How this calculator works
Delta and wye conversions preserve the resistance seen between any pair of external terminals when the third is left open. Each wye arm is the product of the two adjacent delta branches divided by the sum of all three branches. The inverse divides the sum of wye pair products by the arm opposite the desired delta branch. These real-valued calculations cover positive resistors, without modelling complex impedances.
Formula
Let D = Rab + Rbc + Rca. Ra = Rab Rca/D, Rb = Rab Rbc/D, Rc = Rbc Rca/D. Let S = Ra Rb + Rb Rc + Rc Ra. Rab = S/Rc, Rbc = S/Ra, Rca = S/Rb.
Worked example
Three delta resistors of 3 ohm become three wye arms of 1 ohm. Three wye arms of 2 ohm become three delta resistors of 6 ohm.
Advertisement
Frequently asked questions
Why do terminal labels matter?
A wye arm uses the two delta branches that meet at its terminal. Mixing the labels gives the wrong unequal network.
Can I convert inductors or capacitors directly?
The general transformation applies to complex impedances at a chosen frequency, but this tool accepts only positive real resistances.
Does the conversion preserve internal current?
It preserves terminal behaviour. Individual branch currents and internal power distribution can differ.