kW to kVA

Introduction

Loads are listed in kilowatts, but generators, transformers and UPS units are sold in kVA. The link is the power factor. A plant drawing 400 kW at a power factor of 0.8 needs a 500 kVA source, not a 400 kVA one, because the source must carry the full current, including the part that does no work.

This calculator converts real power in kW to apparent power in kVA at the load's power factor. It also gives the reactive power in kvar and the line current at the supply voltage. It is for engineers sizing standby generators, transformers and UPS systems, and for electricians checking a supply.

Formulas

The power triangle:

S = P / cos φ
Q = S × sin φ = √(S² − P²)

Line current:

three-phase:   I = S / (√3 × V)
single-phase:  I = S / V

• P — real power, kW
• S — apparent power, kVA
• Q — reactive power, kvar
• cos φ — power factor of the whole load

Assumptions and limitations

• The power factor is that of the whole load. For a mix, divide the total kW by the total kVA; do not average the power factors.
• Generators are rated at a power factor of 0.8 by convention (ISO 8528-1). A 500 kVA generator delivers 400 kW, and loads below 0.8 are limited by its kVA.
• The result is the running load. Add margin for motor starting, inrush, growth and the generator's own derating for altitude and temperature.

Worked example

A plant draws 400 kW at a power factor of 0.8 from a 400 V three-phase supply. What size of generator does it need?

1. Apparent power: S = 400 / 0.8 = 500 kVA.
2. Reactive power: Q = 500 × 0.6 = 300 kvar.
3. Line current: I = 500 000 / (1.732 × 400) = 722 A.

So the generator must be rated at least 500 kVA, before margins. Raising the power factor to 0.95 with capacitors would cut the requirement to 421 kVA.

FAQ

Related calculators

• kVA to kW — the usable kW of a kVA rating.
• kVA to amps — the current of a kVA rating.
• Generator load, kVA and fuel — loading and redundancy of generator sets.
• Transformer sizing and voltage regulation — choosing a transformer for the kVA.