Appliance energy use: watts to kWh

This calculator lets you work out how much electrical energy your appliances use. For that you will need a plug-in energy monitor or something similar. With it you measure the power of, say, a television. The device shows you 100 watts. If you want to know how much energy the television uses in eight hours, enter 100 W and 8 hours into the calculator. The result is a consumption of 0.8 kWh (kilowatt-hours).

How it is worked out

How could we work out the consumption of appliances ourselves? The watt is the unit of power, where 1 watt is the power at which 1 joule of work is done in 1 second. The joules are not important to us now; what matters is that this gives the power per second. If our appliance has a power of 1 W and runs for ten seconds, it has used 1 W · 10 s of energy, that is, 10 watt-seconds of energy.

If an appliance has a power of 5 W and runs for 20 seconds, it uses 5 W · 20 s of energy, that is, 100 watt-seconds.

Now let’s work out the example from the first paragraph. If the power is 100 W and the television runs for eight hours, we first convert the hours to seconds. One hour has 3,600 seconds, so eight hours is 28,800 seconds. The total consumption of the television would therefore be

$$100\text{ W}\cdot 28800\text{ s}=2880000\text{Ws}$$

This is a correct result, but we do not normally use the unit watt-seconds; we use watt-hours or kilowatt-hours. First we convert this result to watt-hours by dividing the number of watt-seconds by 3,600, the number of seconds in an hour:

$$\frac{2880000}{3600}=800$$

Now we know the consumption in watt-hours: it is 800 Wh. We convert that to kilowatt-hours by dividing the number by 1,000:

$$\frac{800}{1000}=0.8$$

And we have 0.8 kilowatt-hours.