You often know real kilowatts from a motor plate or meter—not kVA. This guide shows the real power (kW) to reactive power (kVAR) path: convert kW and PF to apparent kVA, then read kVAR from the power triangle in the calculator.
Benefits
- Bridge: kVA = kW ÷ PF, then kVAR = √(kVA² − kW²).
- Direct form: kVAR = kW × tan(arccos PF) when PF is known.
- Confirms kW output matches your known real load.
How it works
- Start with real power kW (nameplate shaft power ÷ efficiency, or measured kW).
- Divide by power factor to get kVA: kVA = kW ÷ PF.
- Enter that kVA and PF in the tool—read kVAR and verify kW matches input.
FAQ
How do I convert kW to kVAR with power factor?
kVA = kW ÷ PF, then kVAR = √(kVA² − kW²). Example: 9 kW at 0.85 PF → kVA = 9 ÷ 0.85 ≈ 10.59 → kVAR = √(112.1 − 81) ≈ 5.58 kVAR. Equivalently kVAR ≈ kW × tan(arccos 0.85) ≈ 5.58.
I only have kW on the motor—what PF do I use?
Use motor catalog PF at full load (often 0.8–0.9) or measure at the panel. Underestimating PF underestimates kVA and kVAR—size conservatively for distribution. Resistive loads: PF ≈ 1 → kVAR ≈ 0.
Why convert kW to kVAR if billing is in kW?
kVAR does not appear on a simple energy bill but sets apparent kVA and current. Inverter limits, transformer loading, and conductor ampacity follow kVA = √(kW² + kVAR²). Converting from known kW completes the triangle for equipment sizing.
Technical specifications
- kVA = kW ÷ PF.
- kVAR = √(kVA² − kW²) = kW × tan(arccos PF).
- PF = kW ÷ kVA (reverse check).
- Related: kva-to-kw, calculate-kvar-for-inverter-and-conductor-sizing.
Motor plates speak kW; the triangle needs all three
Nameplate kilowatts describe real mechanical or electrical work at rated conditions. Reactive kVAR is not printed but exists whenever PF is below unity. Dividing your known kW by PF yields the kVA to enter in the tool—the output kVAR leg completes the triangle and should reconcile with the kW you started from.
tan φ is the shortcut from kW to kVAR
When PF is stable, kVAR ≈ kW × tan(arccos PF). At PF 0.8, tan φ ≈ 0.75 so kVAR is roughly three-quarters of kW. The calculator path through kVA is equivalent but easier to audit in spreadsheets—publish both kVA and kVAR on the same line item for reviewers.
Stack multiple kW loads with blended PF
Sum real kW across branches, but do not sum kVAR blindly without phase awareness. For a first-pass workshop estimate, weight PF by kVA share per load, compute blended kVA = total kW ÷ PF_blend, then kVAR. Refine with measured panel data when motor starts overlap and PF dips simultaneously.