Delta–Wye (Δ–Y) Conversion Calculator

Some resistor networks — the classic bridge is the standard example — contain three resistors arranged in a triangle (delta, Δ) or a three-spoke star (wye, Y, also called tee or star) that cannot be reduced by series and parallel combinations alone. The delta-wye transformation converts one arrangement into the other so the rest of the network collapses cleanly.

This calculator converts in both directions. Going delta to wye, each wye (star) leg is the product of the two delta resistors that touch its node, divided by the sum of all three: R_a = R_ab·R_ca / (R_ab + R_bc + R_ca), and similarly for R_b and R_c. Going wye to delta, each delta leg is the sum of the three pairwise products of the wye legs, divided by the opposite wye resistor: R_ab = (R_a·R_b + R_b·R_c + R_c·R_a) / R_c, and so on. The tool draws both the input network and the converted network, labelled with your values, so the correspondence between nodes is visible.

The transformation preserves the resistance seen between every pair of the three terminals — that is what makes the swap legal — while changing the internal topology into something the surrounding circuit can absorb. A useful sanity check falls out of the symmetric case: if all three delta resistors are equal to R, the equivalent wye resistors are each R/3, and conversely a balanced wye of R converts to a balanced delta of 3R. Use this to break a bridge, simplify a three-terminal sub-network, or teach the transformation; it handles the three-resistor block itself, not the full network reduction around it.