How to use the Star-Delta Conversion Calculator
- 1. Pick the directionDelta → star or star → delta.
- 2. Enter the three resistorsRab, Rbc, Rca for delta, or Ra, Rb, Rc for star.
- 3. Get the equivalentEach converted value with its formula.
Star-delta formulas
Delta to star: each star arm = product of the two delta sides meeting at that node ÷ sum of all three sides. Ra = Rab Rca / (Rab + Rbc + Rca), Rb = Rab Rbc / Σ and Rc = Rbc Rca / Σ.
Star to delta: each delta side = sum of the pair products ÷ the star arm opposite to it. Rab = (RaRb + RbRc + RcRa) / Rc, Rbc = (...) / Ra and Rca = (...) / Rb.
Worked example: Rab = 10 Ω, Rbc = 20 Ω, Rca = 30 Ω. Σ = 60 Ω, so Ra = 300/60 = 5 Ω, Rb = 200/60 = 3.33 Ω and Rc = 600/60 = 10 Ω. Going back from Ra = 5, Rb = 10, Rc = 15 Ω, the sum of products is 50 + 150 + 75 = 275, so Rab = 275/15 = 18.33 Ω, Rbc = 55 Ω and Rca = 27.5 Ω.
When to use it and exam questions
Use the transform when resistors are neither in series nor in parallel, such as in a bridge circuit. Converting one delta to a star usually turns the network into simple series-parallel parts. For a balanced network, R(star) = R(delta) / 3.
- Find the equivalent resistance between two terminals of an unbalanced Wheatstone bridge.
- Convert a balanced delta of 30 Ω into star (10 Ω each).
- Find the current drawn from a source connected to a bridge network.
The same formulas work for impedances in AC circuits, using complex numbers.
Frequently asked questions
Which star arm goes with which node?
Ra connects node A to the centre. It uses the two delta sides that touch A, which are Rab and Rca.
Does the transform change anything outside the network?
No. Currents and voltages at terminals A, B and C stay exactly the same. Only the inside of the network changes.
What about balanced three-phase loads?
For equal impedances, star = delta / 3 and delta = 3 × star. This is why a motor draws one third of the current when started in star.
Is this tool free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form.