A **Delta to Wye Calculator** is a specialized tool used in **electrical engineering** to convert **delta-connected circuits** to equivalent **wye-connected circuits**. This conversion is crucial for simplifying complex circuit analyses and solving problems involving **three-phase power systems**.

## Delta to Wye Conversion Chart

Step | Delta Configuration | Wye Configuration | Conversion Formulas |
---|---|---|---|

1. Identify | R₁, R₂, R₃ (Delta) | Ra, Rb, Rc (Wye) | – |

2. Calculate Ra | – | Ra = (R₁R₂) / (R₁ + R₂ + R₃) | Ra = (R₁R₂) / Σ |

3. Calculate Rb | – | Rb = (R₂R₃) / (R₁ + R₂ + R₃) | Rb = (R₂R₃) / Σ |

4. Calculate Rc | – | Rc = (R₁R₃) / (R₁ + R₂ + R₃) | Rc = (R₁R₃) / Σ |

5. Verify | Σ = R₁ + R₂ + R₃ | – | Σ used in all formulas |

## Delta to Wye Conversion Formula

The **Delta to Wye conversion formulas** are:

Ra= (R₁R₂) / (R₁ + R₂ + R₃)Rb= (R₂R₃) / (R₁ + R₂ + R₃)Rc= (R₁R₃) / (R₁ + R₂ + R₃)

Where **R₁**, **R₂**, **R₃** are the resistances in the **delta configuration**, and **Ra**, **Rb**, **Rc** are the equivalent resistances in the **wye configuration**.

`First, calculate `**Σ** = R₁ + R₂ + R₃ = 30 + 40 + 50 = **120Ω**

Then apply the formulas:

Ra= (3040) / 120 = *10ΩRb= (4050) / 120 = *16.67ΩRc= (3050) / 120 = *12.5Ω

**The equivalent wye configuration has resistances Ra = 10Ω, Rb = 16.67Ω, and Rc = 12.5Ω.**

## How do you convert delta to wye?

Converting **delta to wye** involves these steps:

Identifythe delta-connected resistances (R₁, R₂, R₃).

Calculatethe sum (Σ) of all delta resistances.

Applythe conversion formulas for each wye resistance.

Verifythe results for consistency.

Delta resistances: **R₁ = 60Ω**, **R₂ = 80Ω**, **R₃ = 100Ω**

**Σ** = R₁ + R₂ + R₃ = 60 + 80 + 100 = **240Ω**

Apply formulas:

Ra= (R₁R₂) / Σ = (6080) / 240 = *20Ω

Rb= (R₂R₃) / Σ = (80100) / 240 = *33.33Ω

Rc= (R₁R₃) / Σ = (60100) / 240 = *25Ω

**Verify**: The sum of wye resistances (20 + 33.33 + 25 = **78.33Ω**) is less than any individual delta resistance, which is correct.

**The equivalent wye circuit has resistances Ra = 20Ω, Rb = 33.33Ω, and Rc = 25Ω.**