Calculate Line Voltage
For balanced star and delta three-phase systems.
Example Data Table
| Phase voltage | Connection | Formula | Line voltage |
|---|---|---|---|
| 120 V | Star (Wye) | 120 × √3 | 207.85 V |
| 230 V | Star (Wye) | 230 × √3 | 398.37 V |
| 415 V | Delta | 415 × 1 | 415.00 V |
| 0.415 kV | Star (Wye) | 0.415 × √3 | 0.719 kV |
Formula Used
Balanced star (wye) connection: VL = √3 × VPh
Balanced delta connection: VL = VPh
VL means line voltage. VPh means phase voltage. The star multiplier is √3, or approximately 1.7320508. Delta windings connect directly across line pairs, so both voltage magnitudes are equal.
How to Use This Calculator
- Enter the known phase voltage.
- Select the unit used by the source value.
- Choose star or delta from the system connection.
- Choose the preferred result unit and decimal precision.
- Select Calculate Line Voltage.
- Review the formula, multiplier, and voltage values before use.
Phase and Line Voltage in Practice
Understanding Phase and Line Voltage
Three phase systems use related voltages that serve different measurement points. Phase voltage is measured across one winding or from line to neutral. Line voltage is measured between any two supply lines. The values differ in many balanced star systems. That difference matters during installation, testing, and equipment selection. A correct conversion prevents confusion between drawings, labels, and meter readings. This calculator converts a stated phase voltage into line voltage. Clear output helps compare units and review the conversion quickly.
Why the Connection Type Matters
The connection type controls the relationship between these voltage values. In a balanced star connection, each phase is separated by 120 degrees. The line voltage is the phase voltage multiplied by the square root of three. That multiplier is about 1.732. In a balanced delta connection, each phase winding lies directly between two lines. Therefore, phase voltage and line voltage have equal magnitudes. Choose the right connection before calculating any value. Check the diagram and nameplate before work begins.
Common Uses for the Conversion
Electricians and engineers use this conversion when checking motors, panels, transformers, and distribution boards. It helps when a schematic lists phase voltage but a device rating lists line voltage. The calculation is useful for comparing regional supply systems too. Contractors may use it while reviewing technical specifications. Students can use it to understand vector relationships in three phase circuits. The calculator provides a quick check. It does not replace engineering review where fault levels, loading, insulation, or protection settings matter.
Measuring Values Carefully
Start with a reliable source value. Check whether the given value is phase to neutral or phase across a delta winding. Verify the unit before entering the number. Volts, kilovolts, millivolts, and megavolts describe different scales. This page converts every input through volts internally. It then shows a readable line voltage output. Use suitable rated instruments when measuring live circuits. Follow lockout procedures before touching equipment. Record the connection type beside each measurement. Clear notes reduce mistakes in later testing.
Reading the Result
The displayed line voltage is an ideal balanced-system result. For a star system, it should be greater than phase voltage. For a delta system, both values should match. Small differences may appear during real measurements. Meter accuracy, conductor losses, load imbalance, and supply variation can affect readings. Compare all three line to line measurements when diagnosing a live system. Large differences suggest further investigation. Do not assume an imbalance is harmless. The formula alone cannot confirm actual system condition.
Safe Design Decisions
Voltage conversion is only one step in electrical planning. Confirm frequency, current capacity, grounding method, insulation class, and applicable regulations. Choose equipment with voltage ratings that suit the actual line voltage. Consider normal tolerance and possible transient conditions. Never use a calculated value alone to approve an installation. Qualified personnel should inspect high energy systems. Update drawings after modifications. Keep conversion records with test documents. A record helps future maintenance teams. Always verify measurements before energizing any three phase equipment.
Frequently Asked Questions
1. What is phase voltage?
Phase voltage is the voltage across one phase winding. In a star system, it is commonly measured from one line to neutral. In a delta system, it is measured across one winding.
2. What is line voltage?
Line voltage is the voltage measured between any two line conductors in a three-phase supply. Equipment ratings often state this value because loads connect across line pairs.
3. Why does a star connection use square root of three?
Star phase voltages are 120 degrees apart. The vector difference between two phases produces a line voltage magnitude equal to phase voltage multiplied by the square root of three.
4. Does a delta connection change the voltage?
No. In a balanced delta connection, each phase winding connects directly between two supply lines. Therefore, phase voltage and line voltage have the same magnitude.
5. Can this calculator solve unbalanced systems?
No. This tool assumes a balanced three-phase supply. Unbalanced systems need individual voltage measurements and phasor analysis because one fixed multiplier may not describe every line voltage.
6. Can I enter kilovolts or millivolts?
Yes. Select mV, V, kV, or MV before calculating. The calculator converts the input through volts and can display the final line voltage in any listed unit.
7. How many decimal places should I use?
Use the precision supported by your source data. Two or three decimal places suit many estimates. Use more only when the measurement accuracy and engineering application justify it.
8. Can I select equipment from this result?
Use it as a preliminary check only. Equipment selection also needs current, frequency, insulation, fault level, grounding, temperature, and local code requirements.
9. Why are negative voltages not accepted?
This calculator reports voltage magnitude. A negative sign may matter in phasor notation, but magnitude conversion needs a non-negative value. Use phasor analysis for angle-sensitive work.
10. Can this calculator convert line voltage to phase voltage?
Not directly. For a balanced star system, divide line voltage by the square root of three. For a balanced delta system, phase voltage equals line voltage.
11. Does this replace a meter test?
No. The result is mathematical. Use correctly rated instruments and qualified procedures to verify actual conditions, identify imbalance, and confirm safe operation.