Reactive Power: How to Calculate It and How to Fix It

I walked into a beverage plant last year where the maintenance manager was annoyed about a $4,200 power factor penalty on his monthly utility bill. But who is the culprit? A 150 HP motor running a compressor, getting massive current, but doing the same work it always had. The plant was not using more real power, they were just circulating reactive power back and forth with the utility.

Reactive power is the power that flows between the supply and inductive or capacitive loads without doing useful work. Its unit is volt amperes reactive (VAR), commonly expressed as kVAR.

In this article, you will get knowledge about reactive power, how it different from the active power, why is its important in electrical circuits, and how it can be calculated easily.

What Is Reactive Power in Actual

Let’s start with the physics, not the beer-foam analogy.

When AC voltage is applied throughout an inductive load, such as a motor or transformer, the current is delayed behind the voltage due to the magnetic field that rises up and collapses with each cycle. Similarly, capacitive loads cause current to lead voltage as a result of the charging and discharging of the electric field. This phase shift between voltage and current means some energy flows from the source to the load during one part of the cycle, then flows back to the source during another part. Reactive power is real energy moving back and forth, but net work is zero at the load. It does not spin the motor shaft or heat the resistor. It just sustains the magnetic fields in inductors or electric fields in capacitors.

The unit used for reactive power is VAR, while larger systems commonly use kVAR. Reactive power can be found with the formula Q = V × I × sinφ, where φ is the angle between the voltage and current waveforms.

Here is what most textbooks touch on briefly: reactive power is not a waste. Motors need magnetizing current to create torque. Transformers require reactive power to establish magnetic flux. Reactive power is not a problem, but when it has excess reactive power cycling through its distribution system, heating cables and transformers, and hogging capacity that could be doing useful work.

Why the beer and foam analogy fails: it indicates reactive power is useless, like foam. It’s not true. Reactive power is useful but only inconvenient when you have too much of it bouncing around.

Active Power vs Reactive Power vs Apparent Power

You’ll hear three types of power in any AC system. Here’s how they relate:

These three make the power triangle. For understanding this topic, it is the single most essential diagram [Suggested diagram: Right triangle with S as hypotenuse, P as adjacent side (horizontal), Q as opposite side (vertical). Label angle φ between S and P. Caption: “Power triangle highlighting the link between active power (P), reactive power (Q), and apparent power (S). The angle φ represents the phase shift between voltage and current.”]

The three key formulas you need to memorize:

• Q = √(S² – P²)
• Q = S × sinφ
• Power Factor = P / S = cosφ

Power factor shows the relationship between useful power and the total electrical power supplied. A power factor of 1.0, or 100%, means the supplied power is used effectively. If a power factor is 0.8 then only 80%, of the apparent power is the active power. The phase angle between voltage and current explains the reactive portion, with its cosine used to determine the power factor. 

Leading vs lagging reactive power:

• Lagging (inductive): Current lags voltage. Motors, transformers, inductors. This is what you see in 95% of industrial plants. Positive Q.
• Leading (capacitive): Current leads voltage. Capacitor banks, long unloaded cables. Negative Q.

In the plants I have worked in, lagging power factor has always been a common challenge. You fix it by adding capacitors, which supply leading reactive power to cancel out the lagging reactive power from motors.

Why Reactive Power Matters in Real Plants

You might think, “If it is not working, why should I care?” Here are four reasons reactive power will cost you money and capacity if you ignore it.

1. Voltage stability and regulation

Reactive power is needed to supply power to the voltage. When the current requires more reactive power from the electric company, the voltage drops on the line. The voltage drop is undesirable because it could cause overheating of motors, dimming of lights, and the possibility of equipment shutdown. The electric company use the injection of reactive power from generators, capacitors or STATCOMs to supply the needed power during the times of high demand.

2. Extra current means oversized equipment and higher losses

Apparent power (S) is what sizes your cables, breakers, and transformers. If you have high reactive power, S is much larger than P, even though P is the only thing doing useful work. That means you are paying for heavier wire, bigger transformers, and more switchgear than you hadd need if your power factor were better.

Worse, current causes I²R losses in cables and transformer windings. Higher current (due to poor power factor) means higher losses and hotter equipment, even though you’re not getting any more work done.

