Most actors don't list their heights (generally it's only the ones about 6'0"-6'2" who do so, apparently because agents think that's how tall a leading man should be), and Jon Pertwee and Tom Baker are the only two who had published physicals during their time in the role, so any answer involves as much guesswork as investigation. Also, some of the actors (notably Hartnell, Pertwee, and McCoy) shrank visibly during their time on the show.

This article attempts to synthesize all the guesswork and investigation, and list how tall each of the Doctors was at his peak, and here's what they come up with:

  1. William Hartnell, 5'8.5".
  2. Patrick Troughton, 5'7".
  3. Jon Pertwee, 6'3".
  4. Tom Baker, 6'3".
  5. Peter Davison, 6'0.25".
  6. Colin Baker, 6'0".
  7. Sylvester McCoy, 5'6".
  8. Paul McGann, 5'8.5".
  9. Christopher Eccleston, 6'0".
  10. David Tennant, 6'1".
  11. Matt Smith, 5'11".

War Dr.  John Hurt, 5' 7.5".

12. Peter Capaldi, 6' 0".

Jon Pertwee was probably slightly taller than Tom Baker if you compare both of them at their peaks, but Baker was taller if you compare them at the time he took over from Pertwee.

Arranged by order (shortest to tallest):

 Sylvester McCoy, 5'6".
 Patrick Troughton. 5'7".
John Hurt. 5' 7.5"
 William Hartnell, 5'8.5'.
 Paul McGann, 5'8.5".
 Matt Smith, 5'11".
 Christopher Eccleston, 6"0.
 Colin Baker, 6'0".
Peter Capaldi, 6'0".
 Peter Davison, 6'0.25".
 David Tennant, 6'1".
 Tom Baker, 6'3.
 Jon Pertwee, 6'3.

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