Delta-to-Wye (Δ→Y) Transform

R_Y = (Ra × Rb) / (Ra + Rb + Rc)

Quick answer

This calculator solves R₁ = (Ra×Rb)/(Ra+Rb+Rc), R₂ = (Rb×Rc)/(Ra+Rb+Rc), R₃ = (Ra×Rc)/(Ra+Rb+Rc) for R_Y. With Delta Ra 0.47 kΩ, Delta Rb 1.03 kΩ, Delta Rc 2.21 kΩ, the result is 130.5.

Calculator

Result
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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.

Symbols and units

Symbol Meaning Default unit Accepted units
Ra Delta Ra Ω mΩ, Ω, kΩ, MΩ
Rb Delta Rb Ω mΩ, Ω, kΩ, MΩ
Rc Delta Rc Ω mΩ, Ω, kΩ, MΩ

Step by step

  1. 1. What you know: Delta Ra 0.47 kΩ, Delta Rb 1.03 kΩ, Delta Rc 2.21 kΩ
  2. 2. The relation: R₁ = (Ra×Rb)/(Ra+Rb+Rc), R₂ = (Rb×Rc)/(Ra+Rb+Rc), R₃ = (Ra×Rc)/(Ra+Rb+Rc)
  3. 3. Substitute: Ra = 0.47 kΩ, Rb = 1.03 kΩ, Rc = 2.21 kΩ
  4. 4. Result: R_Y = 130.5

Worked examples

Minimum range

Given: Delta Ra 1 Ω, Delta Rb 2.2 Ω, Delta Rc 4.7 Ω

Result: R_Y = 0.2785

Low range

Given: Delta Ra 10 Ω, Delta Rb 22 Ω, Delta Rc 47 Ω

Result: R_Y = 2.785

Typical

Given: Delta Ra 0.47 kΩ, Delta Rb 1.03 kΩ, Delta Rc 2.21 kΩ

Result: R_Y = 130.5

High range

Given: Delta Ra 4.7 kΩ, Delta Rb 10.3 kΩ, Delta Rc 22.1 kΩ

Result: R_Y = 1305

Maximum range

Given: Delta Ra 47 kΩ, Delta Rb 103 kΩ, Delta Rc 0.221 MΩ

Result: R_Y = 13050

How R_Y changes with Delta Ra

Delta Ra (input) R_Y (result)
47 Ω 14.73
117.5 Ω 36.05
0.235 kΩ 69.65
0.3525 kΩ 101.1
0.47 kΩ 130.5
0.705 kΩ 184.1
0.94 kΩ 231.6
1.88 kΩ 378.2
3.29 kΩ 518.9
4.7 kΩ 609.7

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Frequently asked questions

How do you calculate Delta-to-Wye (Δ→Y) Transform?

Use R₁ = (Ra×Rb)/(Ra+Rb+Rc), R₂ = (Rb×Rc)/(Ra+Rb+Rc), R₃ = (Ra×Rc)/(Ra+Rb+Rc). With Delta Ra 0.47 kΩ, Delta Rb 1.03 kΩ, Delta Rc 2.21 kΩ, R_Y works out to 130.5.

What is the formula for Delta-to-Wye (Δ→Y) Transform?

The formula is R₁ = (Ra×Rb)/(Ra+Rb+Rc), R₂ = (Rb×Rc)/(Ra+Rb+Rc), R₃ = (Ra×Rc)/(Ra+Rb+Rc). The delta-to-wye transformation converts three resistors arranged in a triangle (delta/Δ) into an equivalent three-resistor star (wye/Y) configuration.

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