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

How Alternating Current (AC) Power Works

AC power can feel confusing at first because voltage and current are constantly changing. This calculator simplifies the process by converting your inputs into the three key power values used in electrical work: real power, reactive power, and apparent power. Whether you are sizing equipment, checking a motor load, or studying basic circuits, it gives you clear numbers you can trust.

Why there are three kinds of power: in AC circuits, voltage and current may be out of phase by an angle \(\varphi\). The part that does useful work is real power \(P\) (watts). The part that sloshes back and forth between source and load is reactive power \(Q\) (VAR). Together they create apparent power \(S\) (volt-amperes), which represents the total electrical “effort.” These are linked by the power triangle: \( S^2 = P^2 + Q^2 \), and the power factor is \( \mathrm{pf} = P/S = \cos\varphi \). A low power factor means more current is required for the same real power.

For single-phase systems, the basic formulas are \( S = V I \), \( P = V I \cos\varphi \), and \( Q = V I \sin\varphi \). For balanced three-phase systems, use line-to-line voltage and line current with the factor \( \sqrt{3} \): \( S = \sqrt{3}\, V I \), \( P = \sqrt{3}\, V I \cos\varphi \), and \( Q = \sqrt{3}\, V I \sin\varphi \). Always use RMS values for voltage and current.

How to use this calculator

1. Select single-phase or three-phase (balanced).
2. Enter RMS voltage and RMS current.
3. Provide either the power factor or the phase angle; the angle will override pf if both are entered.
4. Choose lagging or leading to set the sign of reactive power.
5. Click Calculate to view \(P\), \(Q\), \(S\), and the power factor.

Where this is useful

AC power calculations show up in everyday and professional settings: estimating generator size, selecting UPS capacity, checking HVAC motors, evaluating industrial equipment, and troubleshooting high current draw. They also help explain why utilities care about power factor and why capacitor banks or power factor correction are used. With this tool, you can explore “what-if” scenarios quickly and build intuition about how voltage, current, and phase angle affect real power.

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

All calculations run in your browser—no uploads.

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).