Understanding the differences between kilowatts and kilowatt hours is relatively simple once you understand the basics. The differences include what is measured, over what span of time the measurement is made and how each is calculated.
Power Vs. Energy

Kilowatts measure power. Kilowatt hours measure energy. The power measured is electricity. The energy measured is electricity use over an hour of time. Energy is a calculation of power and is expressed as power multiplied by time.
Demand Vs. Consumption

Kilowatts measure the demand that an electrical device is putting on the supply of electricity. This demand takes into account the demand for power for one second of time. A kilowatt hour measures the consumption of electricity by an electrical device over an hour of time.
Calculation: Kilowatt

One kilowatt is equal to 1000 watts. 1000 watts is 1000 joules of electrical power per second. Most electrical devices are marked with their wattage, expressed in watts; therefore, if an electrical device is rated at 1000 watts, it will require the power of 1 kilowatt to operate for one second of time.
Calculation: Kilowatt hour

One kilowatt hour is simply the use of 1000 watts of power for the length of one hour. This would be calculated by multiplying watts by hours and then dividing by 1000 to obtain one kilowatt hour; therefore, if there is a draw of 100 watts of power for a period of 10 hours, 1 kilowatt hour of energy has been used.
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