Kilowatts and Kilowatt-Hours

A recent article in the local newspaper on a solar-panel installation at a local high school reported that "[t]he entire school uses roughly 700 kilowatts per month." This is a mistake that I have seen several times in the media recently: the confusion between electrical power and energy, kilowatts versus kilowatt-hours. It is as jarring to an engineer like myself as confused homophones (buy/by, their/they're/there) likely are to an newspaper editor.

Power is a time-rate quantity – how quickly energy is used up over time. It is analogous to pounds-per-hour, gallons-per-minute, rods-per-hogshead, etc. The difficulty is that, unlike those other rate quantities, watts aren't expressed as per-whatever - the time portion is already built in. In residential electricity, the typical unit of measure for power is the kilowatt (kW, or 1000 W). A 100-watt lightbulb consumes power at a rate of 100 watts, not watts/second or watts-per-whatever.

If you want a more full answer, a watt can be expressed as a per-whatever; one watt is one joule per second second. A joule is measure of energy that makes wonderful and consistent sense in the SI (metric) units system, but isn't something that people have an intuitive grasp of. A joule is roughly 1/1000 a BTU, if anyone knows what that is, and about 1/4 of a calorie (not the calories listed on food packages, which are actually equal to 1000 of these calories chemists care about). More information on this, and an expanded rant about the weirdness of the watt is here.

Note that the "watt" does have this quirk in common with another power unit: the horsepower. If ever there was an anachronistic unit of measure, it's the horsepower. One horsepower is theoretically the mechanical power output of one horse, 33,000 foot-pounds per minute. Yeah, try to wrap your head around that one. And yet, we use it as some sort of measure of the capability of an internal combustion engine, and somehow people manage to understand that. Horsepower will be useful in a explaining a car analogy a little later in this post.

Energy is power integrated (summed up) over time, like total number gallons used to take a shower at such-and-such gallons/minute. That 100-watt lightbulb, if left on for ten hours, would consume a total of one kilowatt-hour (100 W * 10 h = 1 kWh). A kilowatt-hour is equivalent to 3.6 million joules or about 3400 BTUs. The kWh is a convenient unit of measure for residential electricity, because the typical U.S. household uses between 10 and 30 kWh per day, or upwards of 1000 per month. I say it's convenient, because imagine how much more confusing it would be for folks to be billed in gigajoules of electricity.

The electric utility charges customers based on the number of kilowatt-hours (total energy) they have used in a month, not on how quickly (kilowatts) they were used. The going residential rate (around here) is about $0.11/kWh. A typical household, depending on the time of day and the conscientiousness of its residents, needs between zero and, say, five kilowatts at any moment. When people talk about a new wind farm powering so many thousands of homes, they are assuming the typical home is using about 3 kW all the time. (Three kilowatts, 24x7, is actually an obscene amount of power for a home, but that’s another story.) Summed up over the course of a day, the typical U.S. household usage is around 30 kWh, for which the customer is charged a few dollars. H and I have managed to get our typical daily usage below 10 kWh, and we know of people that have achieved about 5 kWh/day.

This power/energy relationship for electricity is analogous to how your car's engine provides somewhere between a few and several hundred horsepower, depending on whether you are idling or accelerating hard from a stop light. That’s power varying in time. If you sum up that power usage over a long while, you can equate it to total energy in terms of how many gallons of gasoline you’ve used. In time, as hybrid and all-electric vehicles become more prevalent in the market, it may become useful to speak of the power rating of the electric motor in your car, in kilowatts, and the capacity of your battery bank, in kilowatt-hours.

So, back to the recent story reporting that "[t]he entire school uses roughly 700 kilowatts per month." That makes as little sense as saying my car uses 200 horsepower/second or 30 mpg/day. Perhaps the school uses 700 kilowatt-hours per month. That's unlikely, since it would mean their electric bill is only about $75/month. It is more likely that the school uses 700 kilowatts during peak hours of the day, and somewhat less during the night. Over an entire month, then, I estimate the school uses something like 250,000 kilowatt-hours. I can’t guess what the cost for that electricity is, because the school district probably pays a lower rate than residential customers, and they probably co-generate some of their electricity on-site alongside their heating and cooling.

Readers of this blog know that I have an interest in energy policy. In order to have meaningful conversations about energy, energy conservation, and energy policy, it is important to understand the terminology. Even beyond the terminology, it is important to have ballpark ideas of what’s reasonable and what’s not. How much power does a home actually use, how much does it need, how much could be saved with simple measures, and how much does this all cost?

These days, I suspect most people could tell you what their car’s mileage is, and how far they can go on a tank of gas, and how much a gallon of gas costs. I am often surprised, then, how few of those people also know how much energy their home uses each month and what the cost for that energy is.