Delta to Wye Conversion

This delta to wye conversion calculator will help you convert delta networks of resistors to wye networks and vice versa.

Wye arm R_A50 Ω100 × 300 ÷ 600 — the two delta arms meeting at A

Wye arm R_B33.3333 Ω100 × 200 ÷ 600

Wye arm R_C100 Ω200 × 300 ÷ 600

Sum of the delta arms600 Ω

Sum of the wye arms183.3333 Ωalways smaller than the delta sum

Check: back to R_AB100 Ωthe inverse transform returns the original, which is the test that the conversion is exact rather than approximate

Check: back to R_BC200 Ω

Check: back to R_CA300 Ω

Resistance A to B, as a delta83.3333 ΩR_AB in parallel with the other two in series

Resistance A to B, as a wye83.3333 Ωidentical — the two networks are indistinguishable from outside, which is the whole point of the transform

The formula

R_wye = product of adjacent delta arms ÷ sum of all three

Two networks, indistinguishable from outside

A delta of three resistors and a wye of three resistors can present exactly the same resistance between every pair of terminals. The transform between them is exact, not an approximation: each wye arm is the product of the two delta arms meeting at that terminal, divided by the sum of all three.

The reason it matters is that some networks cannot be reduced by series and parallel combination alone — a bridge circuit is the classic example. Converting one delta to a wye usually breaks the deadlock and lets the rest collapse conventionally.

For the balanced case the result is memorable: three equal delta arms become three wye arms of one third the value. That factor of three appears throughout three-phase power work, where the same windings can be connected either way and the choice changes the apparent impedance threefold.

The checks above run the transform backwards. Since both directions are exact, recovering the original values is a genuine verification rather than a formality.