Line-to-Line Voltage Calculator
Convert between line-to-line (V_LL) and line-to-neutral (V_LN) voltages, compute phasor line voltages from phase voltages, and check common system voltages (230/400, 277/480, 240/415).
convert phase voltage to line voltage
Line-to-line Voltage of a three-phase system calculation: Multiply the voltage line to neutral ratio by 0.63. On the other hand, in order to determine the voltage on a line to neutral, we divide the line-to-line voltage by the square root of 3. In case of unbalanced systems, actual line voltages are determined by phasor subtraction (Vab = Va -Vb).
Formula & Table Summary:
- VLL = √3 × VLN
- VLN = VLL ÷ √3
- Vab = Va∠θa − Vb∠θb
- Vpeak = √2 × Vrms
Converter Table
| Input | Formula | Output |
|---|---|---|
| VLN (RMS) | VLL = √3 × VLN | VLL |
| VLL (RMS) | VLN = VLL ÷ √3 | VLN |
| Phasors | Vab = Va − Vb | Line Voltage |
| Vrms | Vpeak = √2 × Vrms | Peak Voltage |
calculate line voltage from phase
A line-to-line voltage calculator is used to convert line-to-line (VLL) line-to-neutral (VLN) voltages in three phase electrical systems. The correlation in a balanced wye connection is easy to understand: VLL = 3 VLN, and VLN = VLL 3. In unbalanced or phasor cases, phasor subtraction is used to determine line voltage, e.g., Vab = Va -Vb. It is necessary in the work of electricians, engineers, and students dealing with three-phase distribution of power, typical utility voltages (230/400 V, 277/480 V), and equipment design. The use of RMS values enables it to make correct sizing of equipment, safe operation, and proper equipment selection.
line to neutral voltage formula
| Scenario | Input | Calculation | Result |
|---|---|---|---|
| EU system | VLN = 230V | VLL = √3 × 230 | ≈400V |
| US system | VLL = 480V | VLN = 480 ÷ √3 | ≈277V |
| Phasor subtraction | Va=230∠0°, Vb=230∠−120° | Vab = Va−Vb | ≈398V |
| RMS to Peak | Vrms = 230V | Vpeak = √2 × 230 | ≈325V |
Frequently Asked Questions - Line-to-Line Voltage Calculator:
What is line-to-line voltage?
It is the voltage measured between any two line conductors in a three-phase system.
How to convert VLN to VLL?
Multiply VLN by √3 to get line-to-line voltage.
How to convert VLL to VLN?
Divide VLL by √3 to get line-to-neutral voltage.
What is the formula for phasor line voltage?
Vab = Va∠θa − Vb∠θb (phasor subtraction).
Why is √3 used in voltage conversion?
It comes from the 120° phase angle geometry in three-phase systems.
What is VLL if VLN is 230V?
VLL = √3 × 230 ≈ 400 V (RMS).
What is VLN if VLL is 480V?
VLN = 480 ÷ √3 ≈ 277 V (RMS).
Does delta connection change VLL?
In delta, line voltage equals phase voltage.
Should I use RMS or peak values?
Use RMS for equipment ratings; convert to peak if needed.
Can this method work for unbalanced loads?
Yes, but use phasor subtraction instead of √3 relation.
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