Convert line voltage to phase voltage for a three-phase wye or delta system, or phase to line voltage, with optional current and power results.

Current and power
Leave blank for voltage only.

Used only when line current is entered.

Line-to-Phase Voltage Formula

For a balanced three-phase wye connection, phase/winding voltage is the line-to-neutral voltage. A delta winding is connected directly between two lines. Use the relationship for the actual connection, with RMS magnitudes:

Wye: Vphase = VL-L / โˆš(3) Delta: Vphase = VL-L

Variables:

  • Vphase is the RMS voltage across one winding or phase load (volts); it is line-to-neutral in wye, and line-to-line in delta
  • VL-L is the RMS voltage between two line conductors (volts)

In balanced wye, divide line-to-line voltage by the full value of โˆš3; reverse the conversion by multiplying phase voltage by โˆš3. In delta, phase/winding voltage equals line-to-line voltage in either direction. These relationships do not determine general line-to-ground voltage. University of Louisville explains the balanced RMS wye and delta relationships.

Balanced Three-Phase Wye RMS Voltage Conversion (VLN = VLL รท โˆš3)
Line Voltage VLL (V) Wye Phase / Line-to-Neutral Voltage VLN (V)
208120.089
220127.017
230132.791
240138.564
380219.393
400230.940
415239.600
440254.034
460265.581
480277.128
575331.976
600346.410
690398.372
1000577.350
24001385.641
33001905.256
41602401.777
69003983.717
110006350.853
138007967.434
Balanced wye only: VLN = VLL รท โˆš3. Values use the full square root and are rounded to 0.001 V. Example: 480 VLL โ‰ˆ 277.128 VLN. In delta, winding voltage equals VLL.

How to Calculate Line-to-Phase Voltage?

The following two examples use balanced three-phase wye RMS voltages. Delta winding voltage would instead equal the entered line-to-line voltage.

Example Problem #1:

  1. First, use a line-to-line RMS voltage of 47 V for the balanced wye example.
  2. Finally, calculate the Line-to-Phase Voltage using the formula above: 

Wye: Vphase = VL-L / โˆš3

Using the full value of โˆš3 and rounding the answer gives:

Vphase = 47 / โˆš3 โ‰ˆ 27.135 V RMS

Example Problem #2: 

Using the same process as example problem 1, we first define the variables outlined by the formula. In this case, the values are:

Line-to-line RMS voltage in the balanced wye system = 69 V.

Entering these values into the formula or calculator above gives us 

Vphase = 69 / โˆš3 โ‰ˆ 39.837 V RMS.