A kilowatt-hour is the energy that a one-kilowatt appliance converts in one hour: 3.6 times ten to the sixth joules. You use E is P times t, with the power in kilowatts and the time in hours. Your energy company charges in kilowatt-hours, because you pay for energy and not for current.
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Your wifi router is on day and night, for a whole year. What does that cost? To work it out, you need the kilowatt-hour.
A joule is very little energy. That's why your energy company uses a bigger unit: the kilowatt-hour. One kilowatt-hour is the energy that a one-kilowatt appliance converts in one hour. You then use E is P times t, with the power in kilowatts and the time in hours. In joules that is a thousand watts times 3600 seconds: 3.6 times ten to the sixth joules.
What you pay for is energy, not current. The current going into the router comes back out through the other wire, and not one electron gets lost on the way. What the electrons do give off is energy: light, heat, a wifi signal. The kilowatt-hour meter in your meter box counts that energy.
In the worked example, an aquarium pump of 5.0 watts runs for a whole year. That is 0.0050 kilowatts times 8760 hours, which is 44 kilowatt-hours, and at thirty cents per kilowatt-hour 13 euros a year. The router of about 8 watts comes to some 70 kilowatt-hours and 21 euros a year.
For upper secondary physics, on electricity.
In this video
The full explanation, in writing
The router
0:00Your wifi router is on day and night, for a whole year. What does that cost? Name an amount.
A thousand watts, for one hour
0:13A joule is very little energy. That's why your energy company uses a bigger unit: the kilowatt-hour. One kilowatt-hour is the energy that a one-kilowatt appliance converts in one hour. You then use E is P times t, with the power in kilowatts and the time in hours.
0:33How many joules is that? A thousand watts times three thousand six hundred seconds: three point six million joules. One kilowatt-hour is three point six times ten to the sixth joules.
You pay for energy
0:47What you pay for is energy, not current. The current going into the router also comes back out, through the other wire, back to the grid. Not one electron gets lost on the way. What the electrons do give off is energy: it becomes light, heat, a wifi signal.
1:05The kilowatt-hour meter in your meter box counts that energy, and that's where your bill comes from. Your turn. An aquarium pump of five point zero watts runs day and night for a whole year. How many kilowatt-hours is that?
From watts to euros
1:22First convert the power to kilowatts, and the time to hours. Five point zero watts is zero point zero zero five kilowatts. A year is three hundred and sixty-five times twenty-four hours: eight thousand seven hundred and sixty hours. Zero point zero zero five times eight thousand seven hundred and sixty is forty-four kilowatt-hours.
1:44Say a kilowatt-hour costs thirty cents. Then that pump costs you thirteen euros a year. And the router from the start is an appliance of about eight watts: some seventy kilowatt-hours, and twenty-one euros a year.
Three things to remember
2:00Three things. A kilowatt-hour is the energy of one kilowatt for one hour: three point six times ten to the sixth joules. If you work in kilowatt-hours, then power in kilowatts and time in hours. And you pay for energy, not for current: it comes back out just as fast.
Two questions
2:20Two questions. One. How many joules is zero point five zero kilowatt-hours? Two. An electric blanket of fifty watts is on for eight point zero hours. How many kilowatt-hours is that?
The answers
2:35The first: zero point five zero times three point six times ten to the sixth is one point eight times ten to the sixth joules. The second: fifty watts is zero point zero five zero kilowatts. Times eight point zero hours is zero point four zero kilowatt-hours.
The fuse
2:52Want to know why the fuse blows when you switch on too much at once? Then watch the video on fuses on my YouTube channel.
Frequently asked questions
How many joules is a kilowatt-hour?
One kilowatt-hour is a thousand watts times 3600 seconds, so 3.6 times ten to the sixth joules, or 3.6 million joules.
How do you work out how many kilowatt-hours an appliance uses?
Use E is P times t, with the power in kilowatts and the time in hours. An aquarium pump of 5.0 watts is 0.0050 kilowatts; a year is 8760 hours, so the pump converts 44 kilowatt-hours.
How much does a wifi router cost per year in electricity?
A router of about 8 watts that is on for a whole year converts some 70 kilowatt-hours. At thirty cents per kilowatt-hour, that is about 21 euros a year.
Do you pay for current or for energy?
For energy. The current going into an appliance comes back out through the other wire, and no electron gets lost. The electrons do give off energy, and that is what the kilowatt-hour meter in your meter box counts.
How many kilowatt-hours is 50 watts for 8 hours?
Fifty watts is 0.050 kilowatts. Times 8.0 hours, that gives 0.40 kilowatt-hours.
Next: why the fuse blows when you switch on too much at once.
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Physics with Thomas: physics explained with pictures where they add something, and without them where they distract.
In this series
Electric current6:12
Voltage and capacity4:43
Connecting ammeter and voltmeter4:10
Resistance and Ohm's law4:21
Resistance of a wire4:40
Variable resistor, NTC, PTC and LDR3:40
Series circuit3:32
Parallel circuit3:56
Series-parallel circuit3:37
Circuits practical test5:13
Power2:58
Kilowatt-hour3:05
About me
My name is Thomas Schuurmans, and I have a passion for physics and for understanding why things work the way they do. What I want is to get young people asking “why is that?” and “how does that work?” more often, and to hand them the tools of physics in a way that is simple and that you can see.
I graduated in applied physics at Delft University of Technology in 2003. After that I spent more than twenty years outside education: first at TNO, the Dutch applied research institute, then at a design agency, and eventually founding Proportion Global, through which I work on innovation questions in Africa, Latin America and South Asia. That work resembles physics more than you would expect: don't start from a solution, first understand what is going on, try something, be wrong, and look again.
Since 2026 I have been teaching physics to both lower and upper secondary classes, and I started a master's at the University of Amsterdam for my full teaching qualification. That is where I learned that a secondary school pupil's real attention for new material lasts about seven minutes. And my own weakness happens to be telling too many side stories.
That is where the idea came from: videos that explain one topic sharply and visually, inside those seven minutes. I make them for my own pupils. Then I publish them, because good explanation should be within reach of anyone who needs it, wherever you live and whatever language you think and speak in.