AC Power Calculator — Real (P), Apparent (S), Reactive (Q)

Enter voltage and current, then either power factor (0–1) or phase angle \( \varphi \) (degrees). Choose single- or three-phase.

Inputs

For three-phase, use line-to-line voltage and line current.
RMS voltage
RMS current
pf = \( \cos\varphi \) (0 to 1). Choose lag/lead for the sign of \( Q \).
If provided, overrides pf. Positive = lagging.

Results

Results will appear here.

Formulas use RMS values. For three-phase (balanced), \(k=\sqrt{3}\) with line-to-line \(V\) and line \(I\).

How Alternating Current (AC) Power Works

In AC circuits, voltage and current can be out of phase by an angle \(\varphi\). This creates three related kinds of power:

  • Apparent power \(S\) (volt-amperes, VA): \(\; S = V \times I\)
  • Real power \(P\) (watts, W): \(\; P = V \times I \times \cos\varphi\)
  • Reactive power \(Q\) (VAR): \(\; Q = V \times I \times \sin\varphi\)

These form the power triangle: \(\; S^2 = P^2 + Q^2 \;\) and the power factor \(\mathrm{pf} = P/S = \cos\varphi\).

Three-Phase (Balanced) Systems

For line-to-line voltage \(V\) and line current \(I\):

  • \( S = \sqrt{3}\, V I \)
  • \( P = \sqrt{3}\, V I \cos\varphi \)
  • \( Q = \sqrt{3}\, V I \sin\varphi \)

Tip: Use RMS quantities. If you only know power factor, \(\varphi = \arccos(\mathrm{pf})\).

FAQs & Tips

Lagging vs. leading?

Inductive loads are lagging (current lags voltage, positive \(Q\)); capacitive loads are leading (current leads voltage, negative \(Q\)).

Why do S, P, Q units differ?

\(S\) is in VA, \(P\) in W, and \(Q\) in VAR—symbols help separate total apparent power, useful real power, and energy-swapping reactive power.

Privacy

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Quick Example (Single-Phase)

Given \(V = 230\,\text{V}\), \(I = 3.5\,\text{A}\), \(\mathrm{pf} = 0.8\) (lagging):

  • \( S = V I = 230 \times 3.5 = 805\,\text{VA} \)
  • \( P = V I \cos\varphi = 230 \times 3.5 \times 0.8 = 644\,\text{W} \)
  • \( Q = \sqrt{S^2 - P^2} \approx 483\,\text{VAR} \) (positive → lagging/inductive)

Checkpoint: \( S^2 \approx P^2 + Q^2 \) should hold (allow rounding).

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