kW and kWh Explained

A lot of people, energy professionals included, don't fully understand the difference between kW and kWh. If you are one of them, fear not, this article should set you straight!

If you're working with energy on a regular basis, and you don't fully understand the difference between a kW and a kWh, we promise you that taking 20 minutes or so to fully understand the concepts explained in this article will save you many headaches in the future. Quite likely it will save you some embarrassment at some point too, as you'll be much less likely to make embarrassing calculation errors.

(If at any point you'd like to thank us for our help in reducing headaches and embarrassment, please point your colleagues and website visitors towards this article so that it can help them too. Or, if you find it useful, you could buy or recommend our Energy Lens software – we really appreciate the customers that keep us in business.)

Anyway, that's more than enough preamble... Let's get to it...

What is the difference between a kW and a kWh?

Well, the difference is really very simple. Though it only seems simple after you understand it.

OK, but a lot of people don't really understand the difference between energy and power either... So let's start at the beginning:

What is energy?

(A physicist might throw their arms up in disgust at how we've over-simplified one of the fundamentals of the universe. But fortunately we're not writing this for physicists...)

The kilowatt hour (kWh) is a unit of energy... The Calorie is a unit of energy... And the joule (J) is a unit of energy... And these aren't the only units of energy – there's the BTU, the watt hour (Wh), the therm, and plenty of obscure units that you're unlikely to have heard of.

It's a bit like how you can measure distance in units of feet, metres, miles, km and so on. The distance between New York and London is fixed, but you can express that distance as 3,459 miles, or 5,567 km, or 18,265,315 feet etc. Similarly, you can express a measure of energy in joules, or Calories, or kWh, or BTU etc.

When people talk about a particular biscuit containing 172 Calories, they're talking about the amount of energy contained within that biscuit. 172 Calories is equivalent to around 0.2 kWh. (That's with "172 Calories" meaning 172 kilocalories, which is the unit that is almost always meant when people talk about the "calories" in food.)

Energy can change form. We could eat the biscuit to provide us with energy. Or we could burn the biscuit and turn it into heat energy. Given the right equipment we could turn the heat energy from the burning biscuit into electrical energy to run lights and fans and so on. Some energy would be wasted in the conversion process, but it should be possible to get that burning biscuit to run a light bulb for at least a few seconds.

Probably the best option would be to eat the biscuit, but hopefully you get the general idea – the biscuit contains energy that can be converted into different forms...

Our biscuits contain a certain amount of energy – 172 Calories or 0.2 kWh per biscuit. But biscuit energy is not in a form that we can easily use to run the equipment in our buildings...

However, we can easily make use of electricity. And, provided we've got a gas or oil burner, we can easily make use of gas or oil. One form of energy comes through wires (isn't electricity clever?!), and others come as gases, liquids, or solids that we burn (to turn into heat). At the end of the day it's all just usable energy in different forms. We can express quantities of these forms of energy in terms of kWh. We buy or generate the kWh of energy, and we use it to fuel the equipment in our buildings.

The relationship between energy consumption (kWh) and time

A typical building uses more energy over long periods of time than it does over short periods of time:

• On February 16th, 2018 a building might have used 95 kWh.
• Over the week starting April 9th, 2018 it might have used 550 kWh.
• From January 1st, 2017 to December 31st, 2017 it might have used 31,250 kWh.

Given the three figures above, we can easily see that the building used more energy over the course of 2017 than it did on February 16th, 2018. No surprises there.

However, we can't immediately compare the efficiency of the building over each of those periods. If a kWh figure covers a day, we can only compare it fairly with other kWh figures that cover a day. If a kWh figure covers a week, we can only fairly compare it with other kWh figures that cover a week.

If we have the kWh from February and the kWh from March, we can't really compare the two figures fairly, because February is typically 28 days long, whilst March is 31 days long. This article explains more about the problems that arise if you compare the kWh used in one month with the kWh used in the next.

Energy consumption expressed in terms of kWh doesn't often mean much unless you also know the length of the period that the kWh were measured over. And it's difficult to make fair comparisons between kWh figures unless they are all from periods of exactly the same length. Figures expressed in terms of power (e.g. kW) make many things more straightforward...

What is power?

