Three-Phase Power Calculator (Balanced Load)
Find real, reactive, and apparent power for a balanced three-phase load from line voltage, line current, and power factor, for star or delta connections.
⚡ What is Three-Phase Power?
Three-phase power is the electrical power delivered by a three-phase supply, three AC voltages 120 degrees apart, to a balanced load. For a balanced load, identical impedance on all three phases, the total apparent power is S = sqrt(3) x VL x IL, using line voltage and line current directly, with real power P = S x cos(phi) and reactive power Q = S x sin(phi) following the same power-triangle relationship used in single-phase analysis.
Electrical engineers use this formula constantly when sizing three-phase motors, transformers, generators, and industrial feeders, since three-phase power delivers more capacity per unit of conductor material than single-phase, and produces smooth, non-pulsating instantaneous power under balanced conditions, a major advantage for rotating machinery.
A common point of confusion is thinking the sqrt(3) formula changes between star (wye) and delta connections. It does not, when line voltage and line current are used directly, the same P = sqrt(3) VL IL cos(phi) formula gives total power regardless of connection type. What differs between star and delta is only the relationship between line and phase quantities, not the total power itself.
This calculator computes total real, reactive, and apparent power directly from your line voltage, line current, and power factor, and also reports the equivalent phase voltage and phase current for your chosen star or delta connection.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Star-Connected Industrial Motor
VL = 400 V, IL = 20 A, PF = 0.85, star connection
Example 2 — Delta-Connected Feeder
VL = 415 V, IL = 50 A, PF = 0.9, delta connection
Example 3 — Unity Power Factor Resistive Heater Bank
VL = 230 V, IL = 15 A, PF = 1.0, star connection
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for three-phase power?
For a balanced three-phase load, apparent power S = sqrt(3) x VL x IL, real power P = S x PF, and reactive power Q = S x sin(acos(PF)), where VL and IL are line (not phase) voltage and current, and PF is the power factor.
Why does the formula use sqrt(3) instead of 3?
The sqrt(3) factor comes from the 120-degree phase relationship between the three phases, when line quantities (rather than phase quantities) are used directly, this single sqrt(3) factor correctly accounts for the vector geometry of a balanced three-phase system without needing separate per-phase calculations.
What is the difference between line and phase voltage/current?
Line voltage and current are measured between the supply conductors themselves, phase voltage and current are measured across or through a single winding or load element. In a star connection, line voltage is sqrt(3) times phase voltage, in a delta connection, line current is sqrt(3) times phase current.
Does the sqrt(3) power formula change between star and delta connections?
No, when you use line voltage and line current directly, P = sqrt(3) x VL x IL x PF gives the same total power regardless of whether the load is star or delta connected, the star/delta choice only affects the relationship between line and phase quantities, not the total power formula itself.
What does 'balanced load' mean?
A balanced three-phase load has identical impedance (same magnitude and phase angle) on all three phases, resulting in equal current magnitudes on each line, all 120 degrees apart. Most industrial three-phase motors and evenly distributed loads are treated as balanced for analysis.
Why is three-phase power preferred for large loads?
Three-phase power delivers more power per unit weight of conductor than single-phase for the same voltage and current rating, and under balanced conditions the total instantaneous power is constant (non-pulsating), unlike single-phase power, which pulses at twice the line frequency, this smoother power delivery is especially valuable for motors.
How do I find phase voltage and phase current from line values?
In a star (wye) connection, phase voltage = line voltage / sqrt(3), and phase current = line current. In a delta connection, phase voltage = line voltage, and phase current = line current / sqrt(3). This calculator computes both automatically based on the selected connection type.
What happens if the load is not balanced?
This calculator assumes a perfectly balanced load. An unbalanced three-phase load has different impedance on each phase, so total power must be found by analyzing (and summing) each phase individually, a single sqrt(3) formula no longer applies directly.
What is power factor in a three-phase system?
Power factor in a balanced three-phase system is the same cos(phi) used in single-phase analysis, the cosine of the phase angle between voltage and current on any one phase, since all three phases are identical in a balanced system, one power factor value describes the whole load.
What units does this calculator use?
Line voltage is entered in volts, line current in amperes, and power factor as a decimal between 0 and 1. Results are shown in watts (W) for real power, volt-amperes-reactive (VAR) for reactive power, and volt-amperes (VA) for apparent power.