Enter your three delta resistor values (Rₐ, R_b, R_c) or three wye resistor values (R₁, R₂, R₃) and choose your conversion direction — the calculator returns the equivalent resistances in the target network. Switch between Delta to Wye and Wye to Delta modes to handle both transformation directions using the standard T-network formulas.
Result R₁ / Rₐ
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Result R₂ / R_b
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Result R₃ / Rc
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Conversion Performed
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A delta (Δ) network has three resistors arranged in a triangle, with each resistor connecting two of the three external terminals. A wye (Y or star) network has three resistors each connected from a common center node to one of the three external terminals. In circuit diagrams, delta looks like a triangle and wye looks like a Y or T shape.
For a balanced delta where Rₐ = R_b = Rc = 4Ω, the wye equivalent is R₁ = R₂ = R₃ = Rₐ / 3 = 4 / 3 ≈ 1.333Ω. In general, use R₁ = (R_b × Rc) / (Rₐ + R_b + Rc). You can verify this with the calculator by entering 4 for all three delta resistors.
The delta-to-wye transformation works for any three-terminal resistor subnetwork arranged in a delta or wye topology. However, the transformation applies specifically to the three-terminal structure — it cannot be directly applied to networks with more than three terminals or to non-planar networks without first isolating delta/wye sub-sections.
For a balanced wye with R₁ = R₂ = R₃ = 4Ω, the equivalent delta resistances are Rₐ = R_b = Rc = R₁ × 3 = 12Ω. The general wye-to-delta formula is Rₐ = R₂ + R₃ + (R₂ × R₃ / R₁). A balanced wye always converts to a delta that is exactly three times larger.
The delta-wye transformation applies to both AC and DC circuits. For purely resistive networks (DC or AC), the formulas use resistance values in ohms. For AC circuits with reactive components (inductors, capacitors), the same transformation formulas apply using impedance (Z) values in ohms, which may be complex numbers.
Delta-to-wye conversion simplifies circuit analysis by transforming a network that cannot be reduced by series/parallel rules alone into one that can. It is especially common in three-phase power systems, bridge circuits (like Wheatstone bridges), and ladder networks where direct series-parallel simplification is impossible.
Yes — a correctly converted delta or wye network is electrically equivalent at the three external terminals. This means the voltage, current, and power seen by external components connected to those terminals are identical. Internal currents and voltages differ, but external behavior is preserved.
For delta to wye: R₁ = (R_b × Rc) / (Rₐ + R_b + Rc), R₂ = (Rc × Rₐ) / (Rₐ + R_b + Rc), R₃ = (Rₐ × R_b) / (Rₐ + R_b + Rc). For wye to delta: Rₐ = R₂ + R₃ + (R₂ × R₃ / R₁), R_b = R₃ + R₁ + (R₃ × R₁ / R₂), Rc = R₁ + R₂ + (R₁ × R₂ / R₃).