Unbalanced Voltage Calculator: Formula and Example

An unbalanced voltage calculator estimates three-phase voltage imbalance from the three measured line-to-line voltages. Enter the readings in volts; the calculator returns the average voltage and the percentage imbalance using the maximum-deviation method.

Formula

The calculator uses the maximum-deviation method commonly used to describe three-phase voltage imbalance:

Voltage imbalance (%) = 100 × largest absolute deviation from average voltage ÷ average voltage

• a = measured voltage between phases A and B, in volts (V).
• b = measured voltage between phases B and C, in volts (V).
• c = measured voltage between phases C and A, in volts (V).
• Average voltage = (a + b + c) ÷ 3, in volts.
• Deviation = the absolute difference between a reading and the average, in volts.

“Largest absolute deviation” means the greatest of the three distances from the average, whether a particular reading is above or below it. The percentage compares that deviation with the average, so the result is dimensionless. Use three readings of the same type: all line-to-line or all line-to-neutral, not a mixture.

Worked Example

Using the calculator’s default readings, AB = 400 V, BC = 398 V, and CA = 402 V:

1. Average voltage = (400 + 398 + 402) ÷ 3 = 1,200 ÷ 3 = 400 V.
2. Absolute deviations are |400 − 400| = 0 V, |398 − 400| = 2 V, and |402 − 400| = 2 V.
3. Largest deviation = 2 V.
4. Imbalance = 100 × 2 ÷ 400 = 0.50%.

The calculator therefore reports voltage imbalance of 0.50% and an average line-to-line voltage of 400.00 V.

What Voltage Imbalance Means

A three-phase supply has three alternating voltages intended to have equal magnitudes and to be separated in phase by 120 electrical degrees. Voltage imbalance describes unequal magnitudes among the measured phase voltages. It is not the same as frequency variation, a phase-angle error, or a voltage that is uniformly too high or too low.

For instance, three readings can all be below a system’s nominal voltage yet be closely matched to one another, producing a low imbalance percentage. Conversely, their average can be near nominal while one reading differs noticeably from the other two. The calculator measures the spread relative to the average; it does not judge whether the system voltage is suitable for connected equipment.

Voltage imbalance matters because three-phase motors and other equipment can respond differently to unequal phase voltages. A percentage is a screening measurement, not a complete diagnosis. Operating conditions, equipment design, the measurement location, and the applicable technical requirements all matter when interpreting it.

How to Take and Enter the Readings

Use a suitable, properly rated instrument and follow the equipment and site procedures. Electrical measurements can expose a person to hazardous voltage; do not open energized equipment or attempt measurements unless qualified and authorized to do so. When readings are taken by a qualified person, record the three phase-to-phase values under the operating conditions being assessed.

• Measure each pair once: A–B, B–C, and C–A. The order does not change the calculation.
• Enter values in volts. If the instrument displays kilovolts, convert consistently: 0.4 kV is 400 V.
• Use readings taken at roughly the same time and operating condition. Loads can change voltage.
• Enter actual readings rather than rounded nominal values; excessive rounding can hide a small imbalance.

The inputs permit zero as a mathematical boundary, but zero or near-zero readings are not normal operating measurements for an energized three-phase supply and should not be treated as a meaningful routine result. The calculator also accepts a broad numerical range to accommodate varied systems; it does not validate whether an entered value is plausible for a particular installation.

How to Interpret the Result

The output is the largest deviation as a percentage of the average. A result of 1% means that the most deviant reading is 1% of the calculated average away from it. It does not mean that every phase differs from every other phase by exactly 1%.

There is no single universal pass/fail threshold appropriate for every supply and item of equipment. Compare the measurement with the equipment manufacturer’s instructions, relevant technical standards, and the requirements that apply to the installation. If a reading is unexpected or equipment is behaving abnormally, have a qualified electrical professional investigate rather than relying on this calculation alone.

The average output is useful context for the percentage, but it is not a nominal-voltage test. For example, an average of 400 V may be balanced while still requiring a separate check against the system’s intended voltage and permitted operating range.

Common Mistakes and Calculation Limits

• Mixing voltage types: Do not combine line-to-line readings with line-to-neutral readings. Calculate from three readings made using the same method.
• Using current instead: Current imbalance is a different calculation. Do not enter phase currents into a voltage calculator.
• Comparing against nominal voltage: This formula compares each measured value with the three-reading average, not with a nameplate or nominal value.
• Rounding too early: Keep the instrument’s available precision in the inputs and round the final percentage for reporting.
• Treating the result as a diagnosis: This arithmetic does not identify the cause, assess phase angles, verify instrument accuracy, or establish equipment safety.

The three line-to-line voltages in a real three-phase system are related, but field conditions and measurement uncertainty can affect the readings. This simple calculator treats the values as three independent numbers for the stated formula. It does not calculate symmetrical components or distinguish supply-side problems from wiring, connection, or load-related issues.

Frequently Asked Questions

What is the formula for voltage imbalance?
Find the average of the three measured phase voltages, find each reading’s absolute difference from that average, and divide the largest difference by the average. Multiply by 100 to express the result as a percentage.

Should I use line-to-line or line-to-neutral voltage?
Use three readings of one kind. Line-to-line readings are commonly used for three-phase assessments; if using line-to-neutral readings, use all three phase-to-neutral values and interpret the result in that context.

Is voltage imbalance the same as voltage unbalance?
In everyday electrical discussion, the terms are often used for the same general condition: unequal phase-voltage magnitudes. Formal methods can define unbalance differently, so check the method required by a specific standard or equipment specification.

What percentage of voltage imbalance is acceptable?
There is no one limit that applies to all equipment and installations. Consult the relevant equipment documentation and technical requirements; the calculator provides a value, not a compliance decision.

Can I use this calculator for current imbalance?
No. It calculates voltage imbalance from three voltage readings. Current imbalance uses current readings and should be calculated and interpreted separately.

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in a | Voltage AB | V | 400 | 0 | 1000000
in b | Voltage BC | V | 398 | 0 | 1000000
in c | Voltage CA | V | 402 | 0 | 1000000
out imbalance | Voltage imbalance | % | 100 * max(abs(a - (a + b + c) / 3), max(abs(b - (a + b + c) / 3), abs(c - (a + b + c) / 3))) / ((a + b + c) / 3) | 2
out avg | Average line-to-line voltage | V | (a + b + c) / 3 | 2