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Delta ↔ wye conversion calculator

Transform a resistor triangle into an equivalent star and back — the unlock for bridges and three-phase networks.

Ra (leg at node A)R(A–B)·R(C–A) / ΣΔ — the two sides touching A100 Ω
Rb (leg at node B)R(A–B)·R(B–C) / ΣΔ100 Ω
Rc (leg at node C)R(B–C)·R(C–A) / ΣΔ100 Ω

How it works

Δ→Y: each star leg is the product of the two delta sides touching that node, over the sum of all three: Ra = R(A–B)·R(C–A) / (R(A–B)+R(B–C)+R(C–A)). Y→Δ: each delta side is the sum of the leg pair-products over the opposite leg. Derive either by equating the terminal-pair resistances and the symmetry does the rest.

Common questions

Why would I ever need this?

Whenever series/parallel reduction gets stuck. A Wheatstone bridge, for example, has no two resistors purely in series or parallel — convert one triangle of it to a Y and the rest collapses with ordinary series/parallel math. In three-phase power it's not even a trick; delta and wye are the two physical ways sources and loads actually connect.

Is the equivalence exact?

Exact at the three terminals — any measurement you make from outside (any pair-wise resistance, any applied source) cannot tell the two networks apart. Inside is a different story: the Y has a center node the delta simply doesn't have, so internal voltages aren't comparable.

Balanced case shortcut?

When all three are equal: R_Y = R_Δ/3, and R_Δ = 3·R_Y. A 300 Ω delta is a 100 Ω wye. For three-phase machines this ratio is why delta termination raises a motor's Kv by √3 in voltage terms — related math, same triangle.

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