Calculators
AC Power Calculator
Calculate AC watts, VA, VAR, and phase angle from voltage, current, and power factor.
Calculate real, reactive, and apparent AC power from RMS voltage, RMS current, and power factor. Balanced three-phase modes are included. Calculations stay in your browser.
Real power (P)
1.84 kW
Apparent power (S)
2.3 kVA
Reactive power magnitude (Q)
1.38 kVAR
Phase angle magnitude36.869898°
This calculator assumes sinusoidal RMS quantities and, for three-phase modes, a balanced load. A power-factor magnitude alone does not identify whether reactive power is leading or lagging.
About This Tool
Alternating-current loads can draw more apparent power than the real power they convert into useful work. This calculator connects the power triangle quantities: real power P in watts, reactive power Q in VAR, apparent power S in VA, power factor, and phase-angle magnitude. Enter RMS voltage, RMS current, and power factor for a single-phase or balanced three-phase system. Everything is calculated locally in your browser.
How To Use It
- Choose single phase, balanced three-phase with line-to-line voltage, or balanced three-phase with line-to-neutral voltage.
- Enter RMS voltage and RMS current using the voltage definition selected above.
- Enter the power-factor magnitude as a decimal greater than 0 and no more than 1, such as 0.8.
- Read real power, apparent power, reactive-power magnitude, and phase-angle magnitude. Use equipment documentation or measurements to determine whether the load is leading or lagging when that distinction matters.
Examples
230 V single-phase load
At 230 V, 10 A, and PF 0.8, apparent power is 2.3 kVA, real power is 1.84 kW, reactive-power magnitude is 1.38 kVAR, and the phase-angle magnitude is about 36.87°.
400 V balanced three-phase load
For 400 V line-to-line, 10 A line current, and PF 0.9, apparent power is about 6.93 kVA and real power is about 6.24 kW.
Unity power factor
At PF 1, phase angle and reactive-power magnitude are zero, so real power equals apparent power for the ideal sinusoidal model.
Useful Notes
Real, reactive, and apparent power
Real power P is measured in watts and represents average power transferred to the load. Apparent power S is measured in VA and combines real and reactive components. Reactive power Q is measured in VAR. Their magnitudes form the power triangle S² = P² + Q².
Single-phase formulas
For sinusoidal single-phase RMS values, S = VI, P = VI × PF, and |Q| = S√(1 − PF²). The phase-angle magnitude is arccos(PF).
Balanced three-phase formulas
With line-to-line voltage and line current, S = √3 VI. With line-to-neutral phase voltage and line current, S = 3VI. Real and reactive power then follow from the same power-factor relationships. These formulas assume a balanced three-phase load.
Power factor and phase angle
For a sinusoidal displacement-power-factor model, PF = cos φ. A value closer to 1 means real power is closer to apparent power. Because this calculator accepts only the magnitude of PF, it reports the magnitude of φ and Q rather than claiming a leading or lagging sign.
RMS values matter
The voltage and current inputs are RMS quantities. Do not substitute peak sinusoidal values into these formulas unless you first convert them to RMS values.
Model limitations
Real installations can be unbalanced or have harmonic current, nonlinear loads, distortion power factor, inrush, losses, and measurement uncertainty. This calculator is an educational and first-pass engineering model, not a replacement for measurements, equipment nameplates, electrical standards, or qualified design review.
FAQ
What is the difference between kW and kVA?
kW measures real power while kVA measures apparent power. For this model, kW equals kVA multiplied by power factor, so they are equal only at unity power factor.
How is kVAR calculated?
The reactive-power magnitude follows the power triangle: |Q| = √(S² − P²), which is also S√(1 − PF²) when power factor is known.
Why does three-phase use √3?
For a balanced three-phase system expressed with line-to-line voltage and line current, the relationships between phase and line quantities combine to give total apparent power S = √3 VI.
Does this tell me whether power factor is leading or lagging?
No. A positive power-factor magnitude alone does not contain that sign information. You need the load type, signed phase angle, or suitable measurement to identify leading versus lagging behavior.
Can I use this for nonlinear loads?
Treat the result cautiously. For distorted waveforms, true power factor includes harmonic distortion and may not equal cos φ. Use measured true-RMS and real-power data when accuracy matters.
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