Delta-Wye Transformation Calculator

Delta (Δ) and Wye (Y) networks are common circuit configurations (Figure 1). To simplify circuit calculations, it is often beneficial to transform a Delta circuit to a Wye circuit (or vice versa). The Delta-Wye transformation is also known as the Y-Δ or “delta-star” transformation because of the shapes of these circuits.

Figure 1. Delta and Wye network circuits

To use the calculator, either:

1. Enter three resistance values for the Delta network. The calculator will then output the Wye network resistor values.
2. Enter three resistance values for the Wye network. The calculator will then output the Delta network resistor values.

To start over, push the Reset button. 

Δ → Y Transformation Equations

Transforming from a Delta to a Wye network adds one node to the circuit.

$$R_1 = \frac{R_bR_c}{R_a+R_b+R_c}$$

$$R_2 = \frac{R_aR_c}{R_a+R_b+R_c}$$

$$R_3 = \frac{R_aR_b}{R_a+R_b+R_c}$$

Y → Δ Transformation Equations

Transforming from a Wye to a Delta network removes one node from the circuit.

$$R_a = \frac{(R_1R_2) + (R_2R_3) + (R_1R_3)}{R_1}$$

$$R_b = \frac{(R_1R_2) + (R_2R_3) + (R_1R_3)}{R_2}$$

$$R_c = \frac{(R_1R_2) + (R_2R_3) + (R_1R_3)}{R_3}$$

Application

Delta and Wye configurations are often used in three-phase power systems. The Delta configuration also appears in bridge rectifier circuits that perform the first step in converting AC voltage to a stable DC voltage. 

Further Reading

• Textbook — What are Wye and Delta?
• Worksheets — Worksheets - Delta and Wye 3-Phase Circuits
• Technical Article — Delta/Wye Transforms: Behind the Scenes