Breaking a Fast
Question
What if someone accidentally ate on a Fast Day?
Answer
Shalom!
Thank you for your question.
These are the halchos of a ta'nit Tsibbur;
One who accidentally ate/drank on a fast day is required to continue fasting for the rest of the day .
One who ate/drank more than a “k’zayis” (Like the volume of a small match box) (some say 30 cc 'shiur Ko'seves') of food, or drank more than “m’lo lugmov” (40 cc) of liquid. should change the "Aneinu" wording from “b’yom tzom ta’aniseinu” to “b’yom tzom ta’anis zeh.” and has to continue fasting as mentioned above.
One should learn the laws of Fast Days to atone for having broken a fast.
One ate less than a kezayit or drank less than a m'lo lugmov is permitted to say “Aneinu” during his Shemoneh Esreh at Mincha.
One who is permitted to eat on a fast day, such as one who is ill, does not say "Aneinu" in the Shemoneh Esrei.
SOURCES: OC 568 and commentaries