Population and Education

As just a quick note: 25-35% of the population of any settlement is children. Half those are of a schoolable age. Go with 15% as an average population. Out of that, 30% are likely to be available for education outside the home. That’s 5% of the population in school at any given time. (This is wibbly wobbly math that can apply to any size school.)
For colleges, out of the people who received basic schooling (30% of the adult population, so let’s round it to 20% of the whole population), maybe 1 in 20 gets the chance to attend a college. That’s 4% of the population with a college education. Probably only 15-20% of the population is of an age to be at the college, so that’s a constant attendance of 0.8% of the population.
For universities, out of the people who received a college education - 4% of the population - let’s say 1 in 20 of those get the chance to attend a university. (This can be straight out of school or after college itself.) That’s a total of 0.8% of the population with a university education. Universities are much less age-based, so let’s say we get a full 25% of the population being a university-acceptable age. That’s a constant attendance of 0.2% of the population.
1 small school for every 500 people in the town (one room, one teacher, elementary school only)

1 teacher per 15 kids

1 in 5 people have this basic education; 15 kids in school at any given time.

1 magic tutor/mentor/trainer for every 1.5k people in the town or city (cantrips, level 1 spells)
1 standard school for every 2k people in the town (4 rooms by age, 4 teachers, elementary and middle school)

1 teacher per 20 kids

1 in 5 people have this basic education; 80 kids in school at any given time.

1 grand school for every 10k people in the city (15-20 rooms by age and subject, 17-23 teachers, elementary, middle, and high school)

1 teacher per 25-30 kids

1 in 5 people have this basic education; 500 kids in school at any given time.

1 college for every 100k people in the kingdom (often replaces high school; community college, trade or tech programs; 40-45 rooms and professors, +5 admin faculty; max attendance 2k)

1 professor per 20 students

1 in 25 people have this higher education; 800 students at any given time

1 university for every 2.5M people in the kingdom (state universities with 4-6 year programs; 250 rooms and professors, +25-30 admin faculty, max attendance 20k)

1 professor per 15-20 students

1 in 125 people have this highest education; 5k students at any given time