Although Juliet and Romeo in William Shakespeare's Romeo and Juliet are often considered archetypal young lovers, Shakespeare does not specify Romeo's age.
We do know that Juliet was 13 at the time of her death. To a modern audience, this may seem rather young for marriage, but in the Renaissance, women were married as soon as they reached puberty, due to the high infant mortality rate. For a woman to bear a male child surviving into adulthood, and a second male child in case the first one died in adulthood (an "heir and a spare"), she needed, on the average, to bear eight children, for which marrying early in her reproductive years was necessary.
For Romeo, the first thing that gives is a clue to his age is his impetuous, imprudent character, something that in drama of this period was normally attributed to the young. As he is still to a degree under parental control, unmarried, and unemployed, and his parents are middle aged rather than elderly and feeble, we can assume that he is under 30. He is referred to in the play as "young" Romeo:
Nurse: ... where I may find the young Romeo?
Romeo: I am the youngest of that name...
Arthur Brooke's The Tragicall History of Romeus and Juliet, which was Shakespeare's main source, describes him as "beardless", which would suggest under 18, but older than 14 or so because he is as tall and strong as adult men, and referred to as a young man rather than as a child.
Overall, a range of approximately 16 to 21 seems most probable.