Inputs — Voltage & Current
Results
Real Power
—
kW
Apparent Power
—
kVA
Reactive Power
—
kVAR
Phase Voltage (Vph)—
Phase Current (Iph)—
Phase Angle (θ)—
Connection—
Three-Phase vs Single-Phase Power
Three-phase power systems use three conductors each carrying alternating current waveforms separated by 120°. Unlike single-phase systems where power pulsates at twice the line frequency, balanced three-phase power delivery is constant and smooth. This makes three-phase ideal for industrial motors, large heating elements, and heavy commercial equipment.
Key advantages of three-phase over single-phase:
- Constant instantaneous power — no pulsation — means smoother motor operation and less vibration
- Higher power density — approximately 1.73× more power for the same current and conductor size
- More economical transmission — less copper required for equivalent power delivery
- Three-phase motors are simpler, more efficient and self-starting without auxiliary windings
Star (Y) vs Delta (Δ) Connection
The two fundamental ways to connect a three-phase load or source determine how line and phase quantities relate:
- Star (Y): All three windings share a common neutral point. Phase voltage = VL / √3. Line current = Phase current. Neutral conductor carries unbalanced current. Common in distribution systems (e.g., 415 V line / 240 V phase).
- Delta (Δ): Windings form a closed loop with no neutral. Phase voltage = VL. Phase current = IL / √3. Used in industrial motor windings and transmission systems.
Three-Phase Power Formulas Reference
Apparent Power: S = √3 × VL × IL [VA or kVA]
Real Power: P = √3 × VL × IL × cos(φ) [W or kW]
Reactive Power: Q = √3 × VL × IL × sin(φ) [VAR or kVAR]
Power Factor: PF = cos(φ) = P / S
Star — Phase Voltage: Vph = VL / √3 ≈ VL / 1.7321
Star — Phase Current: Iph = IL
Delta — Phase Voltage: Vph = VL
Delta — Phase Current: Iph = IL / √3 ≈ IL / 1.7321
Line Current from kW: IL = (P × 1000) / (√3 × VL × PF)
Real Power: P = √3 × VL × IL × cos(φ) [W or kW]
Reactive Power: Q = √3 × VL × IL × sin(φ) [VAR or kVAR]
Power Factor: PF = cos(φ) = P / S
Star — Phase Voltage: Vph = VL / √3 ≈ VL / 1.7321
Star — Phase Current: Iph = IL
Delta — Phase Voltage: Vph = VL
Delta — Phase Current: Iph = IL / √3 ≈ IL / 1.7321
Line Current from kW: IL = (P × 1000) / (√3 × VL × PF)
Frequently Asked Questions
Three-phase power delivers the same amount of energy using less wire and with constant power delivery (no zero-crossing pulsations). In single-phase AC, instantaneous power oscillates at twice the supply frequency, hitting zero 100 times per second (at 50 Hz). Balanced three-phase power is constant at all times. This means motors run smoother, transformers are smaller, and transmission losses are lower for the same transmitted power — approximately 25% less copper for the same power delivery compared to single-phase.
In a star (Y) connected system, line voltage (VL) is the voltage measured between any two lines, while phase voltage (Vph) is the voltage across each winding — equal to VL / √3. For a 415 V star system, Vph = 415 / 1.732 ≈ 240 V, which is why standard Australian and UK outlets deliver 240 V from a 415 V three-phase supply. In a delta (Δ) system, phase voltage equals line voltage because each winding connects directly across two lines.
A balanced three-phase load has equal impedances on all three phases, resulting in equal line currents displaced by exactly 120°. This produces zero neutral current in a star system and makes calculations straightforward — you only need to analyze one phase. Industrial motors, large HVAC compressors, three-phase heaters and industrial drives are typically balanced loads. Unbalanced loads (e.g., uneven distribution of single-phase loads across three phases) carry neutral current and require per-phase analysis.
Use the formula: IL = (kVA × 1000) / (√3 × VL), where VL is the line-to-line voltage in volts. For example, a 100 kVA transformer at 415 V line voltage: IL = (100 × 1000) / (1.732 × 415) = 100,000 / 718.8 ≈ 139 A. This gives you the line current. For a star connection, phase current equals line current. For delta, phase current = IL / √3 ≈ 80 A. Use the calculator above to automate this for any values.