Line to Phase Voltage Calculator
Convert three-phase line-to-line (V_LL) and line-to-neutral (V_LN) voltages for balanced and phasor cases. Includes formulas, examples (230/400, 480/277), and conversion guidance.
line-to-neutral voltage formula
To convert line (line-to-line) voltage to phase (line-to-neutral) in a balanced three-phase wye system use **VLN = VLL ÷ √3**. Reverse with **VLL = √3 × VLN**. For unbalanced systems, compute phasor subtraction (Vab=Va∠θa − Vb∠θb) and take the magnitude to find the corresponding line voltage.
Formula & Table Summary:
Sample Data Table
| Line Voltage (VL) | Phase Voltage (VP) |
|---|---|
| 415 V | 240 V |
| 400 V | 231 V |
| 208 V | 120 V |
three phase phase voltage tool
The Line-to-Phase Voltage Calculator converts between line-to-line (VLL) and line-to-neutral / phase voltages (VLN) for three-phase systems. For balanced wye systems use the simple relation VLN = VLL/√3 (RMS values); conversely VLL = √3·VLN. For unbalanced or phasor inputs, compute each line voltage via phasor subtraction (e.g., Vab=Va∠θa − Vb∠θb) and take magnitudes. Use RMS consistently for equipment sizing; convert to peak if needed (Vpeak=√2·Vrms). This tool helps electricians, engineers and students quickly check standard utility values (230/400, 277/480), design wye/delta connections, and verify per-phase calculations.
line to phase voltage calculator
| Parameter | Symbol | Relation |
|---|---|---|
| Line Voltage | VL | √3 × VP |
| Phase Voltage | VP | VL / √3 |
Frequently Asked Questions - Line to Phase Voltage Calculator:
What is line-to-phase voltage?
Line-to-phase (line-to-neutral) voltage is the voltage from any line conductor to neutral in a three-phase system (V_LN).
How to convert line-to-line to line-to-neutral?
For a balanced wye: V_LN = V_LL ÷ √3 (use RMS values).
How to convert line-to-neutral to line-to-line?
V_LL = √3 × V_LN (RMS, balanced wye).
What is V_LN for a 400 V system?
V_LN = 400 ÷ √3 ≈ 230.94 V (≈230 V).
What is V_LN for a 480 V system?
V_LN = 480 ÷ √3 ≈ 277.13 V (≈277 V).
Do I use RMS or peak values?
Use RMS values for power and equipment ratings; convert to peak with V_peak = √2 × V_rms when needed.
How to compute unbalanced line voltages?
Use phasor arithmetic: V_ab = V_a∠θa − V_b∠θb; then take magnitude |V_ab| for line voltage.
Does delta connection change formula?
In delta, winding (phase) voltages equal line voltages; there is no V_LN unless a neutral is present via star point.
Why √3 appears in conversion?
√3 arises from the 120° phase geometry of balanced three-phase systems when converting vector (phasor) magnitudes.
When is the simple √3 relation invalid?
When the system is unbalanced, has harmonics, or neutral shift—use phasor/sequence analysis instead of √3 relation.
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