# AC Power Calculator - Real, Reactive & Apparent Power, PF Correction, 3-Phase > AC power calculator: P, Q, S and power factor with waveforms, PF-correction capacitors, star/delta three-phase with neutral current, energy bills and THD. - URL: https://qilingtools.com/en/physics/ac-power - Category: Physics Tools (https://qilingtools.com/en/physics) - Tags: [Physics](https://qilingtools.com/en/tags/physics) - Last updated: 2026-10-29 - Price: Free, no sign-up - Privacy: Runs locally in the browser; files are never uploaded Enter a voltage, current and phase angle (or a load’s resistance and reactance) to get real, reactive and apparent power and the power factor, and watch animated waveforms that show when instantaneous power goes negative and energy flows back to the grid. The tool also sizes the capacitor needed to raise the power factor to a target, analyses star and delta three-phase loads (including neutral current and neutral shift when unbalanced), estimates a monthly electricity bill from an appliance list, and shows the harmonics and true power factor of a rectifier load. ## How to use 1. On Single-phase, enter V, I and φ, or V plus the load R and X, and read P, Q, S, power factor and the waveforms 2. On PF correction, enter the load power and the present and target power factors to get the kvar and capacitance (50/60 Hz, single- or three-phase) 3. On Three-phase, choose the connection and per-phase loads, then read phase and line values, total power and neutral current while the phasors rotate 4. On Household energy, edit appliance power and daily hours and enter your tariff; on Harmonics, drag the conduction angle to see the spectrum ## Features - P, Q, S, power factor (leading or lagging) and impedance, with a power triangle and rotating phasors - Animated v(t), i(t), p(t) with the p<0 intervals shaded and their share of each cycle - PF correction from Q_c = P(tanφ₁ − tanφ₂), with capacitance for single-phase, delta and star connections - Three-phase star with or without neutral and delta, balanced or unbalanced, solved with complex arithmetic for phase, line and neutral currents and neutral shift - Household appliance list with kWh per month, monthly and yearly cost, plus RMS vs peak for 220/230/120/100 V mains - Rectifier harmonics: current waveform, odd-harmonic spectrum, THD, true power factor and crest factor ## FAQ ### What is the difference between real, reactive and apparent power? Real power P is the average power actually consumed as heat, light or mechanical work, in watts. Reactive power Q measures the energy that inductors and capacitors shuttle back and forth each cycle without doing net work, in var. Apparent power S = VI is the product of RMS voltage and current, in VA, and sets how much current the wiring and transformers must carry. They form a right triangle, S² = P² + Q², and power factor = P/S = cos φ. ### Why does instantaneous power go negative? When current and voltage are out of phase, there is part of every cycle where v and i have opposite signs, so p = vi < 0: the magnetic field of an inductor or the electric field of a capacitor is returning stored energy to the supply. That part is exactly |φ|/π of the cycle. A resistor (φ = 0) never has negative power; a pure inductor or capacitor (φ = ±90°) is negative half the time and averages to zero. ### How is the correction capacitor sized? First find the reactive power to cancel, Q_c = P(tan φ₁ − tan φ₂), with φ₁ and φ₂ the angles before and after. A single-phase capacitor across voltage V supplies Q_c = ωCV², so C = Q_c/(ωV²). In three-phase, delta-connected capacitors see the line voltage, C = Q_c/(3ωV_L²) per phase; star-connected ones see the phase voltage, C = Q_c/(ωV_L²), three times larger. Real power is unchanged, while current and line losses drop. ### How much current flows in the neutral with an unbalanced load? In a 4-wire star the neutral carries the phasor sum I_N = I_a + I_b + I_c. With a balanced load the three equal currents 120° apart cancel; unbalanced, they don’t. For example 10, 20 and 40 Ω resistors on 400 V give about 15 A in the neutral. Without a neutral wire, the load’s star point shifts instead, the phase voltages become unequal, and the lightly loaded phase can see a dangerously high voltage. ### Is 230 V the peak value, and how is the bill worked out? 230 V, 220 V and 120 V are RMS values; the voltage actually swings between ±√2 times that, about ±325 V for 230 V. RMS means the AC heats a resistor exactly like DC of the same value, so the power formulas use RMS directly. 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