Calculation
Uline = √3 · Uphase
In wye, two phase voltages offset by 120° add geometrically to the line voltage; the factor between them is always √3.
Busch 2006, Abschnitt 5.11.3, Gl. (5.96) und (5.97)
Wye connection: line voltage from phase voltage
In wye, two phase voltages offset by 120° add geometrically to the line voltage; the factor between them is always √3.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Line voltage Uline — RMS voltage between two line conductors of the wye-connected load.
- Phase voltage Uphase — RMS voltage across a single phase, i.e. between a line conductor and the star point.
Example
Uphase=230 V gives Uline=√3·230≈398.37 V (standard value 400 V).
Assumptions and limits
Balanced wye connection with equal phase voltages and 120° phase offset; imbalance and neutral current are excluded.
Understand Wye connection: line voltage from phase voltage
This calculator converts between phase and line voltage of a balanced wye connection, one of the most fundamental relations in three-phase engineering.
What does this quantity describe?
In a wye connection, each phase sits between a line conductor and the common star point. Two phase voltages offset by 120° add geometrically to the line voltage: Uline=√3·Uphase.
Formula and variables
Uline = √3 · Uphase
Uline = √3 · UphaseUphase = Uline / √3
| Symbol / input | Meaning |
|---|---|
| Line voltage Uline | RMS voltage between two line conductors of the wye-connected load. |
| Phase voltage Uphase | RMS voltage across a single phase, i.e. between a line conductor and the star point. |
Choose the inputs correctly
Uphase is the voltage across a single phase (line conductor to star point), Uline the voltage between two line conductors.
How to use the calculator
Take one of the two quantities from a nameplate or measurement; the other follows directly from the factor √3.
Worked example
Uphase=230 V gives Uline=√3·230≈398.37 V, standardised to 400 V on the grid.
Understand the result and units
The factor √3≈1.732 is independent of load and holds for any balanced wye connection.
Uphase and Uline are voltages.
Typical applications
Converting between supply and equipment voltage for three-phase connections, sizing windings in wye, and understanding the German 230/400 V grid.
Assumptions, limits and common mistakes
Balanced wye connection with equal phase voltages and exact 120° offset; imbalance, harmonics and neutral current are excluded.
Common mistake: Do not confuse phase and line voltage when a winding is rated for 230 V rather than 400 V.
Frequently asked questions
What is “Wye connection: line voltage from phase voltage” used for?
Converting between supply and equipment voltage for three-phase connections, sizing windings in wye, and understanding the German 230/400 V grid.
Where do the input values come from?
Uphase is the voltage across a single phase (line conductor to star point), Uline the voltage between two line conductors.
What does the result not cover?
Balanced wye connection with equal phase voltages and exact 120° offset; imbalance, harmonics and neutral current are excluded.