What Is Reactive Power in AC Circuits and How to Calculate It

Reactive power is the portion of alternating current (AC) electricity that oscillates between the source and the load due to inductive or capacitive elements, performing no actual mechanical or thermal work but still occupying physical capacity in your wiring and transformers.

If you only look at the wattage rating on a motor nameplate, you are missing half the story. People commonly confuse reactive power (measured in VAR or kVAR) with apparent power (the total vector sum, measured in VA or kVA) and real power (the actual work done, measured in W or kW). Understanding the difference is the dividing line between a circuit that runs efficiently and one that trips breakers, overheats conductors, or incurs massive utility penalty fees.

The Physics of the Power Triangle

In a purely resistive DC circuit, voltage and current are perfectly in phase. Every electron that leaves the source does work and doesn't return. But in AC circuits with inductors (like motor windings and transformers) or capacitors, the current waveform shifts out of phase with the voltage waveform.

To visualize this, use this single water analogy: Imagine a water pump pushing water through a pipe to turn a heavy, inertial water wheel. The water that actually hits the paddles and turns the wheel is your real power. But because the heavy wheel has momentum, it pushes water back up the pipe during parts of the pump's cycle. That sloshing water doesn't turn the wheel, but it still requires a wider pipe to accommodate the back-and-forth flow. That sloshing flow is your reactive power.

This relationship forms the Power Triangle, governed by the Pythagorean theorem:

• Real Power (P): Measured in Watts (W) or kilowatts (kW). The horizontal vector. This is the power that does actual work (heat, light, torque).
• Reactive Power (Q): Measured in Volt-Amps Reactive (VAR) or kVAR. The vertical vector. This is the power sloshing back and forth to maintain magnetic or electric fields.
• Apparent Power (S): Measured in Volt-Amps (VA) or kVA. The hypotenuse. This is the total power the utility must supply and your wires must carry.

The ratio of Real Power to Apparent Power is your Power Factor (PF). A PF of 1.0 (or 100%) means all supplied power is doing work. A PF of 0.80 means 20% of the current is just sloshing back and forth, heating up your wires without doing any useful work. For a deeper mathematical breakdown of these vectors, the All About Circuits textbook chapter on AC power is an excellent bench reference.

Worked Numeric Example: Sizing a 5 HP Motor Circuit

Let's look at what reactive power changes in a real installation. Suppose you are wiring a 5 HP, 230V single-phase AC motor for a workshop air compressor. If you only size for the real power, your installation will fail.

Step 1: Calculate Real Power (kW)
One mechanical horsepower equals 746 Watts. Therefore, 5 HP = 3,730 W (3.73 kW) of mechanical output. Assuming the motor has an efficiency of 85%, the electrical Real Power (P) drawn from the wall is:
P = 3.73 kW / 0.85 = 4.388 kW

Step 2: Factor in Power to find Apparent Power (kVA)
Induction motors are highly inductive. Let's assume a typical full-load Power Factor (PF) of 0.80. The Apparent Power (S) is:
S = P / PF = 4.388 kW / 0.80 = 5.485 kVA

Step 3: Calculate Reactive Power (kVAR)
Using the Power Triangle formula (Q = √(S² - P²)):
Q = √(5.485² - 4.388²) = √(30.08 - 19.25) = √10.83 = 3.29 kVAR

Step 4: Determine Wire and Breaker Sizing
This is where the rubber meets the road. Your conductors must carry the apparent current, not just the real current.
Total Current (I) = S / V = 5,485 VA / 230V = 23.8 Amps.

Where You Meet Reactive Power in Practice

You won't just see reactive power on a textbook exam; it dictates hardware choices on the jobsite and in the panel.

Industrial Power Factor Correction

In manufacturing plants, hundreds of induction motors create massive inductive reactive power. Utilities penalize facilities with a Power Factor below 0.95 because the utility's transformers and transmission lines have to be oversized to carry that 'sloshing' current. To fix this, plants install capacitor banks. Because motors are inductive (current lags voltage) and capacitors are capacitive (current leads voltage), the capacitor's reactive power perfectly cancels the motor's reactive power locally. The utility only sees the real power, and the penalty disappears.

Commercial HVAC and VFDs

Variable Frequency Drives (VFDs) used on large blower motors rectify AC to DC, then chop it back to AC. The input stage of a standard 6-pulse VFD draws current in sharp, non-linear spikes. This creates distortion reactive power (harmonics), which is different from the displacement reactive power of a standard motor. Fixing this requires active harmonic filters or 12-pulse drives, not just simple capacitors.

Residential LED Drivers

In homes, utilities generally do not penalize residential customers for poor power factor. However, cheap, non-PF-corrected LED drivers in recessed lighting can have a power factor as low as 0.50. While it won't spike your home bill, in a commercial 3-phase wye system, these poor PF loads cause excessive current to pile up on the shared neutral wire, potentially causing neutral overheating and fires.

For field diagnostics, a tool like the Fluke power quality analyzer series is essential for logging kVAR and identifying whether you are dealing with inductive lag or capacitive leading issues.