What Is KVAR? Formula, Calculation, and Real-World Examples

If you work with three-phase electrical systems, you've almost certainly seen kW, kVA, and kVAR used side by side on a spec sheet or utility bill — and if you've ever wondered why there are three different units for what feels like the same thing, KVAR is usually where the confusion starts. Here's what it actually means, how to calculate it, and why it matters in practice.

What Is KVAR?

KVAR stands for kilovolt-ampere reactive, and it measures reactive power — the power that inductive loads (motors, transformers, and similar equipment) draw to establish the magnetic fields they need to operate, without converting that power into useful mechanical work or heat.

This is different from real power (kW), which is the power actually doing useful work, and apparent power (kVA), which is the total power the system has to supply — the combination of both real and reactive power together. The relationship between the three is often visualised as a right-angled triangle, known as the power triangle:

• kW (real power) sits along the base
• kVAR (reactive power) sits along the vertical side
• kVA (apparent power) is the hypotenuse connecting them

The ratio between kW and kVA is your power factor — a number between 0 and 1 that describes how efficiently a load is using the power supplied to it. A power factor of 1.0 would mean all the power drawn is doing useful work; in reality, inductive loads always pull some reactive power, so power factor is always somewhat below 1.

The KVAR Formula

For a three-phase system, reactive power is calculated as:

KVAR = √3 × V × I × sinφ ÷ 1000

Where:

• V = line voltage (volts)
• I = line current (amps)
• φ = the phase angle between voltage and current, where cosφ = power factor
• sinφ = calculated from the power factor as √(1 − cosφ²)

For a single-phase system, the same principle applies without the √3 multiplier:

KVAR = V × I × sinφ ÷ 1000

Worked Example: Calculating KVAR for a Three-Phase Motor

Take a typical three-phase induction motor with the following nameplate figures:

• Line voltage (V): 415V
• Line current (I): 60A
• Power factor (cosφ): 0.75 lagging

Step 1 — Find the apparent power (kVA): kVA = √3 × V × I ÷ 1000 = 1.732 × 415 × 60 ÷ 1000 = 43.14 kVA

Step 2 — Find sinφ from the power factor: sinφ = √(1 − 0.75²) = √(1 − 0.5625) = √0.4375 = 0.6614

Step 3 — Calculate KVAR: KVAR = kVA × sinφ = 43.14 × 0.6614 = 28.5 KVAR

So this motor draws roughly 28.5 KVAR of reactive power alongside its real power output — power the supply system has to provide even though it isn't converted into useful mechanical work.

Calculating KVAR from Real Power (KW) Instead

If you already know a load's real power (kW) and its power factor, rather than voltage and current, there's a more direct route:

KVAR = KW × tanφ

Where tanφ = sinφ ÷ cosφ, both derived from the power factor as above.

Using the same example: real power (kW) = kVA × cosφ = 43.14 × 0.75 = 32.36 kW. tanφ = 0.6614 ÷ 0.75 = 0.8819. So KVAR = 32.36 × 0.8819 = 28.5 KVAR — the same result, calculated a different way, which is a useful way to double-check either method.

Why Reactive Power (and Power Factor) Actually Matters

A low power factor — meaning high reactive power relative to real power — has real, practical costs:

Higher current draw for the same useful output. Because apparent power (kVA) is what the supply actually has to deliver, a poor power factor means more current flows through cables, transformers, and switchgear than the real power alone would require, increasing resistive losses throughout the system.

Utility penalties. Many commercial and industrial electricity tariffs include a power factor penalty, charging extra when a site's power factor falls below a set threshold (commonly around 0.9 or 0.95), since the utility has to size its own infrastructure for the higher apparent power draw.

Reduced effective capacity on generators and transformers. Equipment is rated in kVA precisely because it has to supply apparent power, not just real power. A generator or transformer supplying a load with a poor power factor reaches its kVA capacity limit sooner, even if the actual useful (kW) output is comparatively modest — which is part of why correct kVA sizing accounts for the power factor of the equipment it's expected to run, not just the equipment's kW rating alone.

How to Correct a Poor Power Factor

The standard fix is installing a capacitor bank, which supplies reactive power locally rather than drawing it from the incoming supply, improving the site's overall power factor. The capacitor bank's required size is calculated as:

KVARc = P × (tanφ1 − tanφ2)

Where P is real power (kW), φ1 is the original phase angle (from the existing power factor), and φ2 is the target phase angle (from the desired power factor).

Using the motor example above — improving power factor from 0.75 to a target of 0.95:

• tanφ1 = 0.8819 (as calculated above)
• tanφ2 = √(1 − 0.95²) ÷ 0.95 = 0.3122 ÷ 0.95 = 0.3286
• KVARc = 32.36 × (0.8819 − 0.3286) = 32.36 × 0.5533 = 17.9 KVAR

This tells you the capacitor bank needs to supply roughly 17.9 KVAR of reactive power to bring this load's power factor from 0.75 up to 0.95.

A Few Practical Notes

Always use line-to-line voltage for three-phase calculations, and double-check whether a nameplate or spec sheet is quoting line or phase current, since mixing the two is one of the most common calculation errors.

Power factor correction should be sized to the actual load, not guessed. Oversizing a capacitor bank can push a site into a leading power factor, which carries its own penalties and risks on some tariffs — this is a calculation worth having verified by a qualified electrical engineer for anything beyond a single small motor.

On sites running standby or prime generators, reactive loads matter for sizing too. Because generators, like transformers, are rated in kVA, a generator supplying a site with a poor overall power factor needs enough kVA headroom to cover the reactive demand of the loads connected to it — not just their combined kW rating. If you're specifying a genset for a site with significant motor or inductive load, it's worth having the site's expected power factor confirmed as part of that sizing exercise.

The Bottom Line

KVAR measures the reactive power that inductive equipment needs to operate, and it's a genuinely useful number to understand — not just for utility bills and power factor penalties, but for correctly sizing generators, transformers, and switchgear for the loads they'll actually carry. The formula itself is straightforward once you have voltage, current, and power factor to hand, and the same numbers feed directly into working out how much capacitor correction, if any, a site actually needs.