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).

5 Fun Facts about AC Power

Power factor hides amps

Cut pf from 1.0 to 0.5 and the current doubles for the same watts. Same load, twice the copper heating (\(I^2R\) losses).

Heat tax

pf tells you the angle

Power factor is just \(\cos\varphi\). A pf of 0.8 means voltage and current are ~37° apart; 0.95 is only ~18°.

Triangle decoder

Capacitors pay back VARs

Inductive motors “borrow” reactive power; capacitor banks “lend” it back. Utilities install massive caps to pull pf toward 1 and free grid capacity.

Grid balancing

√3 is everywhere in 3φ

Balanced three‑phase magic: line voltage = phase voltage × √3, and S = √3 × VLL × IL. That constant drops out of the geometry of 120° phases.

Three-phase geometry

Leading vs lagging flips Q

Inductive loads make positive Q (lagging). Capacitive correction pushes Q negative, sometimes even past zero—data centers intentionally run slightly leading to offset cable inductance.

Q sign flip

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