kVA vs. kW vs. kVAR: Understanding the Power Triangle Units

Every electrical bill, generator spec sheet, and transformer nameplate throws around kVA, kW, and kVAR as if they're interchangeable. They aren't. Each describes a different aspect of AC power, and confusing them leads to undersized equipment, poor efficiency, and utility penalties. Here's a clear breakdown of what each unit means, how they relate mathematically, and how to convert between them.

The Three Units at a Glance

Before getting into the geometry, a quick reference table:

The distinction matters because generators and transformers are rated in kVA, not kW. A 100 kVA generator does not necessarily deliver 100 kW of usable power. How much useful work you get out of it depends on your load's power factor.

kW: Real Power

Real power (P) is the power that actually does work. It heats elements, turns shafts, and lights lamps. When you pay your electricity bill, you're paying for kWh, which is real power consumed over time.

In a purely resistive load like an electric oven, all the power drawn from the supply converts to heat. Voltage and current are perfectly in phase, so real power equals apparent power. In most industrial and commercial settings, though, loads include motors, transformers, and variable frequency drives, which introduce a phase shift between voltage and current.

Real power is measured in watts (W) or kilowatts (kW). The formula for a single-phase AC circuit:

P = V × I × cos(φ)

where φ is the phase angle between voltage and current. That cosine term is the power factor.

kVAR: Reactive Power

Reactive power (Q) is the power that oscillates between the source and inductive or capacitive loads without being consumed. Inductors, like motor windings and transformer cores, draw current that lags voltage. Capacitors draw current that leads voltage. In both cases, energy is stored temporarily in magnetic or electric fields and then returned to the circuit.

Reactive power does no net work over a full cycle. It does, however, flow through conductors and transformers, which means it contributes to heating and voltage drop. Utilities have to supply it, and they often penalize commercial customers who draw excessive reactive power because it ties up generation and transmission capacity.

Reactive power is measured in volt-amperes reactive, or VAR (kVAR at the kilovolt-ampere scale). An inductive load produces positive kVAR; a capacitive load produces negative kVAR. When you add capacitor banks to correct power factor, you're injecting negative kVAR to cancel the positive kVAR from motors. See sizing power factor correction capacitors for the math on how much capacitance to add.

kVA: Apparent Power

Apparent power (S) is what the supply actually has to deliver. It's the product of RMS voltage and RMS current, without accounting for phase angle:

S = V × I

Apparent power is the vector sum of real and reactive power, and it's what determines the physical size of electrical equipment. A transformer rated at 500 kVA can push 500 kVA of apparent power through its windings regardless of what fraction of that ends up as useful work.

The relationship between the three quantities is the power triangle:

S² = P² + Q²

This is a direct application of the Pythagorean theorem. kW sits along the horizontal axis, kVAR on the vertical axis, and kVA is the hypotenuse. The angle between kW and kVA is φ, the phase angle, and its cosine is the power factor.

Power Factor as the Link Between kW and kVA

Power factor (PF) ties all three units together:

PF = P / S = kW / kVA = cos(φ)

A load with a power factor of 0.85 drawing 85 kW of real power requires 100 kVA of apparent power from the supply. The remaining 52.7 kVAR is reactive. None of that 52.7 kVAR shows up on the kWh meter, but it flows through every conductor and transformer between the utility and the load.

This is why power factor matters to facility managers and utilities alike. A low power factor means you're pulling more current than necessary for the real work being done, which wastes conductor capacity and increases losses. Improving power factor from 0.75 to 0.95 on a 100 kW load reduces the required apparent power from 133 kVA down to 105 kVA, a significant reduction in current.

Worked Conversion Example

A manufacturing plant has the following measured values:

• Real power: 240 kW
• Reactive power: 180 kVAR (inductive)

Step 1: Find apparent power.

S = √(P² + Q²)
S = √(240² + 180²)
S = √(57,600 + 32,400)
S = √90,000
S = 300 kVA

Step 2: Calculate power factor.

PF = P / S = 240 / 300 = 0.80

Step 3: Interpret the results.

The plant needs a generator or transformer rated for at least 300 kVA, even though only 240 kW of real work is being done. The 60 kVAR gap (the difference between what's needed and what's being used productively) represents inefficiency.

To raise power factor to 0.95, the target reactive power becomes:

Q_target = P × tan(arccos(PF_target))
Q_target = 240 × tan(arccos(0.95))
Q_target = 240 × 0.329 = 79 kVAR

The plant needs to add 180 - 79 = 101 kVAR of capacitance to hit 0.95 PF. After correction, apparent power drops to 252 kVA, freeing up nearly 50 kVA of transformer capacity. For three-phase systems, the calculation follows the same logic but accounts for the line-to-line voltage; power factor in three-phase systems covers that in detail.

Frequently Asked Questions

What's the practical difference between kVA and kW when buying a generator?

A generator's kVA rating is its maximum apparent power output. How much of that translates to kW depends on your load's power factor. Most generator specs include a power factor assumption, typically 0.8. A 100 kVA generator at 0.8 PF delivers 80 kW. If your loads have a higher power factor, you get more usable watts from the same machine. Always check the kW rating alongside kVA, and size for your actual load's power factor.

Can kVAR be negative?

Yes. Reactive power is positive for inductive loads (motors, transformers) and negative for capacitive loads (capacitor banks, lightly loaded cables, some variable frequency drives). On a power triangle, negative kVAR shortens the vertical leg, which reduces the hypotenuse (kVA) and improves power factor. Power factor correction capacitors work specifically by introducing negative kVAR to offset positive kVAR from inductive loads.

Why do utilities charge for kVAR or low power factor?

Reactive power has to flow from the generating station to the load, passing through transmission lines and transformers. Even though it does no net work, it occupies current-carrying capacity and causes resistive losses along the way. When large industrial customers operate at low power factor, the utility must build extra generation and transmission capacity to supply the reactive demand. Reactive power charges or power factor penalties recover those infrastructure costs.

How do I measure kVAR directly?

A power meter or power analyzer that measures both real and reactive power will give you kVAR directly. Most modern digital power analyzers display P, Q, S, and PF simultaneously. If you only have a wattmeter and a clamp meter, you can measure kW and kVA, then calculate kVAR from the triangle: Q = √(S² - P²). The same approach works if you know power factor and apparent power: Q = S × sin(arccos(PF)).