Hogwarts School of Witchcraft and Wizardry has had some stellar witches and wizards at its helm. From the celebrated genius, Everard, to the feared but intellectual Phineas Black, Harry Potter's wizarding school had many pioneering names in the headmaster's chair. But who was the most powerful of them all?
The books don't offer a list of qualifications or even a professional index over how headmasters are chosen, but it does discuss some of them and more knowledge can be gained from official sources. Usually, a tenured professor would be promoted to the position, however, they weren't always selected for their skills but their reputation within the wizarding communities and their global relevance also factored in somewhat. Here's ranking all known Hogwarts headmasters by power
Dexter Fortescue
Dexter was the headmaster of Hogwarts during the 18th century and the reason for his appointment was possibly his traditionalist outlook towards honor and duty, and not his wizarding powers, per se.
He was often seen reprimanding Phineas Nigellus for ‘dereliction of duty’ and criticizing other wizards for making deals with criminals. His profession before his appointment is also not stated in the books, so he obviously did not share the legacy of Everard, Black, or Dumbledore.
Eupraxia Mole
Though the Potter canon offers very little detail about Eupraxia who was the headmistress of Hogwarts in the 1870s, her intelligence and wits were stuff of legends. In 1876, caretaker Rancorous Carpe designed a ‘trap’ to get rid of the resident Poltergeist, from Hogwarts (the school had to be evacuated for three days as Peeves wouldn’t stop firing weapons and threatening students).
Professor Mole agreed to sign a contract with Peeves, so that he would give up the weapons in exchange for additional privileges like a weekly swim in the boys' toilets, opportunity to decide the fate of the kitchen’s stale, and a new custom hat by Madame Bonhabille.
Dolores Umbridge
Dolores Umbridge’s magical proficiency has often been debated by the fandom and chances are she worked her way up the ministry because of her bureaucratic skills and not her magical powers, per se. It is important to note that she was placed as the Defence Against the Dark Arts Professor at Hogwarts School of Witchcraft and Wizardry by the ministry, since they wanted an insider to govern Hogwarts.
Thus, the reasons for her appointment as a professor and her promotion to Headmaster were politically motivated. She was seen performing cruel acts of dark magic on students, particularly Harry, however those don’t exactly require a significant proficiency. But the fact that she could not overpower the centaurs who dragged her away, was actually a good indicator that she was only moderately powerful as a witch.
Armando Dippet
Armando was the headmaster of Hogwarts from the 1940s into the 1960s, and it was during his time as headmaster that the Chamber of Secrets was first opened by Tom Riddle (around mid-forties) since its creation by Salazar Slytherin in around A.D. 993. Dippet was a predecessor to Dumbledore, and though he never abused his powers, he certainly never used them well. The canon also suggests that he was a feeble man, who lacked intuitiveness and was easily misled; in fact, he failed to realize the source of the attacks when Salazar’s basilisk started attacking students.
It is also unknown what his status or profession was between his graduation from Hogwarts and his appointment as headmaster, which is strange since most headmasters have a prolific resume and an impressive professional legacy. Since the source of his skill set or the origins of his power remain largely unknown, it is impossible to determine his relevance in the wizarding world, however, he was certainly less esteemed than Dumbledore or Everard.
Dilys Derwent
Dilys was one of the most celebrated heads of Hogwarts and found resounding success as a powerful healer at St Mungo's Hospital for Magical Maladies and Injuries. Though the novels produce very little information about the extent of her abilities, she was highly revered in the wizarding community which can only mean her powers were extraordinary and were also the reason behind her appointment to Hogwarts.
A copy of her portrait hangs in Dumbledore’s office as he often asks for her counsel in academic or school-related matters or matters of urgency.
Phineas Nigellus Black
Sirius Black’s great-great-grandfather was the least popular headmaster in Hogwarts. Black’s magical knowledge was quite legendary, which also made the pure-blood wizard very arrogant about his superiority as a wizard. This is also why he loathed teaching and particularly disliked youth since he thought of them as novices. His family also had quite a history since it was packed with famous witches and wizards who had earned global recognition (Black considered Sirius a black sheep of the family).
Phineas had also taught his likeness to speak and act like himself and informed it of things he believed later generations of Hogwarts Headmasters or Head Mistresses might need to know.
Professor Everard
Easily one of the most revered and esteemed headmasters in the history of Hogwarts. Professor Everard worked with the British Ministry of Magic before becoming headmaster and despite his old school outlook, he soon found a good footing as a leader as the faculty and students looked up to him.
He was hired as a professor first which means he was particularly skilled in a field of magical study like dark arts or potionry, and was then promoted to the role of headmaster, which means he was quite powerful.
Severus Snape
Snape was perhaps one of the most powerful headmasters Hogwarts has ever seen; though he never found a lot of popularity as a professor or as a headmaster (due to his obvious proximity with the Death Eaters), he had begun creating spells as a student (he created the spell Sectumsempra that lacerates the target and causes severe hemorrhaging) and had actually managed to excel in several fields of wizardry.
He was an expert potioneer and was deft with curses; in fact, even Dumbledore turned to Snape for help with his own curse. Moreover, he was skilled in magical duels and notably defeats both Flitwick and puts up a good fight against McGonagall, who are famed for their dueling skills
Minerva McGonagall
There are many instances throughout the series that prove Professor McGonagall was perhaps the most powerful headmaster in Hogwarts' recent history, at least after Dumbledore. She defeated Snape when he was headmaster and when the Death Eaters invaded Hogwarts she defeated Alecto Carrow after a brief duel and even challenged Voldemort.
Plus, McGonagall's intellectual acumen in wizardry was her biggest asset as it helped her be prepared. For instance, when Voldemort and his army of Death Eaters had surrounded Hogwarts before the ultimate battle, McGonagall played the efficient commander and knew just what to do to secure the castle and its inhabitants
Albus Dumbledore
Albus Dumbledore was the only wizard Lord Voldemort found intimidating enough which is quite telling because Voldemort is widely considered to be the greatest wizard of all time. Dumbledore was a celebrated warlock who was a pioneer in transfiguration and defense against dark arts.
In fact, his prowess in the dark arts spectrum was what made him such a formidable nemesis to the Dark Lord. Not to mention he had control over the elder wand until his death. It's important to note that Dumbledore was a war-time headmaster, and had to surmount some crises which were far greater than what any headmaster has had to handle