About the Star-Delta Conversion Calculator
This star-delta conversion calculator transforms a three-terminal resistor network from delta (Δ, also drawn as a pi) into an equivalent star (Y, wye or tee), or back again. Enter the three resistors of the network you have and it returns the three resistors of the equivalent network, plus the resistance measured between each pair of terminals — which is identical for both forms and lets you check the conversion.
The Δ–Y (Kennelly) transform is the standard trick for solving bridge circuits and other networks that cannot be reduced with series and parallel rules alone. Electronics and electrical engineering students use it constantly in circuit-analysis courses, and it is also used to design resistive attenuators (pi and tee pads) and to reason about three-phase loads, where a balanced delta load of R per phase equals a star load of R/3.
Terminals are labelled A, B and C. In the delta, Rab sits between terminals A and B, and so on; in the star, Ra joins terminal A to the centre point. The same formulas apply to impedances in AC circuits when complex arithmetic is used; this tool handles resistances.
How to use the star-delta conversion calculator
- 1Choose the direction: delta to star or star to delta.
- 2Label the three terminals A, B and C on your circuit.
- 3Enter the three resistor values of the network you have.
- 4Read the equivalent network’s resistors.
- 5Check that the terminal-to-terminal resistances match your original network.
Formula and method
Two three-terminal networks are equivalent when the resistance between every pair of terminals is the same with the third terminal open. Solving those three equations gives the Kennelly transforms. Going from delta to star, each star resistor equals the product of the two delta resistors touching that terminal divided by the sum of all three. Going from star to delta, each delta resistor equals the sum of the pairwise products of the star resistors divided by the star resistor on the opposite terminal.
For a balanced network the formulas reduce to RY = RΔ/3 and RΔ = 3RY. The calculator also reports the terminal-to-terminal resistances (Ra + Rb for the star, Rab ∥ (Rbc + Rca) for the delta), which must match for the two networks — a quick way to verify the result.
- Rab, Rbc, Rca
- Delta resistors between terminal pairs
- Ra, Rb, Rc
- Star resistors from each terminal to the centre node
- Σ
- Sum of the three delta resistors
- P
- Sum of pairwise products of the star resistors
Worked examples
Delta 30 Ω / 60 Ω / 90 Ω to star
Σ = 180 Ω. Ra = 30 × 90 ÷ 180 = 15 Ω, Rb = 30 × 60 ÷ 180 = 10 Ω and Rc = 60 × 90 ÷ 180 = 30 Ω. Check A–B: the star gives 15 + 10 = 25 Ω and the delta gives 30 ∥ 150 = 25 Ω.
Star 15 Ω / 10 Ω / 30 Ω back to delta
P = 15×10 + 10×30 + 30×15 = 900. Rab = 900 ÷ 30 = 30 Ω, Rbc = 900 ÷ 15 = 60 Ω and Rca = 900 ÷ 10 = 90 Ω — the original delta.
Balanced delta of 3 × 300 Ω
For equal resistors each star leg is one third of a delta leg: 300 ÷ 3 = 100 Ω. Either network measures 200 Ω between any two terminals.
Frequently asked questions
How do you convert delta to star?+
Each star resistor equals the product of the two delta resistors connected to that terminal, divided by the sum of all three delta resistors. For example with Rab = 30, Rca = 90 and a sum of 180 Ω, Ra = 30 × 90 / 180 = 15 Ω.
How do you convert star to delta?+
Add the three pairwise products of the star resistors (RaRb + RbRc + RcRa), then divide by the star resistor opposite each delta branch: Rab = P/Rc, Rbc = P/Ra and Rca = P/Rb.
When is a star-delta transformation needed?+
Whenever a network cannot be simplified with series and parallel rules — the unbalanced Wheatstone bridge is the classic case. Converting one triangle of resistors to a star usually turns the rest of the circuit into simple series-parallel combinations.
What is the relationship for a balanced network?+
If all three resistors are equal, RY = RΔ / 3 and RΔ = 3 × RY. In three-phase power the same factor of three explains why star-delta motor starters reduce starting current and torque to one third.
Are star and wye the same thing? What about pi and tee?+
Yes. Star, wye (Y) and tee (T) are the same topology drawn differently, and delta (Δ) and pi (π) are the same as each other. Attenuator designers usually say pi and tee; power engineers say delta and wye.