The perennial problem with compiling lists of Roman emperors is deciding who qualifies as having a legitimate claim to being one. There was an absolute barrowload of them over the years, and a corresponding number of other people who also claimed to be emperor went around calling themselves emperor and yet never achieved anything that could realistically be called legitimacy. In the years between 27 BC, which is traditionally the date from which the reign of Augustus is taken (although he claimed earlier himself) to the sack of Rome in AD 455 by the Vandals under Gaiseric, there was an attempt at usurping the incumbent at an average of once every four years and some of those usurpers were able to display what might otherwise be seen as the trappings of power. This also throws up the possibility of having two incumbent yet opposing candidates at a time. Pescennius Niger claimed the throne in the period following the death of Pertinax (193 - 194) and had all the whistles and bells to go with it. Yet ultimately, he was defeated by the man who held a rival claim, Septimius Severus (r. 193 - 211), and so old Niger just goes down in the book as a 'tyrant'. The book in question is the Historia Augusta, which should always be taken with generous shovels full of salt.
The distinction in the sources between who was a 'tyrant', the usual term for a usurper, and a legitimate claimant is sometimes only a moral one, and as there was no constitutional or legal definition of who the emperor should be or even that there should be an emperor in the first place, so there could be no official candidate and hence no official usurper. The tyrant then simply becomes the man who lost.
So, what criteria should we apply? The obvious one is those who were proclaimed emperor by other emperors whose legitimacy has already been accepted. There are numerous occasions where ruling emperors named co-emperors to rule alongside them. Marcus Aurelius (r. 161 - 180) nominated his adoptive brother, Lucius Verus (r. 161 - 169), at the beginning of his reign - insisted on it, in fact - and then later jointly reigned with his son, Commodus (r. 180 - 192). Commodus became joint emperor in 177, so should we start the date of his reign from that year or from the year in which he became sole emperor? Other so-called co-emperors never got to reign on their own, like Lucius Verus, so there's no other way of calculating them in the list, even if they were legitimate, and there were also some, mostly children in the latter years of the Empire, who could qualify for these criteria but never, realistically, had any legitimate claim to be anything than rather confused, dressed-up children.
The tradition is to dismiss most of these later children but not always the earlier ones. So it seems, if only for some brevity, that it might be an idea to introduce a cut-off point in the date. This is not meant to be an exhaustive list, after all, just an illustrative example of the ages of emperors. A good date to take is AD 235, following the death of Severus Alexander, which plummets the Empire into one of those periods of absolute chaos that it seemed to be very good at, so we'll take Augustus as our starting point and Alexander as the end. In order to be consistent, unless the emperor never ruled on their own, we will take the starting date of their reign as the year in which they became sole emperor.
We'll count all candidates who were proclaimed by the Senate. The Senate was, effectively, a glorified talking shop with very little executive power at all, especially in the imperial years. If we were to answer the question 'what did a Senator do all day?', the answer would be 'not much', at least in terms of political power. One of the greatest tricks Augustus pulled was convincing the Senate that they were essential cogs in the Roman machinery of state to keep them happy and then stripping them of any vestige of power they thought they had whilst they all patted each other on the back for doing a wonderful job. However, a declaration by the Senate was essentially what qualified someone as emperor. The whole idea of constitutional legitimacy was irrelevant - emperors were only emperors in so far as they could convince other people that allowing them to be the emperor was in that other person's best interests. If that convincing had to be done with a show of might, so be it.
There were periods in the later Empire when rulers sat in other cities, away from the Senate, but for our purposes, this isn't an issue.
Lastly, and obviously, we'll include those who qualify because their legitimacy was never questioned, and their rule was absolute. The emperors in question, with the dates of their reign, their birth and their age when they first took office (according to the criteria above), are:
Augustus
Birthday: September 23, 63 BC
Start of Reign: January 16, 27 BC
End of Reign: August 19, 14 AD
Age at Start: 36 years, 3 months, 24 days
Age at End: 75 years, 10 months, 27 days
Tiberius
Birthday: November 16, 42 BC
Start of Reign: September 18, 14 AD
End of Reign: March 16, 37 AD
Age at Start: 55 years, 10 months, 2 days
Age at End: 78 years, 4 months
Caligula
Birthday: August 31, 12 AD
Start of Reign: March 18, 37 AD
End of Reign: January 24, 41 AD
Age at Start: 24 years, 6 months, 17 days
Age at End: 28 years, 4 months, 24 days
Claudius
Birthday: August 1, 10 BC
Start of Reign: January 25, 41 AD
End of Reign: October 13, 54 AD
Age at Start: 50 years, 5 months, 24 days
Age at End: 64 years, 2 months, 12 days
Nero
Birthday: December 15, 37 AD
Start of Reign: October 13, 54 AD
End of Reign: June 9, 68 AD
Age at Start: 16 years, 9 months, 28 days
Age at End: 30 years, 5 months, 25 days
Galba
