What’s the difference between P, S, and Q?

Real power (P, watts) does useful work, reactive power (Q, VAR) stores and releases energy each cycle, and apparent power (S, VA) combines both (S = V × I). The power factor is P/S.

Should I use power factor or phase angle?

Either. Power factor is cos(φ) and ranges from 0 to 1; φ is the phase angle between voltage and current (lagging is positive). The calculator accepts one and computes the other.

How do three-phase calculations differ?

For balanced three-phase with line-to-line voltage and line current: S = √3 × V × I, P = √3 × V × I × pf, Q = √3 × V × I × sin(φ).

Yes. All calculations run entirely in your browser.

AC Power Calculator (Alternating Current) – Real (P), Apparent (S), Reactive (Q)

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.

System: For three-phase, use line-to-line voltage and line current.

Voltage (V)

RMS voltage

Current (I)

RMS current

Power Factor (pf)

pf = \(\\cos\\varphi\) (0 to 1). Choose lag/lead for the sign of \(Q\).

Phase Angle (φ)

If provided, overrides pf. Positive = lagging.

Results will appear here.

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, \(\varphi = \arccos(\mathrm{pf})\).

Frequently Asked Questions

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—different symbols help separate total apparent power from useful real power and energy-swapping reactive power.

Privacy

All calculations run in your browser—no uploads.

AC Power — Examples, Tips, and Checkpoints

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).

Common Pitfalls

RMS vs. peak: Use RMS voltage/current in the formulas.
Three-phase inputs: For balanced systems, use line-to-line \(V\) and line \(I\), and multiply by \(\sqrt{3}\).
Power factor sign: The magnitude is \(0\ldots1\). Sign of \(Q\) indicates lagging \((+)\) or leading \((-)\); many meters report pf as a positive number plus a lag/lead label.
Unit mix-ups: \(kW \neq kVA\). Only if \(\mathrm{pf}=1\) do they match.

Glossary

Power factor (pf): \(P/S = \cos\varphi\). Efficiency of converting apparent power into useful work.
Displacement angle \(\varphi\): Phase angle between fundamental voltage and current.
Reactive power (Q): Energy exchanged with magnetic or electric fields each cycle, not consumed.