Voltage Drop Calculator

Calculate voltage drop in an AC or DC circuit given wire gauge, voltage, current, and length. You can also determine the correct conductor size and length for a circuit given an allowable voltage drop.

How to Calculate Voltage Drop

Voltage drop is the amount of voltage lost in a circuit due to resistance of the conductor. Voltage drop is an important consideration when planning a circuit to allow equipment using the circuit to run as designed.

Voltage drop in a circuit means less voltage is delivered to connected devices. Electrical devices consume power, and when they get reduced voltages, the current flow increases to meet their power needs. This current increase can overheat the circuit, causing damage to the equipment and devices.

Using Ohm’s Law, the voltage can be calculated by multiplying the current by the resistance.

V_(V) = I_(A) × R_(Ω)

Ohm’s Law states that the voltage is equal to the current times the resistance. You can find the resistance for various conductor sizes in the chart below, or use one of the following voltage drop formulas.

Voltage Drop Formula

Thus, you can calculate voltage drop for single-phase AC and DC circuits using the following formula derived from Ohm’s Law:^[1]

V_{drop (V)} = I_(A) × 2 × ρ_(Ω·m) × L_(m) / A_m²

Where:
V = allowable voltage drop in volts
I = current in amps
ρ = conductor resistivity in ohm-meters (Ω·m)
L = conductor length in meters
A = conductor cross-sectional area in square meters

So, the voltage dropped V in volts is equal to the current I in amps times 2 times the conductor resistivity ρ times the conductor length L in meters, divided by the cross-sectional area of the conductor A in square meters.

The resistivity of copper conductors is 1.7241 × 10^-8 Ω·m and the resistivity of aluminum conductors is 2.6548 × 10^-8 Ω·m.

Alternate Voltage Drop Formula

You may also see voltage drop calculated using an alternate formula, which calculates the conductor resistance in a slightly different way:^[2]

V_{drop (V)} = I_(A) × 2 × K × L_(m) / A_mm²

Where:
V = allowable voltage drop in volts
K = direct current constant – use 12.9 for copper conductors and 21.2 for aluminum conductors. This is equal to the resistance of a conductor that is one thousand circular mils and one thousand feet in length.
I = current in amps
L = conductor length in meters
A = conductor cross-sectional area in square millimeters

Voltage Drop Formula for Three-Phase Systems

The formula to calculate voltage drop in three-phase systems is

V_{drop (V)} = I_(A) × √3 × ρ_(Ω·m) × L_(m) / A_m²

In a three-phase system, the voltage dropped V in volts is equal to the current I in amps times the square root of 3 times the conductor resistivity ρ times the conductor length L in meters, divided by the cross-sectional area of the conductor A in square meters.

How to Calculate the Minimum Conductor Size

Depending on the application, it is important to use conductors of the proper cross-sectional area for economical and reliable power delivery. A large conductor would be a waste of money, and an undersized conductor might not be able to handle the required current flows.

Using the equation for voltage drop and rearranging the variables, the minimum conductor size in square meters for a circuit can be found using the following:

A_(m²) = 2 × ρ_(Ω·m) × L_(m) × I_(A) / V_{drop (V)}

Where:
A = cross-sectional area in square meters
ρ = conductor resistivity in ohm-meters (Ω·m)
L = length in meters
I = current in amps
V = allowable voltage drop in volts

The minimum cross-sectional area A for a conductor in square meters is equal to the product of two, the conductor resistivity ρ in Ω·m, its length L in meters, and the current I in amps, divided by the maximum allowable voltage drop V in volts.

You can multiply the resulting cross-sectional area by 1,000,000 to calculate the area in square millimeters. Then, use our wire size calculator to find the wire gauge with the correct cross-sectional area.

How to Calculate the Maximum Conductor Length

It is essential to use conductors of proper lengths to ensure minimal voltage drop in the conductive element. A longer conductor means the current must travel a longer distance through the conductive material and against more resistance.

This increase in resistance produces more voltage drops across the length of the circuit and causes it to overheat.

The maximum length of a conductor in a circuit can be determined by re-writing the formula for voltage drop like this:

L_(m) = V_{drop (V)} × A_m² / 2 × ρ_(Ω·m) × I_(A)

Where:
V = allowable voltage drop in volts
I = current in amps
ρ = conductor resistivity in ohm-meters (Ω·m)
L = conductor length in meters
A = conductor cross-sectional area in square meters

The maximum conductor length is equal to the maximum allowable voltage drop V in volts times the cross-sectional area of the conductor in square meters, divided by 2 times the conductor resistivity ρ in Ω·m times the current I in amps.

Conductor Size and Resistance Table

Also check out our electricity cost calculator to see how much it will cost to power a device.