There is no easy answer to this question. First, it is bound up in the question of whether or not King Arthur really existed; then, you have to consider, if he did exist, who was he?

If Arthur was a Roman Briton, that might place him in a very different time period than if he was a Welsh warlord. Since there is very little direct evidence for Arthur's existence, we basically have to pick our favorite theory and make assumptions based on that theory.

We can narrow down the Arthurian time period, however. Most of the time, in movies and television shows and in many books, Arthur is depicted as a king in plate armor living in a grand castle, which places him more or less in the high Middle Ages. This is about seven hundred or so years after any of the possible King Arthurs would have lived. The Arthurian era settles around the year 500 AD. We can't know if that was the year he was born, or the year he died, or the year he fought the Battle of Badon, or the year he married, but various early accounts of Arthur pinpoint events in the decades before and after 500 AD.

See the detailed timeline for more specific information.