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Wye-Delta (Y-Δ) Transformation Calculator

Convert a three-resistor Wye (star) network to its electrically equivalent Delta network, or Delta to Wye.

Rab
36.6667 Ω
Rbc
110 Ω
Rca
55 Ω

How it works

A Wye (Y, or star) network has three resistors Ra, Rb, Rc each running from one of three external terminals to a shared center node. A Delta (Δ) network instead has three resistors Rab, Rbc, Rca, each running directly between one pair of terminals. The two networks behave identically from outside their three terminals exactly when their resistances satisfy a fixed pair of transform equations.

Converting Wye to Delta: Rab = (Ra·Rb + Rb·Rc + Rc·Ra) / Rc, and the other two arms, Rbc and Rca, follow the same numerator divided by Ra and Rb respectively. Converting Delta to Wye: Ra = (Rab·Rca) / (Rab + Rbc + Rca), with Rb and Rc following the same pattern using the other two products.

For a balanced network — all three resistors equal — these reduce to the well-known identity Delta = 3 × Wye (and Wye = Delta ÷ 3), which is the quickest way to sanity-check either direction by hand.

FAQ

Why would I need to convert between Wye and Delta at all?

Three-phase power systems and resistor-network analysis sometimes present a circuit as a Wye and sometimes as a Delta, and a network that's awkward to simplify with ordinary series/parallel rules in one form often reduces easily once converted to the other. This conversion lets you move freely between the two without changing the circuit's actual electrical behavior at its terminals.

Is this the same as the Wheatstone bridge or series/parallel resistor calculators on this site?

No. The Wheatstone bridge calculator solves a four-resistor bridge for balance, and the series/parallel calculator combines resistors along a single path or directly in parallel — neither handles a three-terminal network where the resistors meet at a shared internal node (Wye) or form a triangle between terminals (Delta), which is specifically what this transformation is for.

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