# Why is daily power usage measured in kWh and not just kW?

It seems redundant to measure power per hour per day. Is there a good way to understand why they do it this way?

• Rather, kW is power, kWh is energy. But there's already an answer for that. Sep 30 at 1:30
• @steveowen "They charge energy in kw hours per day" No. They don't. They charge in kWh. To use the speed/distance analogy. You were travelling at 30mph for an hour, so you've travelled 30miles. If you're using a 3kW (power) load for an hour, you will have used 3kWh (energy)
– SiHa
Sep 30 at 12:22
• kWh is power times hour, not power per hour. Sep 30 at 17:56
• You confuse "kWh" as meaning "kW/h". Oct 1 at 6:49
• May be a better question would be: Why don't they use kJ instead of kWh? Oct 1 at 15:01

The source of your misunderstanding can be found in your comment above:

@marcelm yes, but we don't say we travel 60miles per hour today -it's just miles per day. They charge energy in kw hours per day.

They don't.

Power companies price energy in dollars (or whatever your local currency is called) per kilowatt-hour. And the size of your electricity bill is directly proportional (at least if you have a fixed-price contract, and ignoring any flat service fees added on top) to the number of kilowatt-hours of energy you've consumed during the billing period, whatever it may be.

It's indeed possible that your power company is reporting your average electricity usage in "kilowatt-hours per day". This is a somewhat silly unit that just equals 1/24 kilowatts, but it kind of makes sense if:

1. your power company is billing you by the kilowatt-hour, and
2. they're reporting your total measured electricity usage per day.

In that case, if you've used a total of X kilowatt-hours of electricity during a particular day, then your average usage during that day is X kilowatt-hours per day (or, equivalently, X/24 kilowatts).

What may be confusing you is that a kilowatt-hour is a somewhat silly unit in the first place.

For most things, such as water, we measure total usage in simple units like liters (or gallons or cubic meters or whatever) and usage rate over time in derived units like liters per hour (or gallons per hour, etc.).

But, for some historical reasons, for electricity (and energy in general) we've decided to start with a unit (the watt, or more commonly the kilowatt, which is just 1000 watts) measuring usage rate over time, which then means that we have to multiply the usage rate unit (e.g. kilowatts) with some unit of time (e.g. hours) to get a unit for measuring total usage.

It's a bit like if we decided to measure water flow in "firehoses" (you know, how fast an industry standard fire hose can spray out water) and then had to measure total water volume in "firehose-hours" (i.e. the amount of water that a stardard firehose sprays out in an hour). And if you wanted to know how much water you used in your house per day on average, your water company might then report that in "firehose-hours per day" (equivalent to the number of hours it would take a standard fire hose to spray out the same amount of water as you used in an average day).

In fact we could've adopted a more sensible system for energy, too. The stardard SI unit of energy is the joule, equal to one watt-second, so one kilowatt-hour is equal to 3600 kilojoules (since one hour is 3600 seconds) or 3.6 megajoules.

If power companies started billing by, say, megajoules of energy used, then they could report average energy usage rates e.g. in megajoules per day, or simply in kilowatts (= 86.4 megajoules per day, since one 24-hour day is 86.4 kiloseconds). But for historical reasons the power delivery industry is firmly stuck with kilowatt-hours and unlikely to change any time soon.

In any case, for practical purposes, just think of a "kilowatt-hour" as a measure of total energy (since that's what it is), just like a liter (or a gallon or a cubic meter, etc.) is a measure of total water volume.

Just like water, energy is a "substance" that you consume, and your power company bills you for the total amount of energy you've consumed, just like your water company bills you for the total amount of water you've consumed.

Here's a convenient table illustrating the parallelism:

Water Energy (kWh) Energy (MJ)
Total amount Liters Kilowatt-hours Megajoules
Usage rate (per second) Liters per second Kilowatt-hours per second Megawatts (= MJ / sec)
Usage rate (per hour) Liters per hour Kilowatts (= kWh / hour) Megajoules per hour
Usage rate (per day) Liters per day Kilowatt-hours per day Megajoules per day
• In fact, in the spreadsheet I use for tracking home energy costs, I convert both kWh and therms of oil into megajoules so I can get a combined total and see how moving between heat pump and furnace affects my actual usage. (Yes, that ignores relative cost of the two energy sources; total cost of operation would be a different column, and is also affected by which electricity source mix I'm paying for. I haven't attempted to come up with a formula for "greenness" that accounts for all impacts; I'll leave that for experts.) Oct 1 at 8:07
• The firehose-hours per day is a good analogy, I'll certainly reuse that in my own explanations to non-engineers... Oct 1 at 12:00
• It's not silly to have a measure of power before a unit of energy. Consider literal horsepower. People needed to figure how many horses they need to pull a coach. They didn't really care about energy, it was just a given that horses needed to eat and could only run for a certain amount of time. It's only in our home lives, having effectively unlimited power, that the distinction between power and energy seems confusing. If you tow a boat then there's no confusion between horsepower and how full the gas tank is. Oct 1 at 13:22
• Another good illustration of circular reasoning is measuring the length of your boat in knot-seconds... Oct 1 at 14:34
• Many photographic flash devices have their output rated in watt-seconds instead of joules Oct 2 at 6:50