Birthday: December 24, 3 BC
Start of Reign: June 8, 68 AD
End of Reign: January 15, 69 AD
Age at Start: 70 years, 5 months, 15 days
Age at End: 71 years, 22 days
Otho
Birthday: April 28, 32 AD
Start of Reign: January 15, 69 AD
End of Reign: April 16, 69 AD
Age at Start: 36 years, 8 months, 17 days
Age at End: 36 years, 11 months, 19 days
Vitellius
Birthday: September 24, 15 AD
Start of Reign: April 17, 69 AD
End of Reign: December 20, 69 AD
Age at Start: 53 years, 6 months, 24 days
Age at End: 54 years, 2 months, 26 days
Vespasian
Birthday: November 17, 9 AD
Start of Reign: July 1, 69 AD
End of Reign: June 23, 79 AD
Age at Start: 59 years, 7 months, 14 days
Age at End: 69 years, 7 months, 6 days
Titus
Birthday: December 30, 39 AD
Start of Reign: June 24, 79 AD
End of Reign: September 13, 81 AD
Age at Start: 39 years, 5 months, 25 days
Age at End: 41 years, 8 months, 14 days
Domitian
Birthday: October 24, 51 AD
Start of Reign: September 14, 81 AD
End of Reign: September 18, 96 AD
Age at Start: 29 years, 10 months, 21 days
Age at End: 44 years, 10 months, 25 days
Nerva
Birthday: November 8, 30 AD
Start of Reign: September 18, 96 AD
End of Reign: January 27, 98 AD
Age at Start: 65 years, 10 months, 10 days
Age at End: 67 years, 2 months, 19 days
Trajan
Birthday: September 18, 53 AD
Start of Reign: January 28, 98 AD
End of Reign: August 8, 117 AD
Age at Start: 44 years, 4 months, 10 days
Age at End: 63 years, 10 months, 21 days
Hadrian
Birthday: January 24, 76 AD
Start of Reign: August 11, 117 AD
End of Reign: July 10, 138 AD
Age at Start: 41 years, 6 months, 18 days
Age at End: 62 years, 5 months, 16 days
Antoninus Pius
Birthday: September 19, 86 AD
Start of Reign: July 10, 138 AD
End of Reign: March 7, 161 AD
Age at Start: 51 years, 9 months, 21 days
Age at End: 74 years, 5 months, 16 days
Marcus Aurelius
Birthday: April 26, 121 AD
Start of Reign: March 7, 161 AD
End of Reign: March 17, 180 AD
Age at Start: 39 years, 10 months, 9 days
Age at End: 58 years, 10 months, 21 days
Lucius Verus
Birthday: December 15, 130 AD
Start of Reign: March 7, 161 AD
End of Reign: March 169 AD
Age at Start: 30 years, 2 months, 21 days
Age at End: ~38 years, 3 months
Commodus
Birthday: August 31, 161 AD
Start of Reign: March 17, 180 AD
End of Reign: December 31, 192 AD
Age at Start: 18 years, 6 months, 16 days
Age at End: 31 years, 4 months
Pertinax
Birthday: August 1, 126 AD
Start of Reign: January 1, 193 AD
End of Reign: March 28, 193 AD
Age at Start: 66 years, 5 months
Age at End: 66 years, 7 months, 27 days
Didius Julianus
Birthday: January 29, 133 AD
Start of Reign: March 28, 193 AD
End of Reign: June 1, 193 AD
Age at Start: 60 years, 1 month, 27 days
Age at End: 60 years, 4 months, 3 days
Septimius Severus
Birthday: April 11, 145 AD
Start of Reign: April 9, 193 AD
End of Reign: February 4, 211 AD
Age at Start: 47 years, 11 months, 28 days
Age at End: 65 years, 9 months, 24 days
Caracalla
Birthday: April 4, 188 AD
Start of Reign: December 4, 211 AD
End of Reign: April 8, 217 AD
Age at Start: 23 years, 8 months
Age at End: 29 years, 4 days
Geta
Birthday: March 7, 189 AD
Start of Reign: December 4, 211 AD
End of Reign: December 26, 211 AD
Age at Start: 22 years, 9 months
Age at End: 22 years, 9 months, 19 days
Macrinus
Birthday: c. 165 AD
Start of Reign: April 11, 217 AD
End of Reign: June 8, 218 AD
Age at Start: ~52 years
Age at End: ~53 years
Diadumenian
Birthday: September 14, 208 AD
Start of Reign: May 218 AD
End of Reign: June 218 AD
Age at Start: 9 years, 8 months
Age at End: 9 years, 9 months
Elagabalus
Birthday: c. 203 AD
Start of Reign: May 16, 218 AD
End of Reign: March 11, 222 AD
Age at Start: ~14 years
Age at End: ~18 years
Severus Alexander
Birthday: October 1, 208 AD
Start of Reign: March 13, 222 AD
End of Reign: March 18, 235 AD
Age at Start: 13 years, 5 months, 12 days
Age at End: 26 years, 5 months, 17 days
So, when asked, 'How old did you have to be to be an emperor?' the answer is, 'There weren't any criteria.' There were no criteria for who could be emperor at all beyond the ability to smack other people over the head, metaphorically or physically, until they accepted that you were emperor.
The average age of all the above at the start of their reign was 37.7 years old. The youngest, the one nobody has heard of, was Diadumenian, the son of Macrinus. Macrinus named him co-emperor in an attempt to ward off a claim to the throne led by the agents of Elagabalus. It didn't work. After Macrinus was defeated in 218, at the Battle of Antioch, he fled, sending Diadumenian into the supposed safety of the care of the Parthians. He was intercepted and beheaded, aged 9 years old. Elagabalus kept his head as a trophy. Elagablus themselves was only 14 when they became emperor.
At the other end of the scale, Galba was 70 years old when he began his brief reign which ended in January 69 with his head also being parted from the rest of him and sold:
" [the head] of Galba was bestowed upon the servants of Patrobius. They took it, and after heaping all manner of insult and outrage upon it, cast it into a place called Sessorium, where those under condemnation of the emperors are put to death. The body of Galba was taken up by Priscus Helvidius, with the permission of Otho; and it was buried at night by Argivus, a freed man."
(Plutarch, Life of Galba, 28)
He wasn't the oldest at death, though. That honour goes to the first emperor, Augustus, who dined on his last meal of figs, if you get my drift, aged 75 years, 10 months and 27 days.
The average age at death of the above is 51.2 years. All of this opens up another question, of how long could a Roman expect to live for? That question must wait for another time.
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