Calculate phase-to-ground voltage from phase-to-phase voltage, or the reverse, for a balanced grounded-wye three-phase system in volts or kV.

Convert the line-to-line voltage using the grounded-wye relationship.

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Phase to Ground Voltage Formula

For balanced sinusoidal three-phase wye voltages, with neutral at ground potential, the RMS phase-to-ground and phase-to-neutral magnitudes are equal. Use the exact square-root-of-three relation:

Vp−g = Vp−n = (Vp−p) / (√(3))

Variables:

  • Where Vp-g is the RMS phase-to-ground voltage (volts), equal to Vp-n under the stated assumptions
  • Vp-p is the RMS phase-to-phase (line-to-line) voltage (volts) 

To calculate the phase-to-ground voltage in this model, divide the phase-to-phase voltage by √3; reverse the conversion by multiplying by √3. The phase voltages must have equal magnitudes and be 120° apart, with neutral at ground potential. Delta, ungrounded, unbalanced or faulted systems can have different voltages to ground; neutral/ground shifts and conductor drops are not modeled. See Schneider Electric’s wye voltage relationship and grounding-system distinctions.

Balanced Grounded-Wye RMS Voltage Conversion Table (VLG = VLN = VLL / √3)
Phase-to-Phase VLL (V) Phase-to-Ground VLG (V)
208120.089
380219.393
400230.940
415239.600
440254.034
460265.581
480277.128
575331.976
600346.410
690398.372
33001905.256
41602401.777
66003810.512
110006350.853
138007967.434
2200012701.706
3300019052.559
6600038105.118
11000063508.530
13200076210.236
* RMS magnitudes for a balanced grounded-wye system with neutral at ground potential. Rounded to 3 decimals using VLG = VLN = VLL / √3. Inverse: VLL = √3 × VLG.

How to Calculate Phase to Ground Voltage?

The following two example problems outline how to calculate the Phase to Ground Voltage.

Example Problem #1:

  1. First, determine the phase to phase voltage (volts). In this example, the phase to phase voltage (volts) is measured to be 45.
  2. Finally, calculate the Phase to Ground Voltage using the formula above: 

Vp-g = Vp-p / √3

Inserting the values from above and solving the equation with the imputed values gives: 

Vp-g = 45 / √3 ≈ 25.981 (volts 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:

phase to phase voltage (volts) = 81

Entering these values into the formula or calculator above gives us 

Vp-g = 81 / √3 ≈ 46.765 (volts RMS)