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SeriesCalc

🔌 AC Power Calculator

Calculate Real, Reactive, and Apparent Power in Alternating Current (AC) circuits.

Inputs

°

Results

Real Power (P)
0.00 W
Reactive Power (Q)
0.00 VAR
Apparent Power (S)
0.00 VA
Power Factor (PF)
0.0000

Power Triangle

P (Real)Q (React.)S (Apparent)θ

Calculator Description

The AC power calculator determines the real (active) power, reactive power, apparent power, and power factor of an alternating-current circuit supplied with sinusoidal voltage and current. Unlike a DC circuit, an AC circuit has a phase difference between voltage and current, so the simple product of the two is not the power that actually does useful work.

What this calculator finds

From the supplied voltage (V), current (I) and phase angle (θ) it computes the three power components and the power factor, for both single-phase and three-phase (with the √3 factor) systems.

Why it matters

  • Sizing cables, breakers and transformers (rated on apparent power) and checking for overload
  • Deciding whether power-factor correction is needed and sizing reactive compensation
  • Estimating true energy consumption (real power) and possible billing savings

Formula

AC Power Formulas

With phase angle θ between voltage and current, apparent power S is the product of the magnitudes, real power P is the work-producing component, and reactive power Q is the oscillating (non-working) component.

S=VIS = V I
P=Scos⁡(θ)=VI PFP = S\cos(\theta) = V I\,\text{PF}
Q=Ssin⁡(θ)Q = S\sin(\theta)
PF=cos⁡(θ)\text{PF} = \cos(\theta)

* For 3-phase systems, multiply apparent power by √3: S = √3 × V_L × I_L

  • S — Apparent Power (Volt-Amperes, VA)
  • P — Real / Active Power (Watts, W)
  • Q — Reactive Power (Volt-Amperes Reactive, VAR)
  • θ — Phase angle between voltage and current [° or rad]
  • V, I — Voltage [V] and Current [A]
  • PF — Power Factor [−1 to 1, usually 0 to 1]

How the formula works

  • As power factor PF approaches 1 (θ → 0), real power P approaches apparent power S, meaning energy is used efficiently.
  • A larger θ lowers cos(θ) and raises reactive power Q = S·sin(θ), requiring a larger current to deliver the same real power.
  • Three-phase systems exploit the 120° phase shift between phases, so the √3 factor appears when using line-to-line voltage.

Worked example

For a single-phase circuit with V = 230 V, I = 10 A and θ = 36.87° (cosθ = 0.8): S = 2300 VA, P = 2300 × 0.8 = 1840 W, and Q = 2300 × sin(36.87°) = 1380 VAR. The 0.8 power factor means 20% of the supplied current is the reactive component.

Useful Tips

Practical tips

  • A low power factor forces a larger current for the same load, increasing I²R wiring losses and voltage drop; PF ≥ 0.9 is usually recommended.
  • Induction motors, transformers and fluorescent lamps are lagging (inductive) loads that generate reactive power, so monitor the average power factor.
  • Connecting capacitors in parallel compensates reactive power and raises the power factor.

Limitations & cautions

  • This calculator assumes ideal sinusoids and linear loads; harmonics from non-linear loads (rectifiers, etc.) must be treated separately.
  • If θ is unknown, measure it directly with a wattmeter or power-factor meter for accuracy.
  • Three-phase values use line-to-line voltage (V_L) and line current (I_L); using phase voltage changes the √3 factor.