kVA to kW Calculator

How it works

In an AC circuit the apparent power (kVA, volts times amps) splits into two parts at right angles: real power (kW), which does work, and reactive power (kVAR), which flows back and forth to build magnetic and electric fields. The three form a right triangle with kVA as the hypotenuse, so kVA² = kW² + kVAR².

The power factor is the ratio kW ÷ kVA, which is also the cosine of the phase angle φ between voltage and current. Knowing the power factor and any one side fixes the triangle; so does knowing any two sides.

Pick which two values you know. The calculator reads only those two fields and fills in the rest, including the phase angle in degrees.

Formula

kW   = kVA × PF
kVAR = kVA × sin φ = kVA × √(1 − PF²)
kVA² = kW² + kVAR²
PF   = cos φ = kW ÷ kVA
φ    = arccos(PF) = arctan(kVAR ÷ kW)

Example

A generator rated 100 kVA at a power factor of 0.8, the defaults, delivers 100 × 0.8 = 80 kW of real power and 100 × √(1 − 0.64) = 60 kVAR of reactive power. The phase angle is arccos 0.8 = 36.87°.

A load drawing 45 kW and 21.7945 kVAR has an apparent power of √(45² + 21.7945²) = 50.000 kVA, a power factor of 45 ÷ 50 = 0.9000 and a phase angle of 25.84°.

Assumptions and limitations

• Steady-state sinusoidal AC. The power factor here is the displacement power factor (cos φ); loads with distorted current have a lower true power factor that this triangle does not capture.
• Leading and lagging power factors give the same magnitudes; the sign of kVAR (inductive or capacitive) is not tracked.
• Typical figures such as 0.8 for generator nameplates and 0.85–0.95 for industrial loads are illustrative defaults, not data about any particular machine; a machine's own rating or measurement governs.
• The relationships are the same in VA, W and VAR or in MVA, MW and MVAR, as long as all three use the same prefix. For three-phase systems, kVA, kW and kVAR are the three-phase totals.
• This is a calculation aid, not an engineering or code compliance determination. Equipment sizing is governed by the manufacturer's ratings, the National Electrical Code (NFPA 70) and the authority having jurisdiction.

Frequently asked questions