Calculate line-to-line voltage from phase or line-to-neutral voltage for balanced wye and delta systems, or solve 3-phase apparent power and line current.
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Line to Line Voltage Formula
The following equation applies to balanced sinusoidal three-phase wye (star) windings using RMS magnitudes. For delta windings, line-to-line voltage equals the voltage across one winding.
- Where VL-L is the line-to-line voltage
- PV is the wye winding (line-to-neutral) RMS voltage
For a balanced wye system, multiply winding (line-to-neutral) RMS voltage by √3 to obtain line-to-line RMS voltage. For a delta winding the factor is1. The calculator supports both directions.
The balanced-wye formula assumes equal phase magnitudes separated by120°. For the additional apparent-power modes, total S = √3 × VLL × IL in volt-amperes, using line current and line-to-line RMS voltage. S is apparent power, not real power in watts. Zero denominators do not determine a unique inverse when S is also zero.
| Phase Voltage (V) | Line-to-Line Voltage (V) |
|---|---|
| 12 | 20.785 |
| 24 | 41.569 |
| 48 | 83.138 |
| 60 | 103.923 |
| 90 | 155.885 |
| 100 | 173.205 |
| 110 | 190.526 |
| 115 | 199.186 |
| 120 | 207.846 |
| 127 | 219.970 |
| 200 | 346.410 |
| 220 | 381.051 |
| 230 | 398.372 |
| 240 | 415.692 |
| 254 | 439.941 |
| 277 | 479.778 |
| 346 | 599.290 |
| 347 | 601.022 |
| 398 | 689.356 |
| 500 | 866.025 |
| * Rounded to 3 decimals. Balanced-wye relation (RMS): V_LL = √3 × V_Ph ≈ 1.732 × V_Ph. | |
What is Line to Line Voltage?
Definition:
Line-to-line voltage and phase-to-phase voltage name the voltage between two phase conductors. Winding or load-phase voltage is different terminology: it is line-to-neutral for a wye winding and line-to-line for a delta winding.
Line-to-line voltage is the potential difference between two line conductors. In the balanced sinusoidal model, the phase voltages are120° apart, not at right angles; their vector difference produces the √3 wye relationship.
A three-phase system has three line-to-line voltage pairs and may have three or four conductors depending on whether a neutral is provided. Line-to-line voltage is not a scalar sum of wire voltages plus neutral. Ground voltage also depends on the grounding arrangement and is not determined by this converter.
