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It is difficult to specify an average without sound statistical data, but you can make a few reasonable assumptions, resulting in a usable estimate. First, a little background:

Any electrical unit consumes electrical power, measured in watt (W). Consume electrical power over time means to 'consume' electrical energy; for example, burn a 100W light bulb for one hour 'consumes' 100Wh, or 0.1kWh, electrical energy. It is the number of kWh that you pay to your electricity supplier; for example, one electricity supplier in the UK charges £0.1152 per kWh.

(I write consume in quotes because it is not really possible to consume energy. According to the first and second law of thermodynamics, energy is only ever converted, but never consumed. The light bulb, for example, converts electrical energy into light and heat.)

Back to the computer.

An average desktop computer is designed to 'consume' up to 250W, but in normal-to-light use, it will consume no more than than 100W. When left to idle, modern computers switch off a number of non-essential units, leading to even lower power consumption (50W?).

Laptop computers will typically consume around 50% of a desktop PC's power consumption.

A CRT monitor will consume 150..250W, depending on its size, whether the computer is idle or not. However, most modern systems are configured to turn-off parts of the monitor in order to reduce the power consumption. This will reduce power to a value in the region of 30W.

Modern LCD displays will consume approximately 50% of the power of a CRT.

Other components, such as keyboards, mice, etc, are negligible.

So, assume your PC is a desktop PC, in use for 3 hours with typical applications, and idle (or in very low and sporadic use) for the other 5 hours:

PC energy = 3h * 100W + 5h * 50W = 300Wh + 250Wh = 550Wh

The display will have similar on/off times, so assume this:

LCD energy = 3h * 80W + 5h * 35W = 240Wh + 175Wh = 415 Wh

Total energy = PC energy + LCD energy = 550Wh + 415Wh = 965Wh (approximately 1 kWh).

So, running this PC for eight hours consumes approximately 1 kWh electrical energy, costing as little as £0.1152 in the above example. While this seems inexpensive, note that this builds up to 24/8 * 365 * £0.1152 = £126 per year.

You might use these figures for an initial estimation, but you must note that the true cost (i.e. the true power consumption) very much depends on make and model, and how you use this PC. Light word processing consumes little power in comparison with an action-packed video game, burning a DVD, or some serious number-crunching.

For a more accurate estimate, you would need to gather statistical data and review the above.

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Q: How much does it cost to run an average size computer for 8 hours?
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