

VdropVoltage Drop
ICurrent
ρResistivity
LLength
ACross-Sectional Area
VSupply Voltage

Variables & Units

Symbol	Variable	Description	Common Units
Vdrop	Voltage Drop	Voltage lost across the conductor run due to its resistance.	V
I	Current	Load current carried by the conductor.	A, mA
ρ	Resistivity	Electrical resistivity of the conductor material - fixed by your Material selection, not user-editable.
L	Length	One-way conductor run length, from source to load.	m, ft
A	Cross-Sectional Area	Cross-sectional area of the conductor.	mm², kcmil, in²
V	Supply Voltage	The circuit's nominal supply voltage, used to express the drop as a percentage.	V, mV, kV

How to Use This Calculator

01Select the circuit type - Single-Phase / DC or Three-Phase.
02Select the conductor material - Copper or Aluminum.
03Enter the load Current, the one-way conductor Length, and the conductor's Cross-Sectional Area.
04If you only know an AWG or kcmil wire size, convert it to conductor area from a wire table or use the Wire Gauge Calculator first, then return here to check the actual voltage drop.
05Enter the circuit's Supply Voltage so the calculator can show the drop as a percentage.
06Select Calculate to see the voltage drop and how it compares to the NEC's 3%/5% recommended design limits. Treat that as an efficiency screen, not an ampacity or breaker approval.

How the Formula Works

A real conductor has resistance, so some of the supply voltage is lost pushing current through the wire itself rather than reaching the load: Vdrop = k × I × ρ × L / A, where ρ is the material's resistivity, L is the one-way run length, A is the conductor's cross-sectional area, and k accounts for the return path - 2 for a single-phase or DC circuit, since current travels out and back through two conductors, or √3 for a three-phase circuit, whose three-conductor geometry reduces the effective voltage drop compared to a single-phase run of the same length and load.

Because voltage drop scales directly with length and inversely with cross-sectional area, the two most effective ways to reduce it are shortening the run or using a larger-gauge (larger cross-section) conductor. Doubling the wire's cross-sectional area halves the voltage drop for the same current and length.

Worked Example 01

Single-phase branch circuit, copper

Known

Current (I): 10 A
Length (L): 50 m
Cross-Sectional Area (A): 2.5 mm²
Material: Copper
Supply Voltage: 240 V

Formula

Vdrop = 2 × I × ρ × L / A

Substitution

Vdrop = (2 × 10 × 1.7241×10⁻⁸ × 50) / (2.5×10⁻⁶)

Result

Vdrop ≈ 6.90 V (≈ 2.87% - within the 3% recommended limit)

A 10 A load on a 50 m run of 2.5 mm² copper wire drops about 6.9 V, roughly 2.9% of a 240 V supply - within the NEC's 3% recommendation for a single branch circuit or feeder.

Worked Example 02

Three-phase feeder, aluminum

Known

Current (I): 15 A
Length (L): 40 m
Cross-Sectional Area (A): 4 mm²
Material: Aluminum
Supply Voltage: 208 V

Formula

Vdrop = √3 × I × ρ × L / A

Substitution

Vdrop = (√3 × 15 × 2.826×10⁻⁸ × 40) / (4×10⁻⁶)

Result

Vdrop ≈ 7.34 V (≈ 3.53% - exceeds the 3% single-circuit recommendation)

The same run distance in aluminum instead of copper, on a three-phase 208 V feeder, drops about 7.3 V - around 3.5% of the supply, over the NEC's 3% guideline for a single feeder, suggesting a larger conductor would be worth considering.

Applications

01Sizing branch-circuit and feeder conductors for long runs
02Checking whether an existing wire size keeps voltage drop within NEC-recommended limits
03Comparing copper vs aluminum conductors for the same run

Assumptions

01The conductor is a single, continuous run of uniform cross-section and material.
02Resistivity is evaluated at 20°C - resistance rises somewhat at higher operating temperatures.
03The load is treated as a simple resistive draw at the stated current; reactive (inductive/capacitive) effects on impedance are not modeled.

Where This Model Stops

01Does not model conductor reactance - for long high-frequency AC runs, impedance (not just DC resistance) affects the true voltage drop.
02Does not account for temperature derating of resistivity at elevated conductor operating temperatures.
03Does not select wire ampacity, insulation temperature rating, conduit fill, terminal rating, breaker size, or parallel conductor sets.
04This calculator provides a reference voltage-drop estimate only - actual conductor sizing must follow the applicable electrical code (e.g. NEC ampacity tables) and, for anything beyond a simple branch circuit, a qualified electrician or electrical engineer.

References

[1]
Voltage drop formula and NEC 3%/5% recommended limits
National Electrical Code (NEC) Informational Note, standard electrical engineering references
Vdrop = k × I × ρ × L / A, with k = 2 (single-phase/DC) or √3 (three-phase).
[2]
Copper and aluminum conductor resistivity
IACS (International Annealed Copper Standard); standard electrical engineering references
Copper: 1.7241×10⁻⁸ Ω·m at 100% IACS. Aluminum: 2.826×10⁻⁸ Ω·m at 61% IACS (EC-grade, alloy 1350 - the standard grade for aluminum building wire). Both at 20°C.

Frequently Asked Questions

What's the difference between single-phase and three-phase voltage drop?

Three-phase circuits use √3 (≈1.732) instead of 2 in the formula, because the three-conductor phase geometry reduces the effective voltage drop compared to a single-phase run carrying the same current over the same length and conductor.

Is exceeding the NEC's 3% or 5% guideline actually a code violation?

Not on its own. The 3%/5% figures come from an NEC Informational Note recommending "reasonable efficiency of operation" - they are not an enforceable requirement in the base code, though some local jurisdictions (AHJs) adopt them as mandatory amendments. Always check your local code.

Why does conductor material matter so much?

Aluminum's resistivity is roughly 1.6 times copper's, so an aluminum conductor needs a proportionally larger cross-section than copper to achieve the same voltage drop over the same run.

Should length be one-way distance or round-trip wire length?

Enter the one-way distance from source to load. The formula multiplier handles the return path: 2 for single-phase or DC circuits, and √3 for three-phase circuits.

How is this different from the Wire Gauge Calculator?

This page checks voltage drop for a known conductor area and run length. The Wire Gauge Calculator is the better starting point when you need to select a conductor size from current, safety factor, and ampacity-style constraints.

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