Transformer Delta-Wye Voltage Calculator

A transformer delta-wye voltage calculation converts a known Primary line voltage through the transformer turns ratio and then determines the usable secondary line-to-phase relationship. The calculator produces the Secondary line voltage first, then applies the selected Secondary connection to produce Secondary phase voltage.

For a wye secondary, the phase voltage is the line-to-neutral voltage used when reviewing 120 V branch-circuit loads, phase loading, neutral loading, panel schedules, and feeder voltage drop. For a delta secondary, phase voltage equals line voltage, which is applicable to the winding voltage relationship and many three-phase load calculations.

The result is an ideal voltage-conversion value. It establishes the electrical voltage basis before conductor ampacity, AWG or kcmil selection, raceway fill, motor-load calculations, overcurrent protection, or equipment-voltage verification are completed.

Input Values

Calculator field	Electrical meaning
Primary line voltage	The incoming primary line-to-line voltage supplied to the transformer.
Primary-to-secondary turns ratio	Primary turns divided by secondary turns. A ratio of 60 x means the primary winding has 60 times as many turns as the secondary winding.
Secondary connection	Selects the line-to-phase relationship at the secondary: delta or wye.

The calculator assumes that Primary line voltage is the line-to-line basis. The Primary-to-secondary turns ratio reduces that voltage to the secondary line-voltage basis.

Secondary Voltage Formula

The first calculation is the transformer voltage ratio:

\(\displaystyle \text{Secondary line voltage} = \frac{\text{Primary line voltage}}{\text{Primary-to-secondary turns ratio}}\)

The selected Secondary connection then determines phase voltage:

\(\displaystyle \text{Wye secondary phase voltage} = \frac{\text{Secondary line voltage}}{\sqrt{3}} ] = [ \text{Delta secondary phase voltage} = \text{Secondary line voltage}\)

For a wye-connected secondary, the calculator reports a Line-to-phase factor of approximately:

\(\displaystyle \sqrt{3} = 1.7321\)

A 208Y/120 V system illustrates the relationship: nominal line-to-line voltage is about 208 V, while line-to-neutral voltage is about 120 V. The 208 V value supports three-phase loads; the 120 V value supports line-to-neutral loads when a neutral is present and properly applied.

Calculation Example

Using the values shown:

Field	Value
Primary line voltage	12,470 V
Primary-to-secondary turns ratio	60 x
Secondary connection	Wye

First, calculate secondary line voltage:

\(\displaystyle \frac{12{,}470\text{ V}}{60} = 207.8333\text{ V}\)

Then convert wye line voltage to phase voltage:

\(\displaystyle \frac{207.8333\text{ V}}{1.7321} = 119.9926\text{ V}\)

Result	Value
Secondary line voltage	207.8333 V
Secondary phase voltage	119.9926 V
Line-to-phase factor	1.7321 x
Primary line voltage used	12,470 V
Turns ratio used	60 x
Secondary connection used	Wye

The calculated result is effectively a 208Y/120 V secondary voltage basis. A three-phase feeder, motor controller, or other line-to-line load is evaluated from the approximately 208 V line voltage. A 120 V branch circuit is evaluated from the approximately 120 V line-to-neutral phase voltage.

Electrical Use of the Result

The secondary voltage result supports several downstream design and installation checks:

• Load review: Convert connected load information into current at the actual secondary system voltage before determining feeder or branch-circuit ampacity.
• Conductor sizing: Select AWG or kcmil conductors only after calculated load current, continuous-load treatment, applicable adjustment factor, correction factor, and terminal rating have been determined.
• Voltage-drop review: Use the correct line-to-line or line-to-neutral voltage basis. A three-phase 208 V load and a 120 V line-to-neutral load do not use the same voltage-drop calculation basis.
• Motor calculations: Confirm whether motor nameplate voltage and controller ratings match the available secondary line voltage rather than relying on a nominal system description.
• Panel and distribution layout: A wye secondary may supply both three-phase line-to-line loads and single-phase line-to-neutral loads, subject to the actual transformer, neutral arrangement, equipment ratings, and load balancing.
• Raceway and feeder planning: The voltage result helps establish the expected current level, but raceway fill and bending layout remain separate physical installation calculations.

A lower secondary voltage produces higher current for the same load demand. That can affect conductor ampacity, voltage drop, overcurrent protective-device selection, and feeder configuration.

Delta and Wye Secondary Conditions

A delta secondary has equal line voltage and phase voltage:

\(\displaystyle V_{LL}=V_{\phi}\)

A wye secondary has line voltage equal to phase voltage multiplied by square root of three:

\(\displaystyle V_{LL}=\sqrt{3}\times V_{\phi}\)

The calculator changes only the secondary line-to-phase arithmetic. It does not determine whether a neutral conductor is installed, whether a particular delta configuration supports a desired line-to-neutral load, or whether a transformer secondary grounding arrangement is suitable for the installation.

Field Verification and Limits

This calculation is limited to ideal transformer voltage conversion. It does not account for vector-group phase shift, tap position, winding impedance, regulation under load, grounding, phase sequence, transformer paralleling, equipment approval, or code compliance.

Verify the transformer nameplate, actual primary supply voltage, selected taps, secondary connection, grounding method, and connected equipment ratings before installation or energization. Final conductor ampacity, insulation temperature rating, terminal rating, voltage-drop performance, overcurrent protection, and AHJ requirements must be evaluated separately.