AC Power & Phasors

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Phasor diagrams, complex power S = P + jQ, real/reactive/apparent power, and the power triangle. Pick a load (R, L, C, RL series, RC series, RLC series) or type in your own impedance. Edit Vrms, current, phase, or frequency; the waveforms, phasors, and triangle redraw instantly.

Input mode

Load parameters

V
Hz
Ω

Waveform x-axis

x-axis: time (s) over the chosen cycles. Wheel = zoom, drag = pan, double-click = reset.

Phasor diagram

Power triangle

Instantaneous waveforms

Computed values

Quick reference

Complex power

S = Vrms · Irms* = P + jQ   (VA)

Real (active) power

P = Vrms · Irms · cos φ = |S| · pf   (W)

Reactive power

Q = Vrms · Irms · sin φ   (VAR)

Apparent power

|S| = Vrms · Irms = √(P² + Q²)   (VA)

Power factor

pf = cos φ = P / |S|

Power triangle

P is the horizontal leg, Q is the vertical (Q > 0 inductive, < 0 capacitive), |S| is the hypotenuse, φ is the angle from P to |S|.

Instantaneous power

p(t) = v(t)·i(t) = Vm·Im·[cos φ + cos(2ωt + θv + θi)]/2

Loads

R: P = V²/R, Q = 0, pf = 1
L: P = 0, Q = V²·BL = V²/(ωL)
C: P = 0, Q = −V²·BC = −V²·ωC