(Strictly speaking energy isn't actually generated or used, it's converted from one form into another. Like how the energy stored in oil is converted into heat when you burn it. And like how the electricity that runs a fan is converted into the motion of the fan blade (kinetic energy). But this is a distinction that people generally don't worry about when they're staring at an excessive energy bill and wondering how they can "use" less energy.)

So power is a measure of how fast something is generating or using energy. The higher a building's kW, the faster that building is using energy.

Joules per second (J/s) is a nice, clear unit of power. Joules per second makes it obvious that power is the rate at which energy is being generated or used. It's like how miles per hour makes it obvious that speed is the rate at which distance is being travelled.

James Watt

The watt (W) is another unit of power. It doesn't make it quite so obvious what power means. But the watt is actually just another name for Joules per second. J/s and W are the same thing. Just some bright spark decided that equations and whatnot would be simpler if power had its own unit (instead of being expressed using units of energy and time together). And they named this unit after James Watt, the Scottish inventor who had an important hand in the development of the steam engine.

So, joules per second (J/s) is a measure of power... The watt (W) is a measure of power... And the kilowatt (kW) is a measure of power too (one kW being 1000 watts).

Things that "generate power"

Items of equipment like boilers, electricity generators, and wind turbines, take energy in one form (e.g. gas or oil or wind) and turn it into another (e.g. heat or electricity).

There's a limit to how much useful stuff these things can generate, and that is expressed as the rate at which they can generate energy. Which is, by definition, their power.

Consider a 10 kW wind turbine... Provided it has the optimum level of wind (which probably doesn't happen nearly as often as its owner would like), it can generate 10 kW of power.

How long does it take to generate 10 kW...? Bzzz! No! Wrong question! That's a question that would only be asked by somebody that didn't understand what power was. It's a bit like asking "how long does it take to travel 10 miles per hour?" It makes no sense.

10 kW is the rate at which the wind turbine can generate energy, not the amount of energy that it can generate in a certain period of time. The two are closely connected, but we'll get to that shortly.

Things that "use power"

Items of electrical equipment like light bulbs, computers, and fans, take energy in the form of electricity, and use it to do useful things for us. Really they're converting the energy into other forms (heat, motion etc.), but we say that they're "using" it because we don't really care about what exactly is happening to it, we just want our equipment to work when we switch it on and stop when we switch it off.

The rate at which these things use energy is their power. Or, depending on the thing, and the person you're talking to, you might hear it called their "load" or their "demand", or you might just hear it referred to in terms of a W or kW value.

Light bulbs are a simple example: if you have a 100 W light bulb you know that it will use 100 W of power when it's running (100 W of power being the same as 0.1 kW of power). The watts aren't affected by how long the 100 W light bulb is running for... A second, an hour, a day – no difference – so long as it's switched on it will be using 100 W of power. If it's not switched on it won't be using any power (i.e. 0 W).

Some equipment is more complicated. Consider a laptop: at any one instant it might be using 50 W of power, or 30 W of power, or 43 W of power, or any similar such value. It depends on what it's doing – if it's sitting there doing nothing it'll probably use less power than if you're hammering away on an Excel spreadsheet, listening to some music, and burning a DVD, all at the same time.

We make a distinction between instantaneous power and average power:

Instantaneous power

The instantaneous power (or instantaneous demand, or instantaneous load) is the power that something is using (or generating) at any one moment in time. Put your laptop on standby and its instantaneous power will drop immediately. Bring it back to life and its instantaneous power will rise immediately.

If, at any particular moment, everything in an office building is switched on, that office building might be using 42 kW of power. That's 42 kW of instantaneous power. If, at any particular moment, everything in the office building is switched off, that building should be using 0 kW of power. That's 0 kW of instantaneous power.

The instantaneous power of most buildings varies constantly. People are constantly switching things on and off, and many items of equipment within the building have instantaneous power that is constantly changing too.

Average power

The average power represents the power that something uses or generates, on average:

• over a specific period of time (e.g. yesterday); or
• over multiple periods of time (e.g. across all the weekends on record); or
• throughout a certain type of operation (e.g. typical laptop usage, or typical building usage – Monday to Friday 09:00 to 17:00, or typical efficiency for something that's generating power).

Remember our example of an office building that uses 42 kW of power when everything's switched on, and 0 kW of power when everything's switched off? If, on average, half the things in the office building are switched on, and half are switched off, then the average power will be around 21 kW overall (21 kW being half of 42 kW).

