Convert resistor networks between Star / Y and Delta / Δ. Also includes a practical 3-phase star-delta motor voltage and current reference.
🧠 Key Insight: In a balanced network, the shortcut is simple: RΔ = 3 × RY and RY = RΔ / 3. For unbalanced networks, use the full formulas because each branch depends on the other two branches.
🔺 Star / Y and Delta / Δ Network
RA / A to Neutral
RB / B to Neutral
RC / C to Neutral
Presets:Balanced 10Ω10 / 20 / 30Ω2.2 / 4.7 / 10kΩ
RAB / A-B branch
RBC / B-C branch
RCA / C-A branch
Presets:Balanced 30Ω30 / 60 / 90Ω
Known Equal Resistance
Known Network Type
Result
Presets:Y 10ΩΔ 30Ω
Line Voltage
Delta / DOL Current
Supply Frequency
Presets:400V / 30A415V / 50A480V / 60A
📐 Formula Reference
Y → Δ Conversion
S = RA×RB + RB×RC + RC×RA RAB = S / RC RBC = S / RA RCA = S / RB
Δ → Y Conversion
T = RAB + RBC + RCA RA = RAB×RCA / T RB = RAB×RBC / T RC = RBC×RCA / T
Balanced Shortcut
RAB = RBC = RCA = 3 × RY RA = RB = RC = RΔ / 3
3-Phase Relations
Star: VL = √3 × VPH, IL = IPH Delta: VL = VPH, IL = √3 × IPH
📋 Quick Reference
🔵 Naming
StarY / Wye
DeltaΔ / Triangle
RABA-B branch
🟢 Balanced Network
Y 10ΩΔ 30Ω
Y 100ΩΔ 300Ω
Δ 15ΩY 5Ω
🟠 Motor Star-Delta
Star winding VVL / √3
Delta winding VVL
Start current≈ 1/3 DOL
📚 Engineering Notes
Network conversion keeps terminals equivalentStar-delta conversion changes the internal resistor arrangement, but the external resistance between A, B and C terminals remains equivalent.
Balanced conversion is very fastIf all three star resistors are equal, each delta resistor is exactly three times that value. If all delta resistors are equal, each star resistor is one-third.
Motor star-delta is a different conceptStar-delta motor starting is used to reduce starting voltage and current. It is not the same as resistor network transformation. For real motor sizing, continue with the Motor Current Calculator or convert available kVA capacity using the kVA to Amps Calculator.
Check units before comparingKeep all three input resistors in the same unit. This calculator uses one unit selector to avoid mixed-unit mistakes.
What is a Star Delta Conversion Calculator?
A star delta conversion calculator converts a three-terminal resistor network between star/Y form and delta/Δ form. It is useful in circuit analysis, bridge networks, equivalent resistance problems, electrical theory and electronics learning.
Where is Y-Delta conversion used?
Y-Delta and Delta-Y conversion is commonly used when a resistor network is not a simple series or parallel circuit. By converting part of the circuit, the remaining network often becomes easier to simplify.
Practical motor workflow after star-delta checks
For 3-phase motor work, star-delta voltage and current relationships are only one part of the sizing process. After checking the starting connection, use the Motor Current Calculator to estimate running current from kW or HP, and use the kVA to Amps Calculator when the supply, transformer, generator or panel rating is given in kVA. This gives a smoother path from star-delta starting theory to practical load-current checking.
❓ Frequently Asked Questions
In star/Y, three resistors meet at a common center node. In delta/Δ, three resistors form a triangle between terminals A, B and C.
For equal resistors, delta resistance is three times star resistance: RΔ = 3 × RY. Star resistance is one-third of delta resistance: RY = RΔ / 3.
The main calculator is for resistor network conversion. A separate 3-phase motor tab is included as a quick practical reference for star-delta starting relationships.