Three-Phase Line vs Phase Voltage
V_line = √3 × V_phase
Quick answer
This calculator solves V_line = √3 × V_phase for Line-to-Line Voltage. With Phase Voltage 26.4 V, the result is 45.73 V. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
In a balanced three-phase wye (star) connected system, the line-to-line voltage is √3 (approximately 1.732) times the phase-to-neutral voltage. This fundamental relationship arises from the 120° phase displacement between phases. In a 208/120 V system (common in North America), V_phase = 120 V and V_line = 208 V. In a 400/230 V system (common in Europe), V_phase = 230 V and V_line = 400 V. Understanding this relationship is essential for three-phase power system design, motor connections, and transformer configurations.
Variables
- V_line — Line-to-line (phase-to-phase) voltage (V)
- V_phase — Phase-to-neutral voltage (V)
Practical Notes
For delta connections, the line voltage equals the phase voltage (V_line = V_phase), but the line current is √3 times the phase current. Three-phase power is P = √3 × V_line × I_line × cos(φ) regardless of wye or delta connection. In a balanced system, the neutral carries zero current.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Vline | Line-to-Line Voltage | V | pV, nV, µV, mV, V, kV |
| Vphase | Phase Voltage | V | pV, nV, µV, mV, V, kV |
Step by step
- 1. What you know: Phase Voltage 26.4 V
- 2. The relation: V_line = √3 × V_phase
- 3. Substitute: Vphase = 26.4 V
- 4. Result: Line-to-Line Voltage = 45.73 V
Worked examples
Minimum range
Given: Phase Voltage 0.726 V
Result: Line-to-Line Voltage = 1.257 V
Low range
Given: Phase Voltage 7.26 V
Result: Line-to-Line Voltage = 12.57 V
Typical
Given: Phase Voltage 26.4 V
Result: Line-to-Line Voltage = 45.73 V
High range
Given: Phase Voltage 0.506 kV
Result: Line-to-Line Voltage = 0.8764 kV
Maximum range
Given: Phase Voltage 5.06 kV
Result: Line-to-Line Voltage = 8.764 kV
Solving for each variable
Solve for Line-to-Line Voltage
Phase Voltage 0.726 V → 1.257 V
Solve for Phase Voltage
Line-to-Line Voltage 0.33 V → 0.1905 V
How Line-to-Line Voltage changes with Phase Voltage
| Phase Voltage (input) | Line-to-Line Voltage (result) |
|---|---|
| 5.81 V | 10.06 V |
| 14.53 V | 25.16 V |
| 29.05 V | 50.32 V |
| 43.58 V | 75.47 V |
| 58.1 V | 100.6 V |
| 87.15 V | 150.9 V |
| 116.2 V | 0.2013 kV |
| 0.2324 kV | 0.4025 kV |
| 0.4067 kV | 0.7044 kV |
| 0.581 kV | 1.006 kV |
The same result in other units
| Unit | Value |
|---|---|
| mV | 45730 |
| V | 45.73 |
| kV | 0.04573 |
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<p><a href="https://vbatpower.com/formulas/three-phase-line-phase/">Three-Phase Line vs Phase Voltage</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Three-Phase Line vs Phase Voltage?
Use V_line = √3 × V_phase. With Phase Voltage 26.4 V, Line-to-Line Voltage works out to 45.73 V.
What is the formula for Three-Phase Line vs Phase Voltage?
The formula is V_line = √3 × V_phase. In a balanced three-phase wye (star) connected system, the line-to-line voltage is √3 (approximately 1.732) times the phase-to-neutral voltage.
How do you find Phase Voltage when you know the other values?
Rearrange for Phase Voltage: with Line-to-Line Voltage 0.33 V, Phase Voltage is 0.1905 V.
What units does Three-Phase Line vs Phase Voltage use?
Line-to-Line Voltage is shown in mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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