Delta-Wye (Δ-Y) Transformation Calculator

A mathematical technique that converts a three-terminal resistor network from a triangular Delta (Δ) arrangement to an equivalent center-tapped Wye (Y) arrangement, or vice versa, so that the network behaves identically at the three external terminals.

When a resistive network (like an unbalanced Wheatstone bridge or a three-phase load) cannot be reduced using simple series/parallel rules alone. Converting one triangle to a star (or vice versa) exposes series/parallel paths.

If all three delta resistors are equal (R_Δ), the equivalent wye resistors are each R_Δ/3. Conversely, an equal-resistor wye (R_Y) converts to a delta of 3×R_Y per resistor.

No — the equivalence is only valid as seen from the three terminals for terminal voltages/currents; internal dissipation in the converted network can differ, so do not use it to analyze internal losses of the original network directly.

In filter/RF design the delta topology is called Pi (Π) and the wye is called Tee (T); "star-mesh" is another name for the same wye/delta pair used in network theory.

Yes, it is fully reversible — converting Delta→Wye and then Wye→Delta with the correct formulas returns the original resistor values exactly.

Loads and transformer windings can be connected in either delta or star (wye); the transformation lets you convert per-phase impedances between the two connection types for load and fault analysis.

Yes, the same formulas apply directly to complex impedances Z_ab, Z_bc, Z_ca and Z_a, Z_b, Z_c in AC analysis.

It is a new, non-physical internal node created purely by the mathematical transformation; it does not exist in the original delta network and has no direct external connection.

Converting the delta formed by three of the bridge's resistors into a wye eliminates the bridging branch, turning the circuit into an ordinary series-parallel network solvable with basic rules.

The corresponding wye resistors that share it in the numerator become relatively large too, while the wye resistor not touching that large resistor tends to be small — the transform still holds exactly, just with widely different magnitudes.

Yes — consistently label terminals A, B, C on both networks. R_a is always the wye arm to terminal A, and it always pairs with the two delta resistors R_ab and R_ca that also touch terminal A.

The classic delta-wye/star-mesh transform is specifically for three-terminal networks; general star-mesh transforms exist for more terminals but use a different (more complex) formula set.

Yes — triangular ground or power-plane resistance meshes can be reduced to a star for quick IR-drop estimates at each of the three connection points.

Delta→Wye divides by the sum of the three delta resistors (Σ=R_ab+R_bc+R_ca); Wye→Delta divides by one wye resistor at a time using the sum of pairwise products (Σ_p=R_aR_b+R_bR_c+R_cR_a) — they are inverse operations, not mirror formulas.