How old are the various incarnations of The Doctor from Doctor Who? While this question is straightforward enough, the actual answers are, as with most things involving The Doctor, maddeningly complicated.
First airing in 1963, Doctor Who is the longest-running science-fiction franchise in television history and it boasts one of the richest mythologies in all of modern fiction. With hundreds of episodes and countless tie-in novels, audio plays, stage shows, comic books, and video games, there is a lot of material within that mythology that is contradictory. It is telling that the first officially endorsed episode guide for the show was titled The Discontinuity Guide and one section of it was devoted to discussing the conflicting reports as to the age of The Doctor.
For easy reference, the following will proceed in chronological order and be limited to the officially numbered Doctors. Future incarnations, such as The Curator, and alternate future versions like The Valeyard, have been omitted since there's no information that can accurately measure their age. Outside reference material, such as the Doctor Who tie-in novels, will be considered only in those cases where the television stories never made a definitive statement about a particular Doctor's age.
The First Doctor
Played by William Hartnell, the grouchy yet grandfatherly First Doctor never made a definitive statement as to his age. However, we can calculate his age through references from later episodes. In the Fourth Doctor episode "The Ribos Operation," The Doctor's companion Romana remarked that he was 759 years old. One episode later, in "The Pirate Planet," Romana confirmed that The Doctor had been traveling through space and time for 523 years. This means that The First Doctor was 236 when he first left Gallifrey.
The Second Doctor
The Second Doctor, who was played by Patrick Troughton, was something unique among the various Doctors, in that he was one of the few who gave a relatively precise and straightforward answer when asked about his age. In "Tomb of the Cybermen," he told his companion Victoria that "if we count in Earth terms, I suppose I must be about... four hundred and fifty years old." This gives us a definitive number and a standard to go by, though there is some question as to whether or not The Doctor has always given his age in Earth years.
The Third Doctor
Exiled as punishment for his interfering in the affairs of other planets (albeit as a force for good) the Third Doctor spent most of his relatively short life trapped on Earth. Played by Jon Pertwee, the Third Doctor never made any definitive statements as to his exact age, though he claimed in "Doctor Who and the Silurians" to have lived for "several thousand years." This suggests that either the Third Doctor was measuring his age in Gallifreyian years (which might pass more quickly than Earth years) or that he was speaking about the span of time he had covered in his travels.
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The Fourth Doctor
Still the most iconic of the classic Doctors nearly four decades after his retirement from the role, Tom Baker's Fourth Doctor is also one of the most long-lived incarnations of The Doctor. He claimed to be "something like seven hundred and fifty years" in "Pyramids of Mars," which he later claimed was middle-aged by Time Lord standards. Perhaps this is why he began lying about his age, claiming to be 756 in "The Ribos Operation," when his companion Romana claimed he was 759. He later admitted to being almost 760 in "The Power of Kroll."
The Fifth Doctor
At the time of his casting as the Fifth Doctor, Peter Davison was the youngest actor to play The Doctor. Despite his youthful appearance, the Fifth Doctor had an old man's soul, yet he never made any statement about his age on the show. He claimed to be 813 at the time of his regeneration in the novel Cold Fusion and told his companion Peri Brown, whom he picked up shortly before his regeneration into the Sixth Doctor, that he was about 850 in Earth years in the novel The Ultimate Treasure.
The Sixth Doctor
Bold and brash as his colorful coat, Colin Baker's Sixth Doctor presented a radically different take on The Doctor. Apparently he took some solo-side trips without Peri Brown, as he claimed to be 900 years old exactly in both "Revelation of the Daleks" and "Mysterious Planet," yet Peri showed no signs of having aged five decades during her travels with the Fifth and Sixth Doctors. He was reportedly 953 years old at the time of his regeneration into the Seventh Doctor.
The Seventh Doctor
Capable of playing both the bumbling buffoon and the cunning chess-master, Sylvester McCoy's Seventh Doctor may have been the most unpredictable of the Classic Doctors. He claimed to be 953 years old in his first appearance in "Time and The Rani," noting that a locked door in The Rani's lab required a three-digit PIN and that the combination, 953, was also his age. While his age when the show went on hiatus with "Survival" is unknown, he celebrated his 1,000th birthday in the novel Set Piece.