Or maybe that's just the average power of the office building on weekdays. On weekends, when people are at home, and most equipment in the building is switched off, the average power might be lower, maybe 5 or 10 kW.

The instantaneous power of a typical building varies all the time. If you try to monitor instantaneous power you get lost in the noise. And figures of energy consumption are meaningless unless you know the length of the periods that they were measured over. But average-power figures smooth out the constant fluctuations of instantaneous power, and make it possible to compare the efficiency of different periods, like for like, without worrying about how long those periods were. For example:

• The building used 41 kW (on average) across the whole of last week.
• The building used 19 kW (on average) across all the Saturdays and Sundays since March 2017. (We don't need to care how many Saturdays and Sundays there were since March 2017.)
• The building used 38 kW (on average) between 09:00 and 17:00 on Tuesday, December 25th, 2018. That's double the average kW of a typical weekend, and that's bad because December 25th was a public holiday and the building was closed.

You can easily use these average-kW figures to compare the energy consumption of different periods and even different buildings (we use the term "energy consumption" loosely because really we're talking about average power, not energy). It's a bit like comparing the fuel consumption of cars:

• On long journeys my car does an average of 45 miles per gallon. My brother's car does an average of 41.
• Around town my car does an average of 32 miles per gallon. My brother's car does an average of 29.

These average-mpg figures would typically be calculated across multiple different journeys, each covering different distances... But you can compare the figures like for like, without worrying about the details of the specific journeys that they were calculated from. Average power works in the same way, but with energy instead of distance.

^*In this instance "energy usage" refers to the rate at which the energy is used (i.e. power). To remove ambiguity we might call it "average power", or "load", or "demand". "Energy usage" and "energy consumption" are somewhat loose terms that can be used to refer to the rate of energy usage (e.g. 10 kW) or the total amount of energy used over a specified period (e.g. 240 kWh on February 21st, 2018).

The beauty of average-kW figures is that you can compare them fairly in an instant. The length of the time period doesn't really matter. So you can look at the average-kW figures from 15-minute interval data and compare them directly with the average-kW figures from 60-minute data or from half-hourly data. Or you can instantly compare the average kW from last month with the average kW from yesterday and the average kW from the whole of last year. If these were kWh figures, the fact that they come from periods of different length would mean that you'd need to normalize them before you could compare them fairly. kW figures come ready normalized.

Different names for power – "load", "demand" etc.

People often refer to power as the "load" or the "demand". So you might hear average power referred to as "average load", or "average demand".

Whilst "power" can refer to the power that something is using or generating, "load" and "demand" only ever refer to the power that something is using. You might hear the power that something is generating, or can generate, referred to as its "output".

People sometimes use the word "mean" in place of "average", so you might also hear of "mean power", or "mean load", or "mean demand", or "mean kW".

And people often don't make the distinction between average power and instantaneous power. You can ask them to clarify, but it can be a little embarrassing if they don't understand the distinction in the first place... Fortunately, when you hear someone talking about "power", or "load", or "demand", or "kW", you can usually tell from the context whether they're talking about average or instantaneous figures.

The relationship between energy and power

The relationship between energy and power is a lot like the relationship between distance and speed:

• Energy is like distance. The amount of energy that you used over a specific period of time is like the distance that you travelled over a specific period of time. (e.g. when driving to work you travelled 2 miles between 08:04 and 08:57 – horrible horrible traffic!)
• Power is like speed. Your instantaneous power is like your speed at a specific instant in time (e.g. right now). Your average power over a specific period of time is like your average speed over a specific period of time. (e.g. when driving to work you travelled at an average speed of 2.26 mph – you might as well have walked...)

Both distance and speed are useful measures. And both are closely related. Sometimes it makes sense to talk in terms of distance, and sometimes it makes sense to talk in terms of speed. It's the same for energy and power – you need both, but usually one makes more sense than the other.

Newbies to energy often try to use energy (kWh) for everything (sometimes calling it kW by accident), but more experienced folks tend to use power (kW) a lot more.

