When precisely does a boy who reaches the age of Bar Misva become eligible to count toward a Minyan?
The Shulhan Aruch addresses this question in Orah Haim 55:9 (listen to audio recording for precise citation), where he writes that a boy is considered a "Gadol" (adult) with respect to Misva obligation once he meets two conditions. The first is that he completes his thirteenth year, as the Mishna in Pirkeh Abot (5:21) states, "Ben Shelosh Esreh Le’misvot" ("A thirteen-year-old – for Misvot"). Secondly, the Shulhan Aruch writes, the boy must have reached the stage of "Sheteh Se’arot" ("two hairs"), referring to a level of physical maturity.
Nevertheless, the Shulhan Aruch writes, a child who has reached the age of thirteen may be counted for a Minyan even without his level of physical maturity being examined. Boys who reach the age of thirteen have a "Hazaka" (presumption) that they’ve begun the process of physical maturation, and they may therefore be counted for a Minyan without inspection. The Shulhan Aruch cites a view that a boy who has reached the age of thirteen cannot be presumed to have reached the stage of "Sheteh Se’arot" with respect to allowing him to fulfill Torah obligations on behalf of others. With regard to a Minyan, however, which means allowing the group to recite Kaddish, Kedusha and so on, a thirteen-year-old boy is presumed to have reached physical adulthood, as these Halachot do not involve any Torah obligation.
The Shulhan Aruch clarifies that a boy becomes eligible to count toward a Minyan immediately upon completing his thirteenth year. The sources speak of the requirement that he reach the age of "Shelosh Esreh Shana Ve’yom Ehad" ("thirteen years and one day"), which some misinterpret to mean that he must wait a complete day after reaching the age of thirteen. The Shulhan Aruch therefore clarifies that this term refers to the moment the fourteenth year has begun. Once the child has completed his thirteenth year, he may be counted for a Minyan.
There is a dispute among the Rishonim (Medieval Halachic scholars) as to how we calculate the completion of thirteen years with respect to this Halacha. According to one view, the child becomes a Bar Misva only at the time of day at which he was born (known in Halachic jargon as "Me’et Le’et"). Thus, if a boy was born at 4pm, he would not count toward a Minyan until 4pm on his thirteenth birthday. However, Halacha follows the majority view among the Rishonim, which considers the child a Bar Misva immediately at Set Hakochavim (nightfall) of his birthday, regardless of the time of day at which he was born. Even if a boy was born late in the afternoon on Rosh Hodesh Nissan, for example, he may count toward a Minyan for Arbit on the night of Rosh Hodesh Nissan thirteen years later. In fact, the Shulhan Aruch rules that if a boy was born during Ben Hashemashot (the 15-minute period after sundown) on Rosh Hodesh Nissan, he may count toward a Minyan for Arbit on the evening of Rosh Hodesh Nissan thirteen years later.
It must be emphasized, however, that the boy becomes a Bar Misva only at nightfall. If a congregation prays Arbit before sundown (as many congregations do on Friday evening during the spring and summer), and the boy’s thirteenth birthday is that night, he does not count toward the Minyan, since his thirteenth birthday has not yet arrived.
The Shulhan Aruch writes that a father who claims that his son is thirteen years old is trusted, as is a person claiming to have heard from a father that his child is thirteen years of age. However, if the father is not present, the boy himself should not be trusted if he claims to be the age of Bar Misva; his claim should be verified before he is counted for a Minyan. Even if he is wearing Tefillin, this does not verify his claim, since many boys begin wearing Tefillin before their thirteenth birthday. However, the Shulhan Aruch adds, if there is no possibility of verifying the young man’s age, or if the congregation would be inconvenienced by having to wait until the boy’s age is confirmed, then they may rely on the child’s claim that he has reached the age of Bar Misva.
Summary: A boy is eligible to count toward a Minyan immediately at nightfall of his thirteenth birthday, regardless of the time of day at which he was born.
