Delta-to-Wye (Δ→Y) Transform

R_Y = (Ra × Rb) / (Ra + Rb + Rc)

Calculator

Result
—

Formula

R₁ = (Ra×Rb)/(Ra+Rb+Rc), R₂ = (Rb×Rc)/(Ra+Rb+Rc), R₃ = (Ra×Rc)/(Ra+Rb+Rc)

Description

The delta-to-wye transformation converts three resistors arranged in a triangle (delta/Δ) into an equivalent three-resistor star (wye/Y) configuration. This is essential for analyzing bridge circuits and complex resistor networks that cannot be reduced by simple series/parallel combinations. The forward result shows R₁ = (Ra×Rb)/(Ra+Rb+Rc). The other two Y resistors follow the same pattern with different pairs. For a balanced delta (Ra = Rb = Rc = R), each Y resistor is R/3.

Variables

  • Ra — Delta resistor between nodes 1-2 (Ω)
  • Rb — Delta resistor between nodes 2-3 (Ω)
  • Rc — Delta resistor between nodes 1-3 (Ω)

Practical Notes

The inverse wye-to-delta transform uses: Ra = (R1×R2 + R2×R3 + R1×R3)/R3, and similarly for Rb, Rc. Delta-wye transforms are commonly needed for Wheatstone bridge analysis, three-phase power calculations, and complex PCB trace resistance networks.

Related Formulas

Series Resistance Parallel Resistance LED Resistor Resistor Power Derating Resistive Attenuator Resistor Tolerance Range

Need more features?

Save calculations, import telemetry data, simulate battery discharge, and collaborate with your team.

Try the App