Electrical · Free Calculator
Delta Star (Δ Y) Conversion Calculator
Transform a delta (Δ) network of three resistances into its equivalent star (Y), or a star into delta, for circuit analysis and three phase load calculations.
Δ to YY to ΔNetwork analysisThree phase loads
Ω
Ω
Ω
Ra10 Ω
Rb10 Ω
Rc10 Ω
How this result was calculated
- Ra = Rab × Rca ÷ (Rab + Rbc + Rca), and similarly for Rb and Rc
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Delta Star Transformation
Δ → Y: Ra = Rab·Rca ÷ ΣRΔ, Rb = Rab·Rbc ÷ ΣRΔ, Rc = Rbc·Rca ÷ ΣRΔ
Y → Δ: Rab = P ÷ Rc, Rbc = P ÷ Ra, Rca = P ÷ Rb, P = RaRb + RbRc + RcRa
Y → Δ: Rab = P ÷ Rc, Rbc = P ÷ Ra, Rca = P ÷ Rb, P = RaRb + RbRc + RcRa
Worked example
Three equal 30 Ω delta resistors are equivalent to three 10 Ω star resistors. For balanced networks RY = RΔ ÷ 3.
Key insight: a balanced delta heater bank draws three times the power of the same elements connected in star, because each element sees √3 times the voltage.
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Frequently Asked Questions
What is delta star conversion used for?
To simplify bridge and three phase networks that cannot be reduced with series and parallel rules alone.
What is the rule for balanced loads?
RY = RΔ ÷ 3 and RΔ = 3 × RY.
Does it work for AC impedances?
Yes, the same formulas apply with complex impedances.
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