The Active / Reactive / Apparent Power Calculator solves the AC power triangle from any two known quantities — active power (kW), reactive power (kVAR), apparent power (kVA), or power factor. Used for transformer sizing, generator selection, and power factor correction analysis.
100
kVA
0.8
36.91
°
100
kVA
0.8
36.91
°
The calculator for active, reactive, and apparent power solves the complete AC power triangle from any two known quantities, returning all remaining power components and the power factor. This tool is essential for transformer sizing, generator selection, power factor correction analysis, and energy billing verification in AC electrical systems.
AC power has three interdependent components that form a right triangle in the complex power plane:
The mathematical relationship: S² = P² + Q², and cos φ = P/S where φ is the phase angle between voltage and current. The kVA calculator handles the simpler case of computing apparent power from voltage and current directly.
Power factor (PF = cos φ) measures what fraction of apparent power is doing useful work. A PF of 1.0 means 100% of supplied power is active; a PF of 0.7 means 30% is reactive overhead. Low power factor has real costs:
Inductive loads (motors, fluorescent lighting ballasts, welding equipment) cause lagging PF; capacitive loads cause leading PF. Power factor correction is achieved by adding capacitor banks sized in kVAR to offset inductive reactive power. Use this online calculator to find the required kVAR of capacitance for any PF correction target. The power factor correction calculator provides the capacitor sizing calculation directly.
Electrical equipment rated in kVA must supply the full apparent power demand, not just the active power. A 100 kVA transformer serving a load with PF = 0.8 can supply only 80 kW of active power — the remaining 20 kVAR of reactive power occupies capacity without contributing to useful output. A facility drawing 150 kW at PF = 0.75 requires a generator rated at least 150/0.75 = 200 kVA. Undersizing based on kW alone is a common and costly mistake in generator procurement. The energy consumption calculator and power and energy calculators category provide complementary tools for electrical system design.
Reactive power Q is positive for inductive loads (current lags voltage) and negative for capacitive loads (current leads voltage). The sign matters for power system analysis: a motor (inductive, +Q) and a capacitor bank (capacitive, −Q) placed in parallel partially cancel each other's reactive power demand, reducing the net apparent power the utility must supply. This is the principle behind power factor correction. Practical power systems have mixed loads and target a slightly lagging overall PF (0.95–0.98 lagging) rather than unity, to avoid leading PF conditions that cause voltage regulation problems in distribution networks. The battery life calculator and BTU to kilowatt converter provide related energy calculations.
S = √(P² + Q²) by the Pythagorean theorem applied to the power triangle. PF = P/S = cos(arctan(Q/P)). Phase angle φ = arctan(Q/P) in radians, converted to degrees. This is the standard power triangle: P is the horizontal leg, Q is the vertical leg, and S is the hypotenuse.
High Q relative to P (large phase angle) indicates low power factor and high reactive burden. S ≈ P when Q is small (near-unity PF). For system design: generators, transformers, and cables are sized to S (kVA). Protective devices and metering account for both P and Q. Targets: PF > 0.95, phase angle < 18° for well-designed industrial systems.
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The classic 3-4-5 power triangle: 80 kW, 60 kVAR, 100 kVA, PF = 0.80. This load requires a 100 kVA transformer even though only 80 kW of real work is done.
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Excellent PF of 0.988. Apparent power nearly equals active power. Minimal reactive burden on supply system.
P and Q are 90° out of phase with each other in the power triangle. Adding them requires the Pythagorean theorem: S = √(P²+Q²), not P+Q. This is because active power is in phase with the voltage reference, while reactive power is 90° out of phase. They are orthogonal vectors, not scalars.
1 kVAR of reactive power flows back and forth between source and load twice per cycle, consuming no average energy but occupying conductor capacity. The conductor must carry the reactive current in addition to active current, increasing I²R losses even though the reactive power itself is 'lossless' in ideal reactive elements.
Synchronous generators produce reactive power by adjusting field excitation. Over-excited generators produce lagging Q (supply reactive power to inductive loads). Under-excited generators absorb lagging Q (act like a capacitor from the system perspective). Generator reactive capability is shown in the P-Q capability curve on its nameplate.
Complex power S = P + jQ (in complex notation). S = V × I* (voltage times conjugate of current). The magnitude |S| = apparent power (kVA). Real part Re(S) = active power P. Imaginary part Im(S) = reactive power Q. This phasor notation is essential for power system network analysis.
Yes. Negative Q means leading reactive power (capacitive behavior). The system is generating reactive power (e.g., lightly loaded cables, capacitor banks, leading PF loads like variable speed drives with active front ends). Negative Q can raise voltage — useful for compensation but potentially dangerous if uncontrolled.
Transformer losses include core losses (fixed) and copper losses ∝ I²R. Current I = S/(√3×V), so I ∝ S. Low PF means high S for same kW, meaning more current and more I²R losses. A transformer delivering 800 kW at 0.8 PF (1000 kVA) has 25% more copper losses than delivering 800 kW at 1.0 PF (800 kVA).
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