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In an AC circuit with any reactance (inductive or capacitive load), the power delivered splits into three related quantities that form a right triangle: real power (P), measured in watts, does actual work (heat, motion, light); reactive power (Q), measured in VAR, is exchanged with the source without net work (stored/released in inductors and capacitors); and apparent power (S), measured in VA, is the vector sum the utility actually has to supply. The angle φ between P and S is the same phase angle between voltage and current, and its cosine is the power factor.
| Quantity | Formula | Unit |
|---|---|---|
| Apparent power | S = √(P²+Q²) | VA (kVA) |
| Power factor | PF = P/S = cosφ | 0–1 (or %) |
| Phase angle | φ = atan(Q/P) = acos(PF) | degrees |
| Real power from S, PF | P = S×PF | W (kW) |
| Reactive power from S, PF | Q = S×sinφ | VAR (kVAR) |
Inductive loads (motors, transformers, ballasts) draw lagging reactive power (current lags voltage); capacitive loads draw leading reactive power. Utilities bill for kVA (what they must supply) even though only kW (P) does useful work, which is why a low power factor costs extra — see our Power Factor Correction Capacitor Calculator to fix it.
A right-triangle representation of AC power showing real power (P, the horizontal leg), reactive power (Q, the vertical leg), and apparent power (S, the hypotenuse), related by S=√(P²+Q²).
Real power (P, watts) does actual work. Reactive power (Q, VAR) is energy that oscillates between source and load (inductors/capacitors) without net work. Apparent power (S, VA) is the total the source must supply, combining both.
The ratio PF=P/S=cosφ, showing what fraction of the apparent power is actually doing useful work. PF=1 (unity) means no reactive power; lower PF means more of the supply capacity is "wasted" on reactive current.
It still flows through wires, transformers, and generators, causing I²R heating and consuming capacity, even though it delivers no net energy to the load — that is why utilities often charge extra for low power factor.
Lagging PF means current lags voltage (typical of inductive loads like motors); leading PF means current leads voltage (typical of capacitive loads). Both represent reactive power, just in opposite directions.
φ is the angle between voltage and current (and between P and S in the triangle); PF = cosφ. A larger φ means more reactive power relative to real power and a lower PF.
Because winding and conductor heating depend on current (which relates to kVA), not on how much of that current does useful work. A device must be sized for the full apparent power regardless of the load's PF.
By convention inductive (lagging) loads have positive Q and capacitive (leading) loads have negative Q; a purely resistive load has Q=0.
Add capacitors (for inductive/lagging loads) to supply local reactive power, reducing the reactive current the source must provide — see our Power Factor Correction Capacitor Calculator.
Often between 0.7 and 0.9 lagging at full load, and considerably lower (0.3–0.5) at light load, since magnetizing (reactive) current stays roughly constant while real power drops.
Yes — the same P, Q, S relationships hold for total three-phase power; just ensure P, Q, and S are all computed consistently as total (all three phases) or per-phase values, not mixed.
P is in watts (W/kW/MW), Q is in reactive volt-amperes (VAR/kVAR), and S is in volt-amperes (VA/kVA/MVA) — all three share the same numeric relationship regardless of the magnitude prefix used.
S = P/PF, which follows directly from PF=P/S rearranged; then Q can be found from S and P using Q=√(S²−P²).
No, PF is bounded between 0 and 1 (or -1 to 1 with sign convention) because P can never exceed S — real power is always the resistive-projection component of the total apparent power.
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