3. Utility power factor penalties

Most commercial and industrial tariffs include power factor clauses. If your monthly power factor falls below a threshold typically 0.90 to 0.95 you get billed a penalty or your kW demand charge gets multiplied by a correction factor.

I have seen penalties range from a few hundred dollars a month at small facilities to $10,000+ per month at heavy industrial sites with large motor loads and no compensation. The utility doesn’t want to supply your reactive power because it eats up their distribution capacity too.

4. Capacity release

When you correct power factor, you free up capacity in your existing electrical infrastructure. I have seen plants avoid transformer upgrades by installing capacitor banks and dropping apparent power by 15–20%. That’s real capital saved.

How to Calculate Reactive Power

Let’s walk through the most common calculations you’ll actually use in the field.

Step 1: If you know apparent power (S) and power factor (PF):

• Real power: P = S × PF
• Reactive power: Q = S × sinφ, where φ = arccos(PF)

Or use the triangle: Q = √(S² – P²)

Step 2: If you know real power (P) and power factor:

• Apparent power: S = P / PF
• Reactive power: Q = P × tanφ, where φ = arccos(PF)

This last formula Q = P × tanφ is the workhorse for motor and load analysis.

Worked Example: 75 kW Motor at 0.75 Power Factor

You have a 100 HP (≈75 kW) motor running at 75% load, so active power P = 75 kW. Measured power factor is 0.75 lagging.

Find current reactive power:

• φ = arccos(0.75) ≈ 41.4°
• tan(41.4°) ≈ 0.882
• Q = 75 kW × 0.882 ≈ 66.2 kVAR

Find apparent power:

• S = P / PF = 75 / 0.75 = 100 kVA

Or verify with the triangle:

• Q = √(100² – 75²) = √(10,000 – 5,625) = √4,375 ≈ 66.1 kVAR ✓

Now let’s say you want to improve power factor to 0.95.

New reactive power at PF = 0.95:

• φ_new = arccos(0.95) ≈ 18.2°
• tan(18.2°) ≈ 0.329
• Q_new = 75 × 0.329 ≈ 24.7 kVAR

Required capacitor kVAR:

• Q_cap = Q_old – Q_new = 66.2 – 24.7 ≈ 41.5 kVAR

You had to install a 40 or 45 kVAR capacitor bank (use the nearest standard size) at or near that motor.

After correction:

• New S = 75 / 0.95 ≈ 78.9 kVA (down from 100 kVA)
• Current drops by roughly 21% (100 –> 79)
• Cable and transformer losses drop by ~38% (since losses ∝ I²)

That’s real capacity and real savings.

Reactive Power Compensation – The Practical Fix

Once you know you have a power factor problem, here is how to fix it.

1. Capacitor banks (most common and budget-friendly)

Capacitors supply leading reactive power (negative Q), which cancels the lagging reactive power (positive Q) from reactive loads. They are passive, reliable, and cheap, typically $50–$150 per kVAR installed for fixed banks.

• Fixed capacitor banks: Switched on/off manually or by contactor. Simple, no maintenance that is good for steady loads.
• Automatic capacitor banks: Use a power factor controller and staged contactors to add/remove capacitor steps as load varies. Perfect for facilities with fluctuating demand.

Where to install: As close to the inductive load as possible. Correcting at the motor saves current all the way back through your panel, feeder, and transformer. Correcting only at the service entrance saves the utility current but doesn’t help your internal distribution.

2. Synchronous condensers

These are synchronous motors running unloaded, overexcited to supply reactive power. Rarely used today except in large substations or very specialized applications, as it is expensive and requires maintenance.

3. Active filters and STATCOMs

Static synchronous compensators (STATCOMs) use power electronics to inject or absorb reactive power dynamically. Fast response, great for variable loads and harmonics; their cost is 5–10× higher than capacitors, so you only use these when harmonics are a problem or when you need very tight voltage regulation (data centers, arc furnaces, EV charging hubs).