The equation connecting energy and power

Following is the fundamental equation that connects energy and power. You might remember it from school:

  energy = power * time  

We can express this equation in terms of kW, kWh, and hours (h):

    kWh  =   kW  *  h    

Where:

kWh is the energy
kW is the power
h is the time in hours

You might also remember from school that equations can be rearranged:

  power = energy  
           time 

or:

    kW  =  kWh    
            h 

Also:

   time = energy  
           power

or:

     h  =  kWh    
            kW

Given a value for any two of the following: average power (kW), total energy (kWh), hours (h), you should be able to use the formulae above to calculate the value of the third.

You should also be able to convert between other units of energy, power, and time, given that:

• 15 minutes is 0.25 hours, 30 minutes is 0.5 hours, a day is 24 hours, a week is 24 * 7 hours etc;
• a kW is 1000 W and a W is 0.001 kW;
• a kWh is 1000 Wh and a Wh is 0.001 kWh;
• a MW (megawatt) is 1000 kW and a kW is 0.001 MW;
• a MWh (megawatt hour) is 1000 kWh and a kWh is 0.001 MWh; and
• any other conversions between units that measure the same thing (like different units of energy, or different units of power, or different units of time) are widely available online.

Our Energy Lens software does a lot of the conversions for you automatically. Once you've loaded some data into Energy Lens you can easily plot charts and calculate figures in units of kWh (energy) or in units of kW (average power), or a mixture of both. It's just a question of choosing the units you want before you click one of the buttons to create a chart or table.

The importance of knowing the units of your source data

When you're working with records of energy consumption, it's critical that you know what units they're in. Otherwise all your calculated figures can easily come out wrong.

Think about it: if you have 30-minute interval data with readings in kWh, but you treat those readings as if they are in kW (average kW, strictly speaking), everything that you calculate further on will be out by a factor of 2:

• 1 kWh over a 30 minute period = 1 kWh
• 1 kW over a 30 minute period = 1 * 0.5 = 0.5 kWh (using kWh = kW * h, and 30 mins = 0.5 hours)

i.e. if your source data has readings in kWh but you treat them as if they are in kW, everything that you calculate from that point on will be working on the assumption that your energy consumption is half what it really is.

Similarly, if your source 30-minute data has readings in kW, and you erroneously treat those readings as kWh, everything that you calculate further on will be twice what it should be.

If you're using 15-minute data, getting the units of the source data wrong can easily make all your calculations out by a factor of 4. (The factor of 4 comes from the fact that there are four 15-minute periods in an hour.)

If you're using Energy Lens for your data analysis, you need to make sure to specify the units correctly when you load the data into Energy Lens. Provided the data is loaded with the right units, you can use whatever units you like for your analysis – Energy Lens will take care of all the conversions correctly. The only requirement is that you specify the correct units at the data-loading stage.

Calculating cost

At the simplest level cost is usually expressed in terms of £/kWh or $/kWh or €/kWh or p/kWh or c/kWh (or whatever-unit-of-currency-you-have per kWh). It makes sense that cost should be calculated per kWh (not per kW), because cost is a cumulative thing – the more energy you use, the more it costs.

Let's pretend we're working in £/kWh... To work out the total cost over a specific period, calculate the total number of kWh over that period, and multiply that by the £/kWh. That will give you the total cost in £. Simple.

However, in reality, cost calculations are usually more complicated:

• Prices change over time. One month you're paying x £/kWh, the next month you're paying y £/kWh. Unfortunately y is usually greater than x, as energy prices typically rise over time.
• Electricity costs can depend on the time of the day, the day of the week, and the time of the year. Energy suppliers/utilities come up with complicated tariffs to define these rules. Just like prices, tariff structures can also change over time.
• Electricity costs can also depend on the maximum demand, or peak load, across a period. For example, given half-hourly data for a month, the peak load or maximum demand could be defined as the half-hour period that had the highest average kW. The higher the peak load, the higher the peak-load charge (or maximum-demand charge).
• Electricity tariffs often charge different rates depending on how many kWh you use. For example, the first 100 kWh might cost x £/kWh, the next might cost y £/kWh.
• There are often standing charges – regular fixed fees that aren't related to how much energy you use.

All in all, if you're looking to reduce energy consumption it's usually much easier to spend most of your time working in units of kW and kWh. The occasional cost figure can be useful for showing to non-technical folks (everyone understands pounds and pence, dollars and cents), but cost figures aren't very good for accurate, in-depth analysis of energy-usage patterns (e.g. to find opportunities to save energy and to track progress at doing so).