Real, apparent, and reactive electrical power
In alternating current (AC) circuits, power comprises three vector components forming the power triangle: Real Power (P in Watts), Apparent Power (S in Volt-Amperes, VA), and Reactive Power (Q in Volt-Amperes Reactive, VAR).
Real power is the actual useful work done by the circuit: P = V × I × cos(θ) for single-phase systems, where cos(θ) is the power factor (PF). For balanced three-phase systems: P = √3 × V_L × I_L × PF, using line-to-line voltage V_L.
Apparent power S = V × I (or √3 × V_L × I_L for 3-phase) represents the total capacity the electrical grid and wiring must deliver. Reactive power Q = √(S² − P²) represents energy oscillating between inductive/capacitive magnetic fields and the supply.
Worked example: 3-phase industrial motor
A three-phase 400V motor draws 25 Amperes with a power factor of 0.85.
Apparent power S = √3 × 400 V × 25 A = 17,320.5 VA (17.32 kVA).
Real power P = 17,320.5 VA × 0.85 = 14,722.4 Watts (14.72 kW).
Running 8 hours per day consumes 14.72 kW × 8 h = 117.76 kWh daily.
Inputs for the power calculator
System type
Choose Single-Phase AC, Three-Phase AC, or DC.
Power factor (PF)
A decimal between 0.1 and 1.0 (1.0 for purely resistive loads like heaters, 0.8 to 0.85 typical for electric motors).
CALCULATOR QUESTIONS
Electrical power & energy calculator questions
What is the difference between kW and kVA?
kW (Kilowatts) is real power that does useful work. kVA (Kilovolt-Amps) is apparent power including reactive energy. kW = kVA × Power Factor.
Why is three-phase power multiplied by the square root of 3 (1.732)?
Because in three-phase systems, line-to-line voltage is √3 times greater than line-to-neutral voltage due to the 120-degree phase separation between phases.