AC Power Calculator
A single-phase load taking 10 A at 230 V and 0.8 power factor uses 1.84 kW of real power, out of 2.3 kVA apparent power.
Between 0 and 1.
1.84 kW
Full answer, then cut to fewer decimals (not rounded):
- 1.84 kW
- 1.8 kW
- Apparent power S
- 2.3 kVA
- Reactive power Q
- 1.38 kVAR
- Phase angle φ
- 36.86989765 °
- Complex power S
- 1.84 + j1.38 kVA
Step-by-step solution
- S = V × I = 230 × 10 = 2300 VA
- P = S cos φ = 2300 × 0.8 = 1840 W
- Q = S sin φ = 1380 VAR (absorbed, lagging)
AC Power Formula
S = VI (√3 V_L I_L), P = S cos φ, Q = S sin φ
P real power (W), Q reactive (VAR), S apparent (VA), cos φ the power factor
Worked Example
A single-phase load drawing 10 A at 230 V with 0.8 power factor lagging:
- S = V × I = 230 × 10 = 2300 VA
- P = S cos φ = 2300 × 0.8 = 1840 W
- Q = S sin φ = 1380 VAR (absorbed, lagging)
Reactive power Q: 1.38 kVAR · Phase angle φ: 36.86989765 ° · Complex power S: 1.84 + j1.38 kVA
GATE tip
Complex power S = VI* = P + jQ. Using I* (the conjugate) makes Q positive for inductive loads, the sign convention GATE and most textbooks use.
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Frequently asked questions
Why √3 in three-phase power?
With line voltage V_L and line current I_L, the total power is √3 V_L I_L cos φ: three phases, each at V_L/√3 for star or carrying I_L/√3 for delta.
What is reactive power?
Power that flows back and forth between source and the load’s inductance or capacitance each cycle. It does no net work but loads cables and transformers.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). AC Power Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/ac-power-calculator/
IEEE
Scientific Converters, "AC Power Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/ac-power-calculator/