AC Power (Real / Reactive / Apparent)
Splits the power of a single-phase AC load into its three parts: the real power that does work, the reactive power that flows back and forth to build magnetic and electric fields, and the apparent power the supply and wiring must carry. Give the voltage, the current and the power factor. The live triangle below the Solution draws the three to scale as you type. Use it to read a motor or appliance nameplate, or to see how much of a circuit’s capacity a load really takes.
Equations
S = V·I P = S·cos φ Q = S·sin φ S² = P² + Q²
V and I are the RMS voltage and current, the values a meter reads. S is the apparent power in kVA, P the real power in kW and Q the reactive power in kVAR [1]. φ is the phase angle between the voltage and the current, and cos φ is the power factor. The three powers form a right triangle with S as the hypotenuse, so a lower power factor means more current for the same real power. The live panel also gives φ in degrees.
The page doesn’t ask whether the current leads or lags. Q is shown as a positive size. A motor or other inductive load draws lagging (positive) reactive power. A capacitor bank supplies it.
Limits and common mistakes
- This is the single-phase formula. For a three-phase load use the Three-Phase Power calculator, which adds the factor √3.
- The power factor here is the displacement power factor of sine-wave voltage and current. Loads with distorted current, such as rectifiers and LED drivers, have a lower true power factor than cos φ.
- Utilities bill real power (kWh), but cables, breakers and transformers are sized on apparent power or current.
- To raise a low power factor, size a capacitor with the Power Factor Correction calculator.
Worked example
A single-phase air compressor on a 230 V supply draws 18.5 A at a power factor of 0.82. How much real, reactive and apparent power does it take?
- Enter Voltage (V) 230 V and Current (I) 18.5 A.
- Enter Power factor (cos φ) 0.82 and press Solve. The Solution shows:
Real power (P): 3.4891 kW
Reactive power (Q): 2.43541 kVAR
Apparent power (S): 4.255 kVA
Check: 230 × 18.5 = 4,255 VA, and 0.82 × 4.255 = 3.489 kW. The triangle closes: 3.4891² + 2.43541² = 12.174 + 5.931 = 18.105, which is 4.255².
