Delta to Wye Calculator
Convert delta (Δ) resistor networks to equivalent wye (Y) resistors using Ra, Rb, and Rc formulas with step-by-step solutions.
What Is Delta to Wye Conversion?
Delta (Δ) and wye (Y) are two ways to connect three resistors in a three-terminal network. A delta network has resistors on each side of a triangle; a wye network has resistors from a central point to each terminal. The same terminal behavior can be represented by an equivalent wye network with different resistor values.
Delta to Wye Formulas
$$R_a = \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_2}$$ $$R_b = \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_3}$$ $$R_c = \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_1}$$\(R_1\), \(R_2\), and \(R_3\) are the delta resistors. \(R_a\), \(R_b\), and \(R_c\) are the equivalent wye resistors connected to terminals A, B, and C.
Example: with \(R_1 = 6\,\Omega\), \(R_2 = 3\,\Omega\), and \(R_3 = 2\,\Omega\), the sum is 36 and \(R_a = 12\,\Omega\), \(R_b = 18\,\Omega\), \(R_c = 6\,\Omega\).
Applications
Delta–wye transformation simplifies analysis of three-phase circuits, balanced and unbalanced loads, and bridge networks. Engineers use it to replace complex delta sections with equivalent wye sections for easier voltage and current calculations.
Frequently Asked Questions
When should I use delta to wye conversion?
Use it when analyzing a three-terminal resistor network and you need equivalent wye values that produce the same terminal voltages and currents as the original delta network.
Are the formulas symmetric?
Yes. Each wye resistor equals the sum of products of delta resistors divided by the delta resistor opposite the corresponding terminal.
Can I convert wye back to delta?
Yes. Wye-to-delta uses a different set of formulas. This calculator performs delta-to-wye conversion only.
What units should I use?
Enter all resistances in the same unit (typically ohms). The output uses the same unit as the inputs.
Do the resistors need to be equal?
No. The formulas work for any positive resistor values. Equal delta resistors produce equal wye resistors.
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