Three-Phase Power Calculation
A three-phase power system uses three alternating voltages that are separated by 120 electrical degrees. Compared with a single-phase system, three-phase power can deliver energy more smoothly and efficiently, which makes it common in motors, industrial equipment, commercial buildings, and electrical distribution systems.
This calculator estimates three important quantities. Apparent power describes the total electrical loading placed on the system and is measured in volt-amperes. Active power is the portion that performs useful work, such as turning a motor shaft or heating an element, and is measured in watts. Reactive power supports electric and magnetic fields in inductive and capacitive equipment and is measured in volt-amperes reactive.
The calculation assumes that the voltage entered is line-to-line RMS voltage and that the current entered is line current. The system should be balanced, and the power factor must be entered as a decimal rather than a percentage. For example, enter 0.8 instead of 80%. A common mistake is using phase voltage with the line-voltage formula, which produces an incorrect result unless the formula is adjusted for the wiring configuration.
How to Calculate Three-Phase Power (step by step)
Step One: Find Apparent Power
Calculate the total apparent power using the square root of three, line-to-line voltage, and line current.
apparent power = √3 × line voltage × line current
Using the calculator’s default values:
√3 × 400 V × 10 A = 6,928.20 VA
Step Two: Find Active Power
Multiply apparent power by the power factor to determine the portion of power doing useful work.
active power = apparent power × power factor
Using the calculator’s default values:
6,928.20 VA × 0.8 = 5,542.56 W
Step Three: Find Reactive Power
Reactive power is calculated from the relationship between apparent power, active power, and reactive power.
reactive power = √(apparent power² − active power²)
Using the calculator’s default values:
√(6,928.20² − 5,542.56²) = 4,156.92 var
Understanding the Results
The default example produces 6,928.20 VA of apparent power, 5,542.56 W of active power, and 4,156.92 var of reactive power. These values describe the same balanced three-phase load from different perspectives. Apparent power represents total system demand, active power represents useful energy transfer, and reactive power represents energy exchanged with magnetic or electric fields.
The relationship between the three quantities is:
apparent power² = active power² + reactive power²
A lower power factor increases the reactive power required for the same active power, which can increase current, voltage drop, and equipment loading. For real installations, confirm the voltage convention, system balance, waveform quality, and equipment ratings before using calculated values for design or protection decisions.