What is a 3-phase Delta/Wye calculator?
Three-phase power systems can connect loads and sources in two common ways: delta (Δ) and wye (Y or star). The relationship between line and phase voltages, currents and impedances is different in each configuration.
This calculator helps you:
- Convert between line and phase voltages and currents
- Compare Δ and Y connected loads at the same line voltage
- Determine equivalent impedances between delta and wye networks
- Size motors, heaters and distribution equipment correctly
Basics of delta and wye connections
In a delta (Δ) connection, the three phase windings or loads form a closed loop. Line conductors connect to each corner of the triangle.
In a wye (Y) connection, one end of each phase is tied to a common neutral point, and the line conductors connect to the remaining ends.
| Quantity | Wye (Y) connection | Delta (Δ) connection |
|---|---|---|
| Line voltage vs phase voltage | VL = √3 × VPH | VL = VPH |
| Line current vs phase current | IL = IPH | IL = √3 × IPH |
| Apparent power | S = √3 × VL × IL | |
Voltage and current relationships
Wye (Y) connected loads
- Phase voltage: VPH = VL / √3
- Line current: IL = IPH
Delta (Δ) connected loads
- Phase voltage: VPH = VL
- Line current: IL = √3 × IPH
The calculator applies these relations automatically to show how a given line voltage and load connection translate into per-phase quantities.
Delta–wye impedance conversion
When converting a three-branch network from wye to delta or vice versa, the branch impedances must be adjusted to preserve the same line-to-line behavior.
From wye to delta
For wye impedances ZA, ZB, ZC, the equivalent delta impedances are:
- ZAB,Δ = (ZAZB + ZBZC + ZCZA) / ZC
- ZBC,Δ = (ZAZB + ZBZC + ZCZA) / ZA
- ZCA,Δ = (ZAZB + ZBZC + ZCZA) / ZB
From delta to wye
For delta impedances ZAB, ZBC, ZCA, the equivalent wye impedances are:
- ZA,Y = (ZAB × ZCA) / (ZAB + ZBC + ZCA)
- ZB,Y = (ZAB × ZBC) / (ZAB + ZBC + ZCA)
- ZC,Y = (ZBC × ZCA) / (ZAB + ZBC + ZCA)
The calculator uses these formulas behind the scenes so you can focus on entering nameplate data and seeing the equivalent values.
Worked examples
Example 1 – 400 V supply, wye-connected load
- Line voltage: VL = 400 V
- Connection: wye (Y)
Phase voltage:
VPH = 400 / √3 ≈ 231 V
If each phase draws 10 A, then:
- IL = IPH = 10 A
- S = √3 × 400 × 10 ≈ 6.93 kVA
Example 2 – same load in delta
To draw the same power at 400 V in delta, the per-phase impedance must change. The calculator can show the required phase currents and new per-phase impedance so that S stays approximately equal.
Design tips for 3-phase Delta/Wye systems
- Know your line voltage: A “400 V” system usually refers to line-to-line voltage. Phase voltage is lower in wye connections.
- Check nameplate connection: Motors and heaters may support Y, Δ or both (e.g. 230/400 V). Connecting incorrectly can over- or under-voltage the windings.
- Balance the phases: Uneven loading between phases causes neutral currents, voltage imbalance and overheating.
- Consider starting methods: Star–delta motor starters temporarily use Y connection to limit starting current before switching to Δ for full power.
This calculator helps you visualize how three-phase quantities change between delta and wye connections so you can choose the right configuration, verify ratings, and design safer distribution and motor control systems.