When capacitors are enough: 90% of industrial plants will solve the problem. If your load is mostly motors, pumps, compressors, and lighting, and harmonics aren’t an issue, standard automatic capacitor banks

 When you need more: High harmonic content (VFDs, rectifiers, switch-mode power supplies), rapidly fluctuating loads (welders, cranes), or if you’ve already installed capacitors and they’re blowing fuses due to resonance.

Realistic benefits of compensation:

• Eliminate or drastically reduce power factor penalties (payback often < 18 months)
• Free up 10–25% capacity in existing transformers and cables
• Reduce losses by 10–30% depending on initial PF
• Improve voltage stability, especially at end-of-run loads

[Suggested diagram: Before/after compensation. Before: utility → transformer → motor (large current loop shown). After: capacitor bank in parallel with motor, smaller current from utility. Caption: “Reactive power compensation: capacitor supplies reactive current locally, reducing current drawn from the utility and upstream equipment.”]

Quick Measurement Notes

How do you actually measure reactive power on site?

Power analyzer (the right tool):

For a proper load calculation, use a 3-phase power analyzer rather than relying only on basic meter readings. Fluke, Dranetz and Hioki analyzers can display active power, reactive power, apparent power, power factor, harmonics, and voltage and current waveforms all together and individually.

Basic clamp meter (limited):

A standard clamp meter measures current and sometimes voltage. Some models calculate apparent power (V × I), but they don’t show power factor or separate P and Q unless they have a true power measurement mode. Cheaper meters assume unity power factor, which gives you garbage data on inductive loads.

Panel meters and building management systems:

Many modern motor control centers and switchboards have multifunction meters that log P, Q, S, and PF. 

Before using a test instrument, check your SCADA or BMS system. You may already have the power data you need. For quick field checks, I use normally Fluke 345 clamp meter, because it can measure true power factor, kW, and kVAR. When I need longer data records or harmonic information data, then I often use a Fluke 435 power quality analyzer to have some more information for analysis..

Frequently Asked Questions

What is reactive power in simple words?

Reactive power flows back and forward between the power source and inductive or capacitive equipment without doing any effective work. It is used to generate magnetic fields but does not produce any heat.

How is reactive power different from active power?

Active power runs motors, heats elements, and powers lights. Reactive power only maintains magnetic or electric fields and vibrates between the source and load. Active power is what you pay for as energy (kWh); reactive power causes current flow and is punished if excessive.

What are the sources of reactive power?

The sources of reactive power are inductive and capacitive loads.  Motors and reactors are inductive loads that draw reactive power from the supply. In contrast, capacitor banks and lightly loaded cables provide reactive power to the system. 

How do you calculate reactive power?

You can find reactive power using Q = √(S² − P²) when apparent power and active power are known. If you know that, the active power and the power factor, use equation like: Q = P × tanφ. For example, a 100 kW load with a power factor of 0.8 has a reactive power of 75 kVAR. which you can easily calculate from the equation.

Why do utilities charge for reactive power?

Because it results in them having to supply more current than they would otherwise have to, which causes losses in the system and reduces their capacity to supply active power.

What is the best way to reduce reactive power?

The best way to reduce reactive power is to install capacitor banks to supply the reactive power for inductive loads. This reduces the amount of reactive power that has to be supplied by the utility. For most industrial facilities, the best option is to install automatic capacitor banks.

Conclusion

Reactive power isn’t a ghost in the machine; it’s measurable, manageable, and fixable. It exists due to reactive loads needing magnetizing current, but excess reactive power costs you in penalties, equipment sizing, and energy losses. The key takeaways: understand the power triangle and the relationship between P, Q, and S; calculate reactive power using the formulas Q = √(S² – P²) or Q = P × tanφ; and compensate with capacitor banks installed close to the load for maximum benefit.

Your next step: Pull a few months of utility bills and look for power factor or kVAR charges. If your facility-wide power factor is below 0.90, you’re leaving money on the table. Run the numbers, size a capacitor bank, and you’ll likely see payback in under two years, plus you’ll free up capacity you didn’t know you had.

Related reading on our site:

• What Is Power Factor and How Can We Improve It to Save Money
• 3-Phase Power Calculator: Formulas, Examples & Industrial Sizing Guide
• Watts to VA Calculator | Convert Watts to Volt-Amps

External reference: Power factor: Wikipedia