Compute active (P), reactive (Q), and apparent (S) power for single‑phase and three‑phase AC systems. Real‑time power triangle visualization.
In alternating current (AC) circuits, power is divided into three components: active power (P) measured in watts (W) that does useful work, reactive power (Q) in volt‑amperes reactive (VAR) that sustains magnetic and electric fields, and apparent power (S) in volt‑amperes (VA) which is the product of RMS voltage and current.
Key Relationships:
P = S · cos φ Q = S · sin φ S = √(P² + Q²)
Power factor PF = cos φ = P / S (0 ≤ PF ≤ 1)
For three‑phase balanced systems (line values): S = √3 · VL · IL
The power triangle visually represents the relationship between P, Q, and S. The angle φ between apparent power (hypotenuse) and active power (adjacent) is the phase shift between voltage and current. A lagging power factor (inductive load) means current lags voltage (positive Q), while a leading PF (capacitive load) means current leads voltage (negative Q).
Calculator Features:
P = V·I·PF (single‑phase)Q = V·I·sin(arccos(PF))S = V·I (single‑phase)P3φ = √3·VL·IL·PFPF = cos φ = P/S