Just for others' reference, the metropolitan area of Stockholm[0] is the whole of the Stockholm county.
Just looking at the map, a slightly better/more conventional measure of Stockholm might be Stockholm municipality[1] + Huddinge, Sundbyberg and Solna, which gives an area of 350 km2 and a population of about 1.1 million.
http://en.wikipedia.org/wiki/Stockholm_City_Centre