The most ambitious use is Jaffna and the northern peninsula. The north is culturally distinct from the rest of Sri Lanka — Tamil and Hindu, with its own food, its own offshore islands and a recent history worth understanding — and it is far enough from everything else that it needs three or four days to justify the drive. Thirteen days is roughly the minimum at which that stops being a rush.
The more popular use is both coasts. Thirteen days lets you finish the circuit on the south coast, then cross to the east for Trincomalee or Pasikuda, or run it the other way depending on the season. Because the monsoons hit the two coasts at opposite times, there is almost always one that is dry, and at this length you are not forced to choose between them.
The quietest use, and the one we recommend most often, is to run a normal ten-day circuit and then not move for three days. Thirteen days with a genuine stop at the end is a materially better holiday than thirteen days of continuous sightseeing, and it costs less, since a stationary stretch means no vehicle and no driver.
13 Days / 12 Nights