The principle of miktzas hayom k’kulo means part of a day counts for an entire day; for example, an aveil can get up from shiva on the morning of the seventh day without having to complete the entire day. My son asked me when we invoke this principle, and to tell you the truth it's something that I have wondered about for some time and never took the pains to figure out.
I assumed what inspired his question is the soon to be holiday of Lag ba’Omer. The Rama (O.C. 493) writes that haircuts should be taken only once the day of Lag ba’Omer has started (i.e. in the morning) and not the night before. The GR”A explains that the mourning period of sefirah ends 15 days before Shavuos, which would be the 34th day of sefirah (which is when the Beis Yosef says mourning is suspended). However, since miktzas hayom k’kulo, once part of the 33rd day is observed in mourning, the aveilus of sefira is complete. (Miktzas hayom starts during the day, not from the night before based on the din of shomeres yom (Meg. 20) -- the gemara says "counting" means counting specifically days.) Others disagree. Aside from when you can take your haircut (most barbers are not open at night anyway), this issue has ramifications with respect to davening: if miktzas hayom is required, tachanun is recited at mincha the day before Lag ba’Omer; if the day is inherently one of simcha without miktzas hayom, tachanun is not be recited the day before at mincha (see Chok Ya’akov s.k. 6).
However, I guessed wrong. My son raised the question for a far less prosaic reason. We learn in Parshas Shmini that a kohen may not enter the mikdash with long hair like mourners were accustomed to have. The shiur of “long hair” is derived from the parsha of nezirus and is defined as going 30 days without a haircut. The Minchas Chinuch (mitzvah 149) raises the question of whether a kohein would be in violation only after going 30 full days without a haircut, meaning on day 31, or whether the kohein would be in violation on day 30, since miktzas hayom without a haircut k’kulo. If this halacha is exactly parallel to nezirus, then just as a nazir fulfills his neder of nezirus (b’di’eved) on day 30 because miktzas ha’yom k’kulo, perhaps here too the kohein is considered too long haired once day 30 has even partially passed. On the other hand, one might argue that nezirus is just a paradigm for what constitutes excessive hair growth, but the details of hilchos nezirus like miktzas hayom k’kulo do not transfer to the parsha that applies to the kohein.
Parenthetically, usually miktzas hayom k'kulo results in a leniency, e.g. ending shiva in the morning, stopping sefira mouring midway though day 33 instead of waiting for day 34. Minchas Chinuch is a twist because he uses it l'chumra -- the kohein would be chayav for his unkempt appearance a half a day earlier. Maybe some of you beki'im can offer other examples like this (l'chumra), because I can't.
Getting back to the point: so where do we apply miktzas yom k’kulo? Just because you observe Shabbos for part of the day does not mean miktzas hayom k’kulo so you are free to go to the ballgame in the afternoon! Why then does it work for nazir, for aveilus?
Second question (which may be easier to answer than the first) is yesh lachkor whether miktzas hayom k’kulo means that the halacha requires observing/counting only part of the day in question, or whether miktzas hayom k’kulo means that even though observing/counting all of the day is required, part of the day counts for the whole thing? More to come bl”n.