kW measures energy per unit time. kWh measures energy. If you consume a steady 1000 Watts for a full hour, you'll have consumed 1 kWh of energy. The power company wants to measure your energy consumption because they charge based on energy consumption. They give you energy consumption in kWh and a price per kWh, where the simple product is your energy cost for the month.

Think of a graph of your household's Watts (energy per unit time) consumed over the course of a month. Turn on a light, then the line jumps up by the light's 10 Watts. Turn off a computer, then the line jumps down by the computer's 200 Watts. The power company charges you based on the area under the line on that graph.

• kW is just plain power. It has no time element. Sep 30 at 1:31
• @Ecnerwal, you didn't read my statement closely enough. "Power or energy per unit time." Sep 30 at 1:35
• @steveowen, you don't "use 10kW per day." A kW is an energy consumption rate. You pay for how much energy you consume, not how fast you consume it. "Us[ing] 10 kW per day" is analogous to "printing 10 ppm per day." The power company's 5 kWh per day is telling you your average daily energy consumption. They just took your monthly energy consumption and divided it by 30. Sep 30 at 4:16
• @Ecnerwal Sorry, you need to check your units: "kW is just plain power. It has no time element" as a Watt is defined as a Joule per second. Therefore is does have a time element. Sep 30 at 7:23
• Funnily enough, I had to explain exactly this misunderstanding to someone with a BEng in electrical and electronic engineering the other day. The best way this was explained to be at school was to mathematically show that 1 KWh = 3,600,000 J. Sep 30 at 16:34

It isn't "power per hour per day" -- that would be written, for example, as kW/h/day. The divide symbol / is read as "per."

The unit "kWh" could be more explicitly written kW ⋅ h. The dot signifies multiplication. Mathematicians and engineers don't verbalize it, though: when we read "kWh" we simply say "kilowatt hours." A person is supposed to recognize that:

• the "kilo" prefix means one thousand,
• Watt is a unit of power,
• hour is a unit of time, and
• when two units are given sequentially, without the word "per" or symbol "/" (slash, as I call it) intervening, it is inferred that the two units are multiplied together.

So kWh is not "power per hour" but rather "power times (multiplied by) hours." Scientifically speaking, power is a quantity measured at an instant in time -- not unlike voltage, or amps, or PSI in water pressure.

The electric utility bills for energy, and one way of expressing energy is power multiplied by time.

• Pretty good answer! Nitpick - your "•" (U+2022) is the "bullet" character. You want to use the dot operator (U+22C5) for kW⋅h. Oct 2 at 6:55
• @Nayuki There's a unicode expert in every crowd. ;-) Thanks! Oct 2 at 14:35

You write:

[W]e don't say we travel 60miles per hour today -it's just miles per day.

That's exactly right, and the same goes for electric power, too.

A kilowatt is kind of like a mile per hour. It's a "speed" at which you're consuming energy. A kilowatt hour, on the other hand, is kind of like a mile. It's an actual amount of energy.

Just like you can say "we travel 60 miles per day," you can say "we consume 60 kilowatt hours per day." But since a kilowatt is like a mile per hour, saying "we consume 60 kilowatts per day" would be like saying "we travel 60 miles per hour per day."

Watts is an instantaneous measurement; an LED bulb draws about 10 watts whenever it is on

Watthours is total usage over a time period; if the 10w bulb is on for 1.5 hours that's 15 Wh; the same would be true of a 15 watt device running for 1 hour, or a 30W draw for half an hour.

Over a billing cycle of a month, I use (and pay for) something like 300 kWh. That means my average usage per day is approximately 10kWh. If we call a day 25 hours to make the math easier, that means the devices in my house are drawing about 400W at any average moment.

I could add up the demand from lights and appliances in the house, figure out how often and how long they're in use, and should come up with roughly the same average use of 400W or (multiplying by hours in a month) 300 kWh over a month.

