Delta–Wye (Δ–Y) Resistor Converter
Convert three resistors between Delta (Δ, pi) and Wye (Y, star, T) configurations in either direction — a standard step in circuit simplification and three-phase power analysis.
Conversion direction
Ω
Ω
Ω
Wye resistor at node A
- 1
Sum of delta resistors
10 + 20 + 30 = 60 - 2
R_A = R_AB × R_CA ÷ sum
10 × 30 ÷ 60 = 5
How does this calculator work?
Delta→Wye: R_A = (R_AB × R_CA) ÷ (R_AB + R_BC + R_CA), cycled for R_B and R_C. Wye→Delta: R_AB = (R_A·R_B + R_B·R_C + R_C·R_A) ÷ R_C, cycled similarly. Balanced case: R_Y = R_Δ/3.
Formula
How this is calculated
Delta and Wye are the two fundamental three-terminal resistor topologies. A Delta (Δ) network places one resistor across each pair of the three terminals, forming a triangle. A Wye (Y, or Star) network connects one resistor from each terminal to a shared central node. Both can be made electrically equivalent from the outside — the same terminal voltages produce the same terminal currents — using transformation formulas.
For Delta→Wye: each Wye resistor equals the product of the two Delta resistors sharing that terminal, divided by the sum of all three Delta resistors. Cycling gives R_A = (R_AB × R_CA) / (R_AB + R_BC + R_CA), R_B = (R_AB × R_BC) / sum, and R_C = (R_BC × R_CA) / sum. For Wye→Delta the inverse applies: R_AB = (R_A·R_B + R_B·R_C + R_C·R_A) / R_C, cycled similarly. The numerator is always the sum of all pairwise Wye products.
This transformation is used in three-phase power engineering (motor starting, load analysis), bridge-circuit simplification (Wheatstone bridge), and filter design (pi-section and T-section equivalence). For a balanced symmetric network where all Delta resistors equal R, each Wye resistor equals R/3, so Wye impedances are always one-third their Delta counterparts in the balanced case.
Frequently asked questions
Most commonly in three-phase AC power systems (to analyse and balance loads) and in DC bridge circuits where a network cannot be solved by simple series/parallel rules. It is also the basis of pi-to-T and T-to-pi filter transformations in RF and audio engineering.
Yes — the same formulas hold for complex impedances Z = R + jX. Replace each resistor with its complex impedance and perform the same arithmetic. This calculator uses real numbers; handle the imaginary part separately if working with AC circuits.
If all three Delta resistors equal R_Δ, then each Wye resistor R_Y = R_Δ/3. Conversely R_Δ = 3·R_Y. This same ratio applies to line vs phase voltages in a balanced three-phase system.
Also known as
TG we-Calculate Editorial Team. (2026). Delta–Wye (Δ–Y) Resistor Converter [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/delta-to-wye-calculator
TG we-Calculate Editorial Team. "Delta–Wye (Δ–Y) Resistor Converter." TG we-Calculate. 2026. https://we-calculate.com/calculator/delta-to-wye-calculator.
TG we-Calculate Editorial Team, "Delta–Wye (Δ–Y) Resistor Converter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/delta-to-wye-calculator
@misc{wecalculate_delta_to_wye_calculator, title = {Delta–Wye (Δ–Y) Resistor Converter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/delta-to-wye-calculator}}, year = {2026}, note = {TG we-Calculate} }
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