Line-to-Line Voltage Calculator and Formula

A line-to-line voltage calculator finds the voltage between two phase conductors in a three-phase system from the phase-to-neutral voltage and the system connection. Enter the phase voltage and choose wye or delta; the calculator returns line-to-line voltage and, where applicable, the corresponding phase voltage.

Formula

For a balanced three-phase wye (star) system, line-to-line voltage is phase-to-neutral voltage multiplied by the square root of three:

V_LL = √3 × V_LN

Here, V_LL is line-to-line voltage in volts (V), and V_LN is phase-to-neutral voltage in volts. The reverse calculation is V_LN = V_LL ÷ √3. In a delta connection, the voltage across each phase winding equals the line-to-line voltage, so V_LL = V_phase. The calculator uses the wye relationship for its numerical result; the connection selector is a reminder that the relationship differs in delta. For a delta system, enter the winding voltage as the line-to-line voltage rather than treating it as a phase-to-neutral value.

Worked Example

Using the default phase voltage of 120 V:

1. Apply the wye formula: V_LL = √3 × V_LN.
2. Substitute the value: V_LL = 1.73205 × 120 V.
3. Calculate: V_LL ≈ 207.846 V, which rounds to 207.85 V.
4. Check the reverse relationship: 207.846 V ÷ 1.73205 ≈ 120 V.

The block’s second output consequently gives a phase voltage of 120.00 V. This example assumes a balanced wye system and uses the standard relationship between phase and line voltages.

What Line-to-Line Voltage Means

In a three-phase circuit, the three phase conductors carry alternating voltages that are separated in phase by 120 electrical degrees. Line-to-line voltage is measured between any two of those phase conductors. In a four-wire wye system, phase-to-neutral voltage is measured between one phase conductor and the neutral conductor.

These measurements are not interchangeable. A familiar example is a nominal 120/208 V wye supply: about 120 V is available from a phase to neutral, and about 208 V from one phase to another. A nominal 277/480 V wye supply similarly has about 277 V phase-to-neutral and 480 V line-to-line. These are common system descriptions, not promises that a live measurement will equal the nominal value exactly; actual readings vary with supply conditions and load.

How the Relationship Works

The factor √3 comes from the vector relationship between two phase voltages, not from simply adding their magnitudes. Because the phase voltages are 120° apart, their difference has a magnitude √3 times one phase-to-neutral voltage in a balanced system. Numerically, √3 is approximately 1.73205.

For a balanced wye connection, each phase winding is connected from one line to the common neutral point. The voltage between two lines is therefore √3 times the voltage across one phase winding. In a balanced delta connection, each winding is connected directly between two lines, so its phase voltage is already the line-to-line voltage. This distinction is why it is important to identify the connection before using a conversion.

When to Use the Calculator

Use the wye calculation when you know the phase-to-neutral voltage and want the voltage between phase conductors, or when you know line-to-line voltage and need to estimate phase-to-neutral voltage using the inverse relationship. It is useful for checking a three-phase system description, interpreting equipment labels, or doing basic electrical calculations where the assumptions match.

• From 230 V phase-to-neutral in a balanced wye system: 230 × √3 ≈ 398.37 V line-to-line, often described nominally as a 400 V class supply.
• From 400 V line-to-line in a balanced wye system: 400 ÷ √3 ≈ 230.94 V phase-to-neutral.
• In delta, a 400 V line-to-line supply has 400 V across each delta winding; do not divide by √3 to find the winding voltage.

The calculator is mathematical, not a method for selecting wiring, protective devices, or equipment ratings. For installation work or measurements on energized equipment, use applicable procedures and consult a qualified electrical professional.

Common Errors and Limits

• Mixing up wye and delta: The √3 conversion between line and phase voltage applies to the balanced wye relationship. In delta, winding phase voltage equals line-to-line voltage.
• Using the wrong phase voltage: The wye formula requires phase-to-neutral voltage as its input. A voltage already measured between two lines should not be multiplied by √3.
• Assuming balance: The simple relationship assumes balanced three-phase voltages. With significant imbalance or distortion, individual measured voltages may not follow the ideal relationship precisely.
• Confusing voltage and power: This calculation gives voltage only. It does not determine current, power, energy use, or whether a system can supply a particular load.
• Rounding too early: Keep √3 at full calculator precision through the calculation, then round the final display. The result is in the same voltage unit as the input.

For US customary and metric contexts, voltage is measured in volts in both; the SI unit is the volt. The system’s nominal voltage convention and connection matter more than whether a location commonly uses metric or US customary measurements. The calculator does not account for frequency, load, conductor impedance, transformer regulation, or voltage drop. Those factors can affect actual operating measurements but do not change the ideal balanced-system formula.

Frequently Asked Questions

How do I calculate line-to-line voltage from phase voltage?
For a balanced wye system, multiply phase-to-neutral voltage by √3, approximately 1.732. For example, 120 V × 1.732 is about 207.85 V line-to-line.

How do I find phase voltage from line voltage?
For a balanced wye system, divide line-to-line voltage by √3. A 208 V line-to-line supply gives approximately 120.09 V phase-to-neutral; nominal systems may be described using rounded standard values.

Is line voltage the same as line-to-line voltage?
Usage varies. In three-phase contexts, “line voltage” often means the voltage between two lines, but it can be ambiguous. Specify line-to-line or phase-to-neutral to avoid confusion.

Does the √3 formula apply to delta?
Not for converting line voltage to delta winding voltage: in a delta connection, each winding voltage equals line-to-line voltage. The √3 relationship is used for balanced wye line and phase voltages.

Why does my measured voltage differ from the calculator?
The calculation assumes a balanced, ideal system and exact input. Supply variation, load, measurement accuracy, or an unbalanced system can produce a different reading. Confirm the measurement points and system connection.

Related

• First Light Clearing England & Final Damien Fight Ch 17
• Ys VIII Switch 2 Edition Storage & Startup Checks
• Desert Detectors Codes: How They Work

in v | Phase voltage | V | 120 | 0
sel conn | System connection | Wye=1, Delta=1
out ll | Line-to-line voltage | V | v * sqrt(3) | 2
out ph | Phase voltage | V | ll / sqrt(3) | 2