Note that dividing by 30 to get an average day doesn't remove time from the equation. Months times days per month equals days, still a unit of time,and still typically given in kWh rather than kWd(ay). To convert to the latter, you'd need to multiply by hours per day, and it would still be per unit time since hours per day is time per time and dimensionless.

(Dimensional analysis works, but only if you are careful to track the dimensions of every value.)

Watts, by the way, is volts times amps. Amps is coulombs per second, but unless you are going down to coulombs that's irrelevant.

The analogy between speed and distance, with watts as speed and watt hours as distance, is entirely valid. Speed is distance per unit time; multiply it by time to get distance. Amps is coulombs per hour, scaled, if you want to go to that level; the "per hour" is cancelled out by the "times hours" in watt-hours to give you units of coulombs times voltage, which is a pretty decent measurement of how much "oomph" was delivered/consumed during that measurement period. (BAD analogy: if coulombs were mass, volts would be pressure, sort of; amps would be how fast you are releasing that pressure to get work done.)

Does that help? If we go much further I'm going to have to issue a freshman physics quiz...

• (I once got extra points from a science teacher by pointing out that power in Watts was both directly proportional to resistance, and inversely proportional to resistance, depending on whether you were holding volts or amps constant.) Sep 30 at 5:49
• So as part of the dimensional analysis that you mention a Watt is defined as a Joule per second... So Watts does include time... Sep 30 at 7:25
• See en.wikipedia.org/wiki/Watt and don't confuse with Joule-second... Perhaps you need to start with just using M, L and T to derive the units. Sep 30 at 9:58
• The Wikipedia article does not disagree with me. There are multiple ways to derive any unit from other units (there have to be if they're to be consistent), , and when starting with volts and amps seconds don't appear because they're already part of the ampere's definition. Unless you want to go down to coulombs, which aren't used in the home improvement domain Sep 30 at 10:16
• dropped objects? like improvement or provement? But do you favor Rayleigh or Buckingham? Sep 30 at 10:17

Let's clarify some concepts.

why is Daily power usage measured in kWh and not just kW?

kWh is not a unit of power, it is a unit of energy. In contrast, kW is a unit of power.

Why is that?

By definition, power is the rate at which work (or energy) is done per unit of time. Mathematically: Where:

• P is the power, measured in watts (W) in the SI
• W is the work (or energy), measured in (J) in the SI
• t is the time, measured in seconds (s) in the SI

Note that: From the above equation it is evident that if we multiply the power by a time (T), we will obtain a unit of energy.

For example, suppose we have 1 kW, and we multiply it by 1 h which is equal to 3600 s: This demonstrates that 1 kWh = 3600 kJ, which is a unit of energy.

Finally, power can be understood as the rate at which energy is supplied or consumed. When you pay your electricity bill, you are actually paying for the energy consumed, not for the power. This makes more sense. For example, a 9-watt lamp consumes 9 joules per second. Therefore, you need to know how long the lamp is on to determine the total energy consumed. If the lamp is on for 1 hour, then 9 watt-hours have been consumed, or 9·3600 = 32400 joules.

Watts is an instantaneous rate. While its units may be the same as kWh/day it doesn't convey the same idea.

By analogy, km/h is a rate. If you go 10km/h for one hour each day for a month, you've gone 300km. You could say "I've gone 10 km per day this month". You would not say "I went 0.42 km/h this month". In a contrived way you did, but it fails to communicate what you want.

Similarly daily power usage is expressed in kWh/day rather than just kW because it provides a familiar, accessible way for people to understand the energy usage. Although it can mathematically be reduced to kW, the resulting number is not meaningful to most people. "I used 100 Watts this month" sounds like you have a 100 Watt light bulb that was on all month, not what you probably mean if you consumed energy at various rates and times, averaging 2.4 kWh/day, even though that's mathematically equivalent.

One can measure in either.

If you measure your daily usage in kWh - you get to add together your 30 daily usages and you get your monthly power bill.

On the other hand, you may divide the above by 24 (hours) and you will get the average power over the day (in kW). This may be somewhat useful number if you are debugging your power usage.

To clear up some terminology. You consume energy, not power. Power is energy used per unit time.

The simple answer to your actual question is because power companies believe the public is uneducated.

Most home appliances list power consumption in Watts (1 joule of energy per second). So it's inherently understandable that if you use 1kW for 1h you get billed for 1kWh.

1kWh is directly equivalent to 3600kJ of energy.