Star-Delta Conversion Calculator
Enter three elements and pick a direction to get the equivalent wye or delta network and line/phase values.
Step-by-step
- Enter valid values to begin.
Resistive (or equal-angle) elements assumed. For complex impedances, apply the same formulas with complex arithmetic. Elements are labelled a, b, c for wye and ab, bc, ca for delta; element 1 is a / ab, element 2 is b / bc, element 3 is c / ca.
Star-Delta Conversion: Wye and Delta Without the Confusion
Core Engineering Principles
A three-phase load or winding can be connected two ways. In a wye (star), three elements join at a neutral point and each one sees the line voltage divided by 1.732. In a delta, the elements sit between the lines and each one sees the full line voltage. The currents flip the same way: in a wye the line current equals the element current, in a delta the line current is 1.732 times the element current. That’s why a motor wired in wye draws only a third of the line current it would draw in delta for the same supply, which is the entire trick behind star-delta starters.
For network analysis you sometimes need to replace a wye with an equivalent delta, or the other way around, so the rest of the circuit can be simplified. For a balanced set, a delta impedance is exactly three times the wye impedance, so ZΔ = 3 × ZY. For an unbalanced set, you use the full transformation: each delta element is the sum of the pairwise wye products divided by the opposite wye element.
Balanced: ZΔ = 3 ZY • Wye: Vph = VL / √3, Iph = IL • Delta: Vph = VL, Iph = IL / √3
NEC & Standard References
The transformation comes from basic circuit theory (Kennelly, 1899), not a code. But the practical rules are in the standards. IEEE C57.12.00 covers transformer winding connections and the 30° phase shift between a delta-wye bank’s primary and secondary. NEMA MG-1 Part 2 defines lead markings T1 to T6 for wye-delta motors, and a motor with 12 leads can be connected for either series or parallel wye or delta. NEC 430.6 and the nameplate tell you which connection the motor was designed to run in. Never run a motor in a connection its nameplate doesn’t list.
1. Balanced Y to Δ: each delta resistor = 3 × 10 = 30 Ω.
2. Check with the general formula: (10×10 + 10×10 + 10×10) / 10 = 30 Ω.
3. Motor in wye: winding voltage = 400 / 1.732 = 231 V, winding current = 10 A.
4. The same motor in delta: winding voltage = 400 V, winding current = 10 / 1.732 = 5.8 A.
- Wye start, delta run. A wye-connected motor winding sees 58% of the voltage and produces about a third of the torque. That’s useful to cut inrush and bad if the load needs breakaway torque.
- Check the open transition. When a star-delta starter opens the wye, the motor coasts. If the delta contactor closes at the wrong moment you get a transient several times the nominal inrush.
- Don’t mix phase sequence. Swapping two leads on the delta side reverses the motor. Verify rotation before coupling.
- Unbalanced loads need the general formula. The 3× shortcut only applies when all three elements are equal.