# Why do (kilo)watt-hours double-count units per time?

A watt is defined as 1 joule per second and is therefore a measurement of energy transfer over a period of time.

A kilowatt-hour is a measurement of energy equal to one kilowatt sustained over a period of one hour.

What is the point in double counting units per time? It seems to me that a kilowatt-hour could be more simply expressed as 3.6 megajoules.

This question was prompted by this article which triple-counted the time unit (using seconds, hours, and days): "New York City [uses] about 12 gigawatt-hours of electricity a day" Would it not be simpler and more intuitive to just state: "New York City uses 43.2 terajoules per day" or "New York City uses 500 megawatts"?

Is there a justification for using kilowatt-hours or is it used for historical reasons?

• I've removed a number of comments that were attempting to answer the question and/or responses to them. Please keep in mind that comments should be used for suggesting improvements and requesting clarification on the question, not for answering. – David Z May 1 at 22:19

There is historical reason behind using kWh as well as matter of general convenience. Many people around the world pay their electricity bills using the "per unit of electricity" concept that energy provider companies have defined as 1kWh.

Generally, the supplier has a base charge/connection charge for a certain number of electricity units (say "$$b$$"). Any usage above $$b$$ would be charged extra based on different price brackets. As you mentioned NYC in your question, here is an example [2] :

Now, why Wh or kWh is used here? It is because the general consumer has an easy way of verifying how much electricity they have been using by simple multiplication. All electrical appliances come with a power rating in W or kW, simply multiplying this number with the hours of usage with give kWh. Unarguably, this is much easier than calculating everything in Joules.

Summary: It is much more convenient for the general public to find out their electricity usage in kWh than J. This also gives much more sense to these usage numbers as different appliances have different range of wattage (LED light bulb ~ 5-20W, Fan ~ 55-100W, A.C. unit ~ 900-3000 W, etc.).

• Isn't that a chicken-and-egg issue though? It's easier to measure in KwH because your fridge has its power rating in kW. But why does the fridge have its power rating in kW? If it had its power rating in joules per hour and the electricity companies billed you per joule, wouldn't the calculation be just as simple? – JBentley May 1 at 9:43
• @JBentley: It is kind of a chicken-egg problem but not really. A common refrigerator can have a wattage rating of 200W. As you would know it is nothing but 200J/s converting to J/h gives a pretty big number of 720000 J/h. It seems that, writing in Watts seems more straightforward for an avg. consumer to compare energy efficiency and make a purchase decision. – user115625 May 1 at 15:53
• @JBentley The power bill is not the only place where you need the power rating. Wiring and circuit breakers generally have an ampere rating. If I multiply that by the nominal voltage, I get the maximal power rating of that circuit in kW. So if I want to know if I can use the fridge, the toaster and the tea kettle at the same time, I need their power rating in kW. – mlk May 1 at 17:38
• @JBentley You are correct that it's just as easy for the consumer for appliances to be rated in kJ/h (which gives numbers in a similar range to the usual power ratings in W) or MJ/h (which gives similar numbers to a power rating in kW). The only reason one unit is used over the other is because people arbitrarily chose that one decades ago. Hence, it's a historical reason, as the answerer said in his first sentence. – probably_someone May 1 at 17:42
• @JBentley: Then you'd be asking why power consumption ratings are given in this weird joules per hour unit when we have watts. Either way, some unit is weird. – user2357112 supports Monica May 1 at 20:02

Practically speaking, maybe you want to know how much energy it takes to keep your refrigerator running for one hour. On the back of a fridge you can find the power in watts. If you measure energy in units of $$kW\cdot h$$, it's easier to figure out how long you can keep it running.

You can call it the "natural unit for a thrifty man".

• The joule is a watt-second. We rescale and use kilowatt-hours instead because many appliances use power in the range of kilowatts and an hour is a reasonable timescale over which to consider energy consumption of appliances. Saves end users (who do not know physics) some complicated conversions. – jgerber May 1 at 9:14
• It's more confusing when appliances such as air conditioners or burners on gas stoves in the US are rated in" BTU". When buying my gas cooktop I saw the BTU rating and asked the salesperson BTU per what? ---per second, per hour, per day, total lifetime of the appliance? The salesperson had not a clue. I eventially discoved tha sales-speak "BTU" means one BTU/per hour. Even worse Industrial AC units and freezers are rated in "Tons." "One Ton" means capable of freezing one US (2000 lb) ton of ice per day. kWh is simple compared to this – mike stone May 1 at 13:32

The way you phrase the question is slightly ambiguous, it doesn't double count units per time. One is per time, the other is $$\times$$ time. And therefore cancels to get joules. However just using joules, you get no idea on the time period that amount of energy was used, just the amount. Using $$kW\cdot h$$ gives you a reference for how long you used an amount of power for. Joules has no real practical meaning to the lay-man whereas all appliances are in Watts, because you need to know how much energy an appliance uses in a specific time ($$1s$$). You can't have appliance ratings in joules that makes no sense.

• But kWh doesn't tell you how long you used the power for - using 1kWh of energy doesn't tell you if you used one 1kW device for 1 hour, or one 100W device for 10 hours. 1kWh is absolutely no different from 3.6MJ in that regard, which also tells you absolutely nothing about the time period over which the energy was used. An appliance rating in J/s is perfectly equivalent to a rating in W. I agree that kWh is a more "natural" unit since everyone is so used to it at this point, but there's nothing fundamentally different between the two. – Nuclear Wang May 1 at 20:13
• @NuclearWang This is why appliances are rated in Watts. Sure the overall power consumption you cannot tell how long it was used, but when determining usage of individual things against a set $kWh$ you can tell. And yes$Js^{-1}$ is perfectly equivalent, but what's easier? A capital $W$ or $Js^{-1}$? – SamuraiMelon May 1 at 21:45

# Kilowatt-hours without time information are useless

"1 kW⋅h" does not give any information about how much time was needed in order to transform this amount of energy. It could have been either 1000W during an hour or ~114mW during a year.

Similarly, my household could also consume 12 gigawatt-hours worth of electricity. It would just need 4000 years to do so.

# Watts without time information are (typically) useless

New York City uses 500 megawatts

Some duration information is also missing in this sentence. Is this peak power? Is this in winter or in summer? Is this an average over a whole year, or was it during the last 24h?

# Pick the unit which allows the easiest comparison

One way or another, you probably should specify either :

• Energy & Duration
• Power & Duration

In theory, you could always pick the same units (e.g. W and s) but there's a very wide variation of orders of magnitude for energy and power.

People usually know how long a kilometer or a mile is, or how cold 10°C or 50°F are.

Most people will have no clue what 43TJ represent, though.

Depending on your audience, you should then pick the units and magnitudes which help compare to more tangible things, such as a horsepower, the energy content of 1l of gasoline, the average yearly consumption of a household or the power output of a nuclear power reactor.

• Downvoter : constructive criticism is welcome! – Eric Duminil May 2 at 7:35