THE AGE OF THE DOCTOR
This is the age of the Doctor, split up into the length of time each regeneration spent puttering around the universe. His total age is 3,325, and this is how I put it together:
The lifespan of the classic-era Doctors was really simple. Ironically, their continuity was pretty damn good compared to revived-era, and the ages discussed all add up and fit together. (Except for a few figures that are clearly complete outliers, like the Third Doctor claiming to be 1,000 one time, which I ignored).
A few things to note are that the First Doctor didn’t steal the Tardis until he was in his 230s, and that the Eighth Doctor spent 600 years trapped on the planet Orbis.
The revived series is where it starts to get tricky, though. (We’ll get to the War Doctor in a moment, pun intended.) The Seventh Doctor claimed he was “starting to lose count”, though, so I’m taking that into consideration: I’ve made judgments based on the lengths of time that we-the-audience actually see evidence of the Doctor living for, rather than simply what age he cites. (Though I accepted the latter in the absence of contradictory evidence.)
The Ninth Doctor claims to be around 900 - which already can’t be true, since the Fifth Doctor was around that age when he regenerated into the Sixth. I put solving that discrepancy on hold for a minute, and decided to first figure out the length of time the Doctor lived for between his Ninth and Eleventh incarnations - regardless of the starting age of the Ninth Doctor, the same amount of time passed between Nine and Eleven.
We know that the Eleventh Doctor spent 900 years on Trenzalore, and that just before going to Trenzalore, he was 400 years older than the War Doctor. Which means there’s a 400 year gap in which the Ninth, Tenth, and (pre-Trenzalore) Eleventh’s lives take place. But how to split that 400 years between the three of them?
The Eleventh Doctor claimed to be 907 just after regenerating and 1,200 just before Trenzalore, giving him 293 of those 400 years - consistent with other figures we see over Eleven’s adventures. That leaves 107 to divide between the Ninth and Tenth Doctors. The Tenth Doctor has lived for at least 3 years when he gives his age as 903, putting his starting age at around 900 (on the revived-series age numbers) rather than the Ninth. With that and his regeneration in mind, the Tenth Doctor lived for 7 years, leaving a square 100 for the Ninth.
…which doesn’t really add up. The Tenth Doctor travelled with three companions for around a year each, spent a year trapped by the Master, and almost 3 years searching for Martha, plus he had then “lived too long” in solitary by his own admonition - hardly the words of a man who used up an entire regeneration to stay around a bit longer, if he was only 7. Since that figure contradicts evidence we can see, I’m going to assume the Seventh Doctor was right, and that he’s lost track a bit. It’s also implied that the Ninth Doctor had just regenerated when he met Rose, and he had (from what we see) fewer solo adventures than the Tenth Doctor. So I’m going to split that remaining 100 years between the two, resulting in 50 for the Ninth and 57 for the Tenth. This is also consistent with the lifespan of the classic-era Doctors, so I argue it’s the most elegant possible decision.
So: now to settle the “900” problem. We know the War Doctor fought the Time War for 400 years, but if the Tenth was 907 when he regenerated, that would put the Eighth Doctor’s age around 400 when he regenerated. But we know he was still the First Doctor at that age! The solution is remarkably simple. The age of “900” was already suspect, so instead, I went with the evidence of what we’ve seen - which says the Eighth Doctor was 1,725 when he regenerated. So I just kept counting from there. And surprise, the numbers are now entirely consistent!
The Doctor, when he finished his first regeneration cycle, was approximately 3,425 years old. So when the Twelfth Doctor says he’s lived for over two thousand years, he really means it.
Sources: mostly me watching the show itself for decades, but this page gives a nice outline. I’ve also included the tenures of each actor as the current Doctor, to see how they match up to their in-universe duration.