The question asks the size of the home range (the territory that a tiger calls his/her own) of wild tigers i.e. usually Bengal and Siberian tigers primarily. Dr Desmond Morris says that each wild tiger has a territory about as big as a modern city. This paints a very nice and clear picture.
On a more technical level, my research indicates that the average home range size of Bengal tigresses in Chitwan National Park (in India) is a fairly small 20 km² but some reached 51 km². These are home ranges in floodplains where prey is abundant or was (the data was published in 1981). Things change of course. In fact, they are changing rapidly. Adult male tigers in Chitwan NP maintain their own home ranges i.e. no overlap with other male tigers but their territories were 2 to 15 times larger than those of females. Each male range normally overlap several female ranges. The variation in male territory sizes depends on the number of females within that male tiger’s territory. Female tigers are a more important resource than food in the area.
The home range size of female tigers in Nagarahole National Park where there are or were high prey densities is about 15 to 20 km². Males have home ranges which typically overlaps several female ranges. You can tell, therefore, that the land that they need is far, far larger than those of females. Prey density dictates the size of territory as where prey is easy to find the tiger roams over a smaller distance.
Siberian tigers, based on snow tracking data, were estimated to have home ranges of 200 to 400 km² for females and between 800 and 1,000 km² for males. These are very large territories partly because their prey migrates in large numbers to winter feeding areas along the coast and partly because of lighter prey densities. They are about ten to twenty times larger than the territories of tigers in Chitwan NP. Other surveys have concluded that female tiger ranges in the Sikhote-Alin region about 450 km² while male home ranges are estimated to be 25 to 50% larger.
Please ask if you want detailed references. The sources are Wild Cats of the World and Cat World.
SOME MORE ON THE TIGER: