The formula
Δ→Y: R_a = (R_ab × R_ca) / (R_ab + R_bc + R_ca) | Y→Δ: R_ab = R_a + R_b + (R_a R_b / R_c)
- R_ab, R_bc, R_ca
- the three sides of the delta (ohms)
- R_a, R_b, R_c
- the three arms of the star, meeting at a common node (ohms)
Worked example
A delta with R_ab = 10 Ω, R_bc = 20 Ω, R_ca = 30 Ω.
- Sum of the sides: 10 + 20 + 30 = 60 Ω
- R_a = (10 × 30) / 60 = 5 Ω
- R_b = (10 × 20) / 60 = 3.33 Ω
- R_c = (20 × 30) / 60 = 10 Ω
Star arms of 5 Ω, 3.33 Ω and 10 Ω replace the delta exactly.
Where you'll use it
Unbalanced bridge problems, three-phase load conversion, and any network where series-parallel reduction stalls. For a balanced delta the star arms are simply one third of each side.