Three-Phase Voltage Unbalance Calculator
Percentage voltage unbalance from the three line-to-line voltages, as used for motor derating. With the formula, a worked example and typical values.
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
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About this calculator
This page calculates average line voltage and voltage unbalance from line voltage Vab, line voltage Vbc and line voltage Vca. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
A small voltage unbalance causes a much larger current unbalance in an induction motor. Fix the cause before relying on derating.
Cross-check: 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | ANSI/NEMA MG 1, 2021, Part 14.36.2 |
| Standard review state | Public-scope screened; licensed clause review still pending |
| Scope-screening note | The calculator uses the maximum-deviation-from-average definition published in NEMA MG 1. IEC 60034-26:2026 addresses effects of unbalanced voltages on three-phase cage motors but uses a different analytical context; do not interchange definitions. |
| Cross-check test cases | 6 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; licensed clause-by-clause standard review; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Line voltage Vab | 400 V |
| Line voltage Vbc | 410 V |
| Line voltage Vca | 395 V |
- Average = (400 + 410 + 395) / 3 = 401.67 V
- Largest deviation = 8.33 V
- Unbalance = 8.33 / 401.67 × 100 = 2.075 %
Assumptions
- Line-to-line voltages measured at the motor terminals
- NEMA definition; the IEC method uses symmetrical components and gives slightly different values
A small voltage unbalance causes a much larger current unbalance in an induction motor. Fix the cause before relying on derating.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Line voltage Vab | V | greater than 0 V | |
| Line voltage Vbc | V | greater than 0 V | |
| Line voltage Vca | V | greater than 0 V |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Average line voltage | V | Shown to 1 decimal place | |
| Voltage unbalance (%) | (number) | Shown to 2 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with line voltage vab
| Line voltage Vab (V) | Average line voltage (V) | Voltage unbalance |
|---|---|---|
| 40 | 281.7 | 85.8 |
| 100 | 301.7 | 66.85 |
| 200 | 335 | 40.3 |
| 400 | 401.7 | 2.07 |
| 800 | 535 | 49.53 |
| 1,600 | 801.7 | 99.58 |
| 4,000 | 1,601.7 | 149.74 |
Other inputs are the same as in the worked example above.
Standards and further reading
These are textbook relationships (Ohm's law, series and parallel networks, AC phasors, three-phase quantities). No standard sets the method; standards apply when the result feeds a design, for example cable or protection selection.
Frequently asked questions
What do I need to enter?
Enter line voltage Vab, line voltage Vbc and line voltage Vca. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Line-to-line voltages measured at the motor terminals. NEMA definition; the IEC method uses symmetrical components and gives slightly different values.
Which calculators should I use next?
Common next steps are Motor Full-Load Current and Neutral Current from Unbalanced Load. The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Unbalance Formulas: Voltage and Neutral Current: Three-phase unbalance formulas: percent voltage unbalance
- Induction Motor Formulas: Induction motor formulas for synchronous speed, slip, shaft torque and full-load current
More Electrical Fundamentals calculatorsAll engineering calculatorsThree-Phase Voltage Unbalance in Elecmetric