3 Phase Voltage Calculator: Formula and Examples

This 3 phase voltage calculator finds line-to-line voltage from phase voltage, or phase voltage from line voltage, for a balanced three-phase system. Enter the known RMS voltage and choose the relationship that matches the wiring; the result is the other voltage in volts.

Formula

For a balanced star (wye) connection, line voltage is √3 times phase voltage: V_L = √3 × V_ph. In the reverse direction, phase voltage is line voltage divided by √3: V_ph = V_L / √3. The selector applies the appropriate multiplier: 1.7320508075688772 for phase-to-line, or 0.5773502691896258 for line-to-phase.

V_L means line-to-line voltage in volts RMS, measured between two line conductors. V_ph means phase voltage in volts RMS; in a star system, this is the voltage from a line conductor to neutral. The input v is the known voltage in volts, and c is the selected conversion factor. This relation assumes three equal phase voltages separated by 120 degrees and a balanced system.

Worked Example

The defaults are a known voltage of 400 V and the “Phase to line (star)” selection. The selected factor is 1.7320508075688772.

Calculated voltage = 400 V × 1.7320508075688772 = 692.820323… V. Rounded to the calculator’s two decimal places, the result is 692.82 V. The helper output repeats the known input as 400.00 V.

1. Convert phase voltage to line voltage in a star system

Choose “Phase to line (star)” when you know the line-to-neutral phase voltage and need the voltage between two lines in a balanced star-connected circuit. For example, a nominal 230 V phase voltage corresponds to about 398.37 V line-to-line; systems commonly described as 230/400 V reflect the rounded relationship. This calculation helps interpret nameplate data or check expected voltage relationships, but it does not establish that a particular installation is safe or correctly wired.

2. Convert line voltage to phase voltage in a star system

Choose “Line to phase (star)” when the known value is measured between two line conductors and the desired value is from a line to neutral. A 400 V line-to-line supply gives approximately 230.94 V phase-to-neutral, using 400 ÷ √3. The result is meaningful only when the system has a neutral reference and is star-connected; a three-wire system may not provide an accessible neutral.

3. Use the relationship as a quick system check

This calculator is useful for checking whether stated line and phase voltages are consistent with a balanced star system: their ratio should be close to √3. Real readings can differ because of instrument accuracy, supply variation, voltage drop, or imbalance among phases. If measured values depart substantially from the expected relationship, treat that as a reason to investigate the measurement setup and system configuration rather than changing the conversion factor.

How to Choose

First identify what the voltage measurement is between. A line-to-line reading is taken across two phase conductors; a phase-to-neutral reading is taken from one phase conductor to neutral. Select the direction that converts the value you already have into the value you need, and enter RMS volts rather than peak voltage.

Next confirm the connection type. The √3 relationship applies to balanced three-phase star (wye) systems. It is not the general conversion rule for a delta-connected system: in a balanced delta, the line voltage equals the phase-winding voltage, while the line current and phase current have the √3 relationship. Do not use this voltage calculator to infer delta winding voltage from a line voltage using the star rule.

Also consider the system’s actual condition and measurement point. The formula describes an ideal balanced set of sinusoidal voltages; it does not account for phase imbalance, harmonics, transformer arrangements, grounding, or voltage drop through conductors. When readings are unusual or the result will inform electrical work, verify the system documentation and have a qualified electrical professional assess it. A calculated voltage is not a wiring or equipment rating.

Frequently Asked Questions

What does “line voltage” mean?
It is the RMS voltage measured between any two line conductors in a three-phase circuit.

What is phase voltage?
In a star-connected system, it is the RMS voltage from one line conductor to the neutral point. In other contexts, “phase voltage” can refer to the voltage across an individual winding, so confirm the connection.

Why is √3 used?
The three phase voltages are 120 degrees apart. The vector difference between two phase-to-neutral voltages has a magnitude √3 times either phase voltage in a balanced star system.

Does this apply to delta connections?
Not as a line-to-phase voltage conversion. For balanced delta, line-to-line voltage equals the voltage across each phase winding; √3 instead relates line current to phase current.

Should I enter peak or RMS voltage?
Enter RMS voltage, which is the standard way AC system voltages are specified. Do not mix peak and RMS values; for a clean sine wave, peak voltage is RMS voltage multiplied by √2.

Why might a meter reading not match exactly?
Supply variation, phase imbalance, instrument tolerance, waveform distortion, and measurement location can affect readings. The calculator assumes a balanced system and does not correct for those conditions.

Final Thoughts

For a balanced star-connected system, multiplying phase voltage by √3 gives line voltage, and dividing line voltage by √3 gives phase voltage. Confirm the connection and measurement points before using the result, especially when readings are being used to assess electrical equipment or installation conditions.

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in v | Known voltage | V | 400 | 0
sel c | Calculate | Phase to line (star)=1.7320508075688772, Line to phase (star)=0.5773502691896258
out r | Calculated voltage | V | v * c | 2
out known | Entered voltage | V | v | 2