kW vs kWh vs kVA

The plumbing version

Rate versus quantity is the whole of the kW/kWh distinction. A tap running at 2 gallons per minute is a rate; 120 gallons in the bucket is a quantity. Run the tap for an hour and you get both.

• kW is the rate. How hard the facility is drawing electricity at this instant, or on average across an interval.
• kWh is the quantity. kW multiplied by hours. A 5 kW load running 3 hours consumes 15 kWh.
• kVA is the size of the pipe. Apparent power — the vector sum of the useful power and the reactive power the utility must also carry.

The power triangle

Alternating-current systems have three power quantities and they combine vectorially, not arithmetically:

kVA² = kW² + kVAr² Power factor = kW ÷ kVA

• kW — real power. Does the work. Turns the shaft, heats the element.
• kVAr — reactive power. Sustains the magnetic fields that motors and transformers need. Does no work, but occupies the conductors.
• kVA — apparent power. What the transformer, the switchgear and the utility feeder must be sized for.

Because they add vectorially, kW plus kVAr does not equal kVA. 212 kW and 131 kVAr is 249 kVA, not 343.

Worked example

A 480 V three-phase load drawing 300 A at a power factor of 0.85:

• kVA = (√3 × 480 V × 300 A) ÷ 1,000 = 249.4 kVA
• kW = 249.4 × 0.85 = 212 kW
• kVAr = √(249.4² − 212²) = √(62,200 − 44,944) = 131 kVAr

Run that load at a 60% duty cycle over a 730-hour month:

• kWh = 212 kW × 730 h × 0.60 = 92,856 kWh

Now put it on a bill at $0.09/kWh energy and $14.50/kW-month demand:

• Energy: 92,856 × $0.09 = $8,357
• Demand, if this load sets the peak: 212 × $14.50 = $3,074
• On a kVA-demand tariff instead: 249.4 × $14.50 = $3,616 — $542 a month more, entirely because of the 0.85 power factor

That last line is the practical reason kVA matters to a facility manager. See what is power factor.

Which unit each line of the bill uses

Bill line	Unit	Set by
Energy charge	kWh	Total consumption over the period
Demand charge	kW (or kVA on some tariffs)	The single highest demand interval
Power factor penalty	derived from kVAr	Coincident kW and kVAr at the billed meter
Capacity / transmission	kW at coincident peak	Load during system peak hours

The other units that turn up

• kVAr — reactive power, as above.
• kBtu — a heat unit, used in benchmarking. 1 kWh = 3.412 kBtu. 1 therm of natural gas = 100 kBtu. Benchmarking converts every fuel into kBtu so they can be summed. See energy benchmarking.
• Tons of refrigeration — 1 ton = 12,000 Btu/hour of cooling. A chiller at 0.6 kW/ton drawing 500 tons is consuming 300 kW.
• hp — motor nameplate horsepower. 1 hp = 0.746 kW of output. A 100 hp motor at 92% efficiency and 75% load draws roughly 100 × 0.746 × 0.75 ÷ 0.92 = 61 kW, not 74.6 kW and certainly not 100 kW.

What these units are not

kW is not kWh, and the two are not interchangeable in a sentence. "The building used 400 kW last month" is not a statement about consumption; it is either a statement about peak demand or a mistake. Utilities bill them on separate lines at separate rates, and the confusion is the single most common error in facility energy discussion.

kVA is not kW. A 500 kVA transformer does not deliver 500 kW to a load at 0.85 power factor; it delivers about 425 kW. Sizing a transformer from a kW load figure without accounting for power factor produces an undersized transformer.

A motor's nameplate rating is not its draw. Nameplate horsepower is mechanical output at full load. Actual electrical input depends on loading and efficiency, and most industrial motors run well below full load — which is also why plant power factor is usually worse than the nameplate suggests.

kWh is not a measure of cost. Two facilities consuming identical kWh can pay very different amounts, depending on when the consumption occurred, what peak it set, and what power factor accompanied it.

Prefixes matter. kW is one thousand watts; MW is one million. PJM capacity prices are quoted in dollars per MW-day, and a facility working in kW must convert before comparing.