Three Phase
Calculate apparent, active, and reactive power for balanced three-phase AC circuits from line voltage, current, and power factor. Free online 3-phase calculator with charts.
About This Calculator
The Three Phase Power Calculator helps electrical engineers, technicians, electricians, and students analyze balanced three-phase AC circuits. Three-phase power systems are the backbone of industrial and commercial electrical distribution, offering higher efficiency and more constant power delivery compared to single-phase systems.
This calculator computes apparent power (S), active power (P), and reactive power (Q) using the standard three-phase formulas: S = √3 × VL × IL, P = √3 × VL × IL × PF, and Q = √3 × VL × IL × sin φ, where PF = cos φ is the power factor and φ is the phase angle between voltage and current. The calculator also derives phase voltage and phase current based on Star (Wye) or Delta connection type.
In a Star connection, the phase voltage is VL / √3 and phase current equals line current. In a Delta connection, phase voltage equals line voltage and phase current is IL / √3. Despite these differences, the total power equations remain the same for both configurations when using line quantities. Understanding these relationships is essential for proper motor connection, transformer sizing, and power system design.
Regional Notes: Standard three-phase voltages differ worldwide. North America commonly uses 208V and 480V systems. Europe and the UK standardize on 400V. India, Australia, and many Asian countries use 415V. Always consult local electrical codes (NEC in the US, BS 7671 in the UK, IS 732 in India) for installation requirements. Power factor correction is mandated in many industrial installations to avoid utility penalties.
Frequently Asked Questions
What is a three-phase power system and how does it work?
A three-phase power system uses three alternating currents that are 120 degrees out of phase with each other. This configuration delivers constant power transfer, reduces conductor material requirements, and enables higher power transmission efficiency compared to single-phase systems. Three-phase power is the standard for industrial, commercial, and large residential buildings worldwide.
How do you calculate apparent power in a three-phase circuit?
Apparent power (S) in a balanced three-phase circuit is calculated using the formula S = √3 × V_line × I_line, where V_line is the line-to-line voltage and I_line is the line current. The result is in volt-amperes (VA) or kilovolt-amperes (kVA). For example, a circuit with 415V line voltage and 100A line current has 415 × 100 × 1.732 = 71.88 kVA.
What is the difference between active power and apparent power?
Active power (P), measured in watts (W), is the real power that does useful work like turning motors or heating elements. Apparent power (S), measured in volt-amperes (VA), is the total power supplied by the source. The ratio of active to apparent power is the power factor (PF = P/S). Reactive power (Q), measured in VAR, oscillates between source and load due to inductive or capacitive elements.
How does power factor affect three-phase power calculations?
Power factor (PF = cos φ) represents the phase angle between voltage and current. A PF of 1.0 means all power is active (purely resistive load). Lower PF values (0.7-0.9 typical for motors) indicate more reactive power. Active power P = √3 × V × I × PF, while reactive power Q = √3 × V × I × sin(arccos(PF)). Improving PF reduces current draw and energy losses.
What is the difference between Star (Wye) and Delta connections?
In a Star (Wye) connection, phase voltage equals line voltage divided by √3, and phase current equals line current. In a Delta connection, phase voltage equals line voltage, and phase current equals line current divided by √3. The total power remains the same for both connections with identical line voltage, line current, and power factor values.
What are standard three-phase voltage levels around the world?
Standard three-phase line-to-line voltages vary by region: 208V and 480V are common in North America (US/Canada), 400V is standard in Europe and the UK, 415V in India, Australia, and many Asian countries, 380V in China and Russia, and 440V in some Middle Eastern and African countries. Always verify local utility specifications for your installation.
How do I convert three-phase power from kVA to kW?
To convert apparent power (kVA) to real power (kW), multiply by the power factor: kW = kVA × PF. For example, a 100 kVA transformer with PF = 0.85 can deliver 100 × 0.85 = 85 kW of real power. The remaining power is reactive (kVAR), calculated as kVAR = kVA × sin(arccos(PF)).
What causes low power factor and how can it be corrected?
Low power factor is primarily caused by inductive loads such as induction motors, transformers, welding equipment, and fluorescent lighting ballasts. It can be corrected by adding power factor correction capacitors, using synchronous motors, installing automatic PF correction panels, or using variable frequency drives (VFDs) for motor speed control. Utilities often charge penalties for PF below 0.9.