How Alternating Current (AC) Power Works
Release Updates
v1.1 (May 21, 2026)
- Added reverse calculation modes for amps, power factor, kVA, and kVAR.
- Added three-phase voltage type support for line-to-line and line-to-neutral inputs.
- Added optional energy use and electricity cost estimates based on real power.
- Added a visual power triangle for \(P\), \(Q\), \(S\), \(\varphi\), and power factor.
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 with line-to-line voltage and line current, use the factor \( \sqrt{3} \): \( P = \sqrt{3}\, V I \cos\varphi \). With line-to-neutral voltage and line current, use \( P = 3\, V I \cos\varphi \). Always use RMS values for voltage and current.
How to use this calculator
- Choose what you want to calculate: watts, amps, power factor, kVA, or kVAR.
- Select single-phase or three-phase (balanced); for three-phase, choose line-to-line or line-to-neutral voltage.
- Enter the values required for that mode. Phase angle overrides power factor if both are entered.
- Choose lagging or leading to set the sign of reactive power where needed.
- Optionally add hours, days, and electricity cost per kWh to estimate energy use and cost.
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.