Three Phase Calculator
Calculate power, voltage, and current in three-phase AC systems
Calculate Three Phase Power
RMS voltage between phase and neutral
RMS current in each phase
Angle between voltage and current (degrees)
Ratio of real power to apparent power
Three Phase Power Results
Power Triangle: S² = P² + Q²
Line Relations (delta): V_line = V_ph, I_line = √3 × I_ph
Total Power: P = √3 × V_line × I_line × cos(φ)
System Analysis
Example Calculation
Industrial Motor Drive
Application: 3-phase induction motor
Connection: Delta (Δ)
Phase voltage: 400 V
Line current: 8.6 A
Power factor: 0.84
Calculation
Apparent Power: S = √3 × V_line × I_line = √3 × 400 × 8.6 = 5.96 kVA
Active Power: P = S × cos(φ) = 5.96 × 0.84 = 5.0 kW
Reactive Power: Q = S × sin(φ) = 5.96 × 0.543 = 3.24 kVAR
Phase Current: I_ph = I_line / √3 = 8.6 / 1.732 = 5.0 A
Total power delivered to motor: 5.0 kW
Three Phase Formulas
S = √3 × V_L × I_L
Apparent Power
P = S × cos(φ)
Active Power
Q = S × sin(φ)
Reactive Power
Connection Types
Star (Y) Connection
Delta (Δ) Connection
Power Types
Power Factor Guide
0.95 - 1.0: Excellent
Very efficient, minimal reactive power
0.85 - 0.95: Good
Acceptable for most applications
0.70 - 0.85: Poor
Power factor correction needed
< 0.70: Very Poor
Significant efficiency losses
Understanding Three Phase Power Systems
What is Three Phase Power?
Three-phase power is a method of electrical power transmission that uses three alternating currents, each 120° out of phase with each other. This system provides constant power delivery and is more efficient than single-phase systems for large loads.
Key Advantages
- •More efficient power transmission
- •Constant instantaneous power
- •Reduced conductor material requirements
- •Better motor performance
Power Relationships
Power Types Explained
Note: This calculator assumes balanced three-phase systems where all phases have equal voltage magnitude and are equally spaced in time.
Applications & Use Cases
Industrial Motors
Induction motors, synchronous motors, variable frequency drives
Power Transmission
Grid transmission, distribution systems, power substations
Heavy Machinery
Pumps, compressors, elevators, HVAC systems
Design Guidelines
Power Factor Improvement
- • Install power factor correction capacitors
- • Use synchronous motors where possible
- • Minimize reactive loads (inductors, transformers)
- • Regular power quality monitoring
- • Proper cable sizing and installation
System Efficiency
- • Balance loads across all three phases
- • Minimize line losses through proper conductor sizing
- • Regular maintenance of electrical connections
- • Use high-efficiency motors and drives
- • Monitor harmonics and power quality