Convert RMS line-to-line and phase/winding voltage for balanced, steady-state sinusoidal three-phase wye or delta systems in either direction. Optional line current gives phase current and total apparent power; a supplied power factor also gives real power.

RMS magnitudes for balanced sinusoidal three-phase wye or delta. Phase voltage means voltage across one winding; delta phase voltage is not line-to-neutral.

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 / sqrt(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 √3; reverse the conversion by multiplying phase voltage by √3. 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 ÷ √3)
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 ÷ √3. Values use the full square root and are rounded to 0.001 V. Example: 480 VLL ≈ 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 / √3

Using the full value of √3 and rounding the answer gives:

Vphase = 47 / √3 ≈ 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 / √3 ≈ 39.837 V RMS.