Three-Phase Voltage Unbalance Calculator

A three-phase voltage unbalance calculation converts three measured line-to-line voltages into one percentage that describes how far the most off-nominal phase-to-phase reading varies from the three-voltage average. The calculator reports Voltage unbalance using Vab, Vbc, and Vca, along with the average line voltage, minimum and maximum measured voltages, and the largest deviation from average.

This value is used during power-quality investigation, motor circuit review, feeder troubleshooting, voltage-drop review, and load-balance checks. A relatively small line-voltage unbalance can produce substantially greater current unbalance in a three-phase motor, increasing winding heating and reducing operating margin. The calculation helps identify whether an observed motor-current problem may originate upstream in the supply, distribution equipment, connections, or unequal loading.

It does not calculate conductor ampacity, AWG or kcmil conductor size, raceway fill, branch-circuit protection, or feeder voltage drop. Those design and code decisions require the applicable installation data, including conductor insulation temperature rating, terminal rating, adjustment factor, correction factor, current-carrying conductor count, equipment listing, and AHJ requirements.

Measured Line-to-Line Voltages

Enter the three measured phase-to-phase voltages:

Calculator field	Electrical measurement
Vab	Voltage measured from phase A to phase B
Vbc	Voltage measured from phase B to phase C
Vca	Voltage measured from phase C to phase A
Nominal system voltage	System nameplate or design voltage recorded for context
Entered reference unbalance	Optional project, equipment, or procedure reference percentage
Measurement label	Location and operating condition, such as Panel P1 / Load on

Vab, Vbc, and Vca should be taken at the same electrical location and under the same load condition. A measurement label such as Panel P1 / Load on preserves the operating context, which is critical when comparing readings taken before and after load changes, equipment shutdown, or corrective work.

Nominal system voltage is not used to establish the average line voltage or the voltage-unbalance percentage. It provides system context—for example, confirming that readings were taken on a nominal 480 V system rather than a nominal 208 V or 240 V system.

Unbalance Formula

The calculator first finds the arithmetic average of the three measured line-to-line voltages:

\(\displaystyle V_{\text{avg}}=\frac{V_{ab}+V_{bc}+V_{ca}}{3}\)

It then calculates the absolute deviation of each voltage from that average:

\(\displaystyle D_{ab}=|V_{ab}-V_{\text{avg}}|\)

\(\displaystyle D_{bc}=|V_{bc}-V_{\text{avg}}|\)

\(\displaystyle D_{ca}=|V_{ca}-V_{\text{avg}}|\)

The Maximum deviation is the largest of those three deviations:

\(\displaystyle D_{\text{max}}=\max(D_{ab},D_{bc},D_{ca}\)

The reported Voltage unbalance is:

\(\displaystyle \text{Voltage unbalance (\%)}= \frac{D_{\text{max}}}{V_{\text{avg}}}\times100\)

This is an average-deviation method based on the three measured line-to-line voltages. It is not a phase-to-neutral voltage calculation and does not perform a symmetrical-components analysis.

Calculation Example

For a measurement labeled Panel P1 / Load on, enter:

Input	Value
Vab	480 V
Vbc	476 V
Vca	482 V
Nominal system voltage	480 V
Entered reference unbalance	0%

The average line voltage is:

\(\displaystyle V_{\text{avg}}=\frac{480+476+482}{3}=479.3333\text{ V}\)

The deviations from average are:

\(\displaystyle |480-479.3333|=0.6667\text{ V}\)

\(\displaystyle |476-479.3333|=3.3333\text{ V}\)

\(\displaystyle |482-479.3333|=2.6667\text{ V}\)

The largest deviation is 3.3333 V, occurring on Vbc. The voltage-unbalance result is:

\(\displaystyle \frac{3.3333}{479.3333}\times100=0.6954\%\)

The calculator output is therefore:

Result	Value
Average line voltage	479.3333 V
Minimum line voltage	476 V
Maximum line voltage	482 V
Maximum deviation	3.3333 V
Voltage unbalance	0.6954%
Margin vs entered reference	0%

With an Entered reference unbalance of 0%, the result displays a 0% margin. Enter a project, equipment, or maintenance-procedure reference when a documented comparison value is required.

Motor and Feeder Review

Voltage unbalance is commonly checked when a three-phase motor has unequal phase currents, elevated winding temperature, nuisance overload operation, inconsistent torque, or a current pattern that does not align with the connected mechanical load.

A 480 V motor feeder can have adequate conductor ampacity and acceptable calculated voltage drop yet still show phase-to-phase voltage imbalance at the motor terminals. Possible field causes may include unequal single-phase loading, high-resistance terminations, deteriorated disconnect or breaker contacts, transformer issues, utility-supply variation, or a defective conductor or splice. The voltage readings identify the electrical symptom; they do not identify the failed component by themselves.

For a useful comparison, record the same three voltages at more than one point when the work scope permits:

• Service or secondary distribution location
• Panelboard or switchboard supplying the feeder
• Motor controller, VFD input, or disconnect line side
• Motor disconnect load side or motor terminals, as appropriate for the equipment and safe work method

A materially different result between locations can help isolate whether the condition is supply-side, feeder-related, or associated with a connection or piece of distribution equipment. Measurements must be made using appropriate test equipment and safe electrical work practices.

Field Verification Limits

The calculator uses the three values entered for Vab, Vbc, and Vca. It cannot determine whether readings were taken simultaneously, whether the load was stable, whether a VFD output is suitable for the meter and measurement method used, or whether the source waveform contains harmonics or other power-quality distortion.

For an energized system, verify the following separately:

• Measure at a consistent load state; cycling loads can materially change the three readings
• Confirm phase identification so Vab, Vbc, and Vca represent the intended phase pairs
• Compare measured voltage unbalance with the motor manufacturer’s published operating limits and the applicable project or maintenance criteria
• Investigate current unbalance, connection condition, load distribution, and voltage-drop conditions rather than relying on voltage percentage alone
• Apply site safety procedures, equipment instructions, and AHJ-enforced requirements for all energized testing and corrective work