If you have ever looked closely at an electric meter or utility bill, you may have noticed that the units of electricity consumption are given in kWh, or kilowatt-hours. If you don't have a formal background in physical science, this unit is likely to be confusing. Does it represent energy? Power? Or are these the same? Or is a kilowatt-hour something else entirely?

Of course, the main issue here for anyone who pays an electric bill is to understand consumption, how it might fluctuate over the course of a year and what might be done to lower consumption in a given period of time without compromising essential home or workplace functions. To do this, you first need to understand what a kilowatt-hour is and why this unit is employed in calculations rather than something more basic.

If nothing else, you're probably familiar with the concept of a watt, the unit used to classify light bulbs. A watt is the standard unit of power in physics, and power in turn is energy per unit time. The standard unit of energy is the joule and can be derived in a number of ways; the most common one is force multiplied by distance. The the standard unit of force is the newton, while that of distance is the meter, so a joule is really a newton-meter. Energy, by the way, has the same units as work and heat, and can be expressed in terms of ergs, calories or British thermal units, depending on the nature of the problem to be solved.

If power is energy divided by time, then a kilowatt-hour must have units of energy because multiplying a unit of power by a unit of time cancels out the time factor in the denominator of the power portion of the unit. Knowing that a kilowatt is 1,000 watts and one hour includes 3,600 seconds, you then have:

1 kWh = (1,000 J/sec)(3,600 sec) = (3,600,000 J) = 3.6 megajoules = 3.6 MJ.

According to the U.S. Energy Information Administration, the average home used slightly under 10,800 kWh of electrical energy in the year 2017. Some household items are notorious power hogs. For example, a dryer uses about 5,000 watts, or 5 kW, while a range top eats up over 8,000 watts, or 8 kW. A water heater checks in at 2,500 watts (2.5 kW) and a typical air conditioner is rated at about 1,600 watts (1.6 kW).

10,800 kWh in one year is about 900 kWh per month (10,800/12 months = 900) and about 30 kWh per day (using a month of 30 days, 900/30 = 30). Drilling down even deeper, since there are 24 hours in a day, this translates to about 1.25 kWh per hour (30/24 = 1.25). Since the "hour" unit in kWh/h is canceled out, it follows that expending 10,800 kWh of energy over the course of a year requires a steady power draw of 1.25 kW, or 1,250 watts.

If 10,800 kWh per year translates to 1.25 kW, then the conversion factor is:

(10,800 kWh/1.25 kW) = 8,640 h.

This is a step-by-step means of establishing what may have been clear to math nerds from the outset: To get from kWh per year to kW, you merely need to divide by the number of hours in a year. Although the above example arrives at 8,640, this figure is inexact owing to the rounding done in the problem. In reality, you need to multiply the number of hours in a day by the number of days in a year, and if you really want to get fancy and factor in leap years, the average number of days in a year is 365.25, not 365, since a leap year occurs every four years. Thus a more accurate way to derive kW from kWh/year means dividing by:

(365.25)(24) = 8,766 h.

To go from kWh/year to watts instead, just multiply this result by 1,000, since a kilowatt is 1,000 watts.