The Eighth Doctor
With only a single TV movie and one webisode officially counted as canon by the BBC, Paul McGann's Eighth Doctor is the most difficult to pin down in terms of age. He calculated his age as 1013 years old in the novel Vampire Science. Fearing that he had lost count somewhere, he briefly only counted the years lived by his current incarnation and gave his age as 3 years old. Eventually, he tired of this and went back to trying to calculate the total age of all his incarnations. When McGann returned to play the Eighth Doctor after his TV movie, the audio play Orbius confirmed that he did try for a time to keep recalculating his age based on the local standards, noting that there was one obscure galaxy where he was only two years old. His oldest recorded age came in the novel The Dying Days, where he estimated that he was 1200 years old.
The War Doctor
Played by John Hurt, the War Doctor was an incarnation who had denied himself the name of The Doctor as he fought in the Last Great Time War between the Time Lords and the Daleks. Calculating his age is tricky, as the short story Doctor Who and the Time War confirmed that the various reality-altering weapons employed during the Time War resulted in whole sections of time being erased from continuity and rewritten, as whole worlds were aged or de-aged out of existence. As such, it is entirely possible that the War Doctor was 1200 years old when the Time War started and that he ended it somewhere around 800 years old. This is apparently how old the War Doctor was in The Day of the Doctor, as he claimed the Eleventh Doctor (who gave his age as over 1200 years old) was 400 years older than him.
The Ninth Doctor
The first Doctor of the New Who era, the Ninth Doctor's adventures only lasted for a single season but Christopher Eccleston made him into a memorable if conflicted character in that brief time. He claimed to be 900 years old in the episode "Aliens of London." Based on the given age of the War Doctor, this means that the Ninth Doctor spent roughly 100 years traveling on his own before he met Rose Tyler in "Rose."
The Tenth Doctor
As a boy, David Tennant dreamed of playing The Doctor someday and got into acting with that goal in mind. That enthusiasm may be a part of what made the Tenth Doctor into the most popular incarnation of The Doctor in modern times. In any case, the chronology of the Tenth Doctor is surprisingly well mapped compared to earlier Doctors. He aged roughly one year per season through the New Who era, claiming to be 903 years old in the 2007 Christmas Special "Voyage of the Damned." He gave his age as 906 years old in his final adventure, "The End of Time."
The Eleventh Doctor
Played as an absent-minded professor by Matt Smith, the Eleventh Doctor continued the New Who trend of aging the Doctor one year for every season at first. Shortly after he first began traveling with Amy Pond, he claimed to be 907 years old in the episode "Flesh and Stone." One year later, in the Series 6 premiere "The Impossible Astronaut," Amy claimed that The Doctor was 908 the last time she saw him while comparing notes with River Song. They were soon met by an older version of The Eleventh Doctor, who claimed to be 1103 years old. By the time of the Series 7 episode "A Town Called Mercy," The Eleventh Doctor gave his age as roughly 1200 years old; the same age he gave to the War Doctor in "The Day of the Doctor." He later claimed to be 1000 years old when he first met the original Clara Oswald in 2013 London in the episode "The Bells of Saint John," but he may have started lying about his age at that point, which he freely admitted to doing in "The Day of the Doctor."
The Eleventh Doctor's age during his final battle during the Siege of Trenzalore is another point where the lore of the show becomes conflicted. The Eleventh Doctor claimed to be almost 1500 years old in the short story "An Apple A Day..." though he confessed he could have been off by a few hundred years either way. In either case, the short story anthology Tales of Trenzalore confirmed that The Doctor spent 900 years protecting the city called Christmas, meaning that the Eleventh Doctor was somewhere between 2100 to 2600 years old when he regenerated into the Twelfth Doctor.
The Twelfth Doctor
Played by Peter Capaldi, the Twelfth Doctor was sarcastic, surly, and Scottish and frequently described as an aging punk. He claimed to be over 2000 years old in his first appearance in "Deep Breath" and continued to describe himself as such throughout most of his life. He became the oldest of Doctor Who's leads in terms of longevity after the events of "Hell Bent," where he was trapped in a confessional dial for approximately 4.5 billion years. He rounded his age down to 4 billion in the comic book story "Doorway to Hell," but was back to claiming he was just over 2000 years old by the time he began traveling with Nardole and Bill Potts in the episode "Smile."
The Thirteenth Doctor
Jodie Whittaker plays the 13th and latest incarnation of The Doctor, who has been far more secretive regarding her past than any other New Who Doctor. She didn't tell her companions anything about her past or her homeworld of Gallifrey, though she did reveal in "Fugitive of the Judoon" that she was thousands of years old and claimed to have forgotten just how old she was. With the revelation that The Doctor might be an immortal being known as The Timeless Child, there is a fair chance that The Doctor may have never really known how old they are and that Doctor Who history will have to be rewritten once again.