Convert line-to-line voltage (VLL) to line-to-neutral phase voltage (VLN), or back, for a balanced three-phase wye or a split-phase system.

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Line To Neutral Voltage Formula

The following formula applies to balanced sinusoidal three-phase wye RMS voltages with a defined neutral. For ideal equal center-tapped split phase, replace √3 with2; both directions are available in the calculator.

VLN = (VLL) / (√(3))

Variables:

  • VLN is the line to neutral voltage
  • VLL is the line to line voltage
  • √3 is the square root of 3 (approximately 1.732)

For balanced wye, divide RMS line-to-line voltage by √3 to obtain RMS line-to-neutral voltage. For equal center-tapped split phase use2 instead. Select the actual topology and input/output units.

Line-to-Line (VLL) to Line-to-Neutral (VLN) Conversion Table (Balanced three-phase wye, RMS: VLL = √3 × VLN, √3 ≈ 1.732)
Line-to-Line Voltage (VLL), V Line-to-Neutral Voltage (VLN), V
208120.1
220127.0
230132.8
240138.6
380219.4
400230.9
415239.6
440254.0
460265.6
480277.1
575332.0
600346.4
690398.4
1000577.4
24001385.6
41602401.8
66003810.5
110006350.9
132007621.0
138007967.4
*Three-phase wye systems: VLL = √3 × VLN. Values rounded to one decimal place after using the full square root of3.

What is Line To Neutral Voltage?

Line-to-neutral voltage is measured between a line conductor and the system neutral. It is the winding voltage in a wye system. Equal center-tapped split-phase legs use a different factor, and delta systems may lack a neutral or have unequal neutral voltages. This arithmetic converter does not assess grounding, faults or equipment compatibility.

How to Calculate Line To Neutral Voltage?

The following steps outline how to calculate the Line To Neutral Voltage.

  1. First, confirm a balanced wye system and determine the RMS line-to-line voltage (VLL).
  2. Next, use the formula VLN = VLL / √3.
  3. Finally, calculate the line to neutral voltage.
  4. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Line to Line Voltage (VLL) = 400 V

√3 ≈1.73205, so400V line-to-line gives approximately230.940108V line-to-neutral for balanced wye. In equal center-tapped split phase,240V gives120V.