Understanding AC wattage
On an AC circuit, "watts" and "volt-amps" are not always the same thing. This calculator converts voltage, current, and power factor into the three quantities that describe AC power: real power (the energy that actually does work, in watts), apparent power (what you get from simply multiplying voltage by current, in volt-amps), and reactive power (the non-working portion that oscillates in and out of magnetic or electric fields, in VAR).
The formulas
- Apparent power: S = V × I for a single-phase circuit, or S = √3 × V × I for a balanced three-phase circuit using line-to-line voltage and line current.
- Real power: P = S × PF, where PF is the power factor — a unitless number between 0 and 1 describing how in-phase the voltage and current are.
- Reactive power: Q = √(S² − P²), the component of apparent power that does not convert to real work.
Why power factor matters
For a purely resistive load (a heater, incandescent bulb, or toaster), current and voltage rise and fall together, PF = 1, and watts equal volt-amps exactly. Motors, transformers, and many electronic power supplies present an inductive or capacitive load, so current lags or leads voltage. That phase shift means some of the apparent power sloshes back and forth without doing useful work — the power factor is the fraction that remains real, useful power. A lower power factor means more current is required to deliver the same wattage, which is why utilities sometimes charge industrial customers extra for poor power factor.
Single-phase vs. three-phase
Household and small-appliance circuits are almost always single-phase, so apparent power is simply voltage times current. Three-phase power, common in commercial and industrial equipment, splits the load across three conductors 120° apart; for a balanced three-phase load the total power is √3 (about 1.732) times the single-phase calculation using the line-to-line voltage and line current.