# The kilowatt hour

As I am wont to do, I listened to the 6:30pm Radio 4 comedy program this evening.  It was an enjoyable, and mostly erudite program called The Manifesto.  It featured a comedian asking audience members to come up with ideas of what they would suggest for a political manifesto if they were standing for election.  Mostly they were a bit silly, and I don’t want to spoil any punchlines, so take a listen on the BBC website if you are reading this post within a week of when it was posted.

What I thought I’d mention, though, is a scientific inaccuracy that popped up in the program. One of the audience members suggested making it a law that power companies, when advertising, should only be able to say “look, our tariff is such-and-such” and nothing else.  The host, comedian Mark Thomas, picked this up and said (and I paraphrase) “right, so they’d have to say what the kilowatt-per-hour cost is, and nothing else?”

The point is that he got the units wrong.  No big deal in some sense, but telling in some ways that a rather intelligent guy, who showed a lot of political insight, didn’t understand the unit of electricity usage.  To be fair, it is quite a strange unit.  So, a kilowatt is a thousand watts.  So far so easy.  The kilo bit just means 1000.  A watt is a unit of power.  Power stations produce power, and they are rated in how many watts (or kilowatts or megawatts etc) they produce. Power is a measure of how much energy is produced or used in a given time.  A power station with twice the power of another one will produce twice as much energy in the same time.

Okay, so energy.  In physics, energy is a sort of virtual concept that can manifest itself in lots of non-virtual ways, and they can generally be transformed between the different forms.  Heat is a form of energy, there are lots of so-called potential energies associated with things like gravity or electricity or even mass (as Einstein realised). Motion has an energy associated with it.  It’s a kind of measure of how much useful work an object can do.  For example, the unit “Calorie” is a unit of energy.  When food is rated in terms of Calories (in fact the term is confusingly and colloquially used to actually refer to kilocalories), it refers to the amount of energy the food contains and that it can give someone as it is consumed, or can be turned into fat if it is not used to do energetic things.

The standard physicists unit of energy is the Joule, named after James Joule, a physicist and brewer from Salford.  It is related to the calorie by a fixed conversion rate, and measures the same kind of thing.  The watt, and kilowatt are then a rate of burning energy, and are basically the same unit as “joules per second”.  This kind of way of talking about units makes common sense, I think.  “Miles per hour” is understandable as the number of miles travelled per hour. “Joules per second” is the amount of energy used up (or provided, in the case of power stations) every second.  It’s perhaps not surprising that people think of the units of electricity used as “kilowatts per hour”.  In fact the units are “kilowatt-hours”.  That’s something quite different.  Rather than kilowatts divided by hours, it is kilowatts multiplied by hours.

Perhaps confusingly, what we have done is started from energy, and defined as unit (watt) as “energy per time”.  Then we take that unit and multiply by time, and we get back … energy. Electricity units are then just a unit of energy.  It is the same kind of things as a calorie, or a joule, but for the purposes of electricity consumption we call it a kilowatt hour.

Out of interest, you can use google to easily convert between units of things that measure the same kind of quantity, and it has a kind of internal calculator that does not condescend to bother the rest of the internet.  I typed “one kwh in kcal” into google, and it came back with “1 kilowatt hour = 860.42065 kilocalories.”

So every time you eat 860 “calories” of food, you have eaten an amount of energy equal to the standard unit of electricity billing.