The long exile gave rise to uncertainty regarding the size of a kezayit. According to Rambam, a kezayit is slightly less than a third of the volume of an egg; according to Tosafot, it is about the volume of half an egg. In practice, due to this uncertainty, the custom is to follow the stricter ruling of Tosafot. The equivalent of half an egg was calculated as being a third of a piece of machine matza and as a similar-sized piece of hard handmade matza, whose thickness is similar to that of a machine matza.
This is the consensus of all Sephardic and most Ashkenazic authorities. However, one of the most prominent Ashkenazic Aĥaronim, R. Yeĥezkel Landau (also known as “Noda Bi-Yehuda”), reached the conclusion, based on his own calculations, that our eggs are half the volume of the eggs that existed at the time of the Sages. It follows that a kezayit is not half the size of one of our eggs, but is the size of a whole contemporary egg. R. Avraham Yeshaya Karelitz (“Ĥazon Ish”) concurred with Noda Bi-Yehuda’s calculations. Thus, in order to fulfill the Torah commandment using the “Ĥazon Ish shi’ur,” one must eat an egg’s bulk of matza. Although the halakha usually follows the standard shi’ur and does not take Ĥazon Ish’s shi’ur into consideration, when it comes to the Torah commandment of eating matza, it is proper le-khatĥila to satisfy all opinions. Ideally, then, one should eat a Ĥazon Ish kezayit of matza, or approximately two-thirds of a matza.
This, however, is not really much of a stringency, since anyway our custom is to eat two kezeytim initially – one for “ha-motzi” and another for “al akhilat matza” (SA 475:1). Since these two kezeytim contain a single Ĥazon Ish kezayit, we fulfill the Torah commandment according to all opinions.
One who finds it difficult to eat two-thirds of a piece of machine matza can eat one third, because according to the standard calculation, a third of a matza contains a kezayit. One even recites the “al akhilat matza” blessing before eating this amount, for the standard measure is so well founded that it is not considered the sort of uncertainty that causes the berakha to be canceled.
. The size of a kezayit is a very long topic, and is explained in Peninei Halakha: Berakhot 10:5-6 and in the notes there. I will summarize it here.
SA 486:1 rules that regarding the requirement to eat matza, we follow Tosafot that a kezayit is the size of half an egg’s bulk. SAH (486:1) states that for Torah commandments, one must be stringent and follow Tosafot, but for rabbinic mitzvot, such as eiruvin, one may follow the lenient opinion of Rambam, who maintains that a kezayit is slightly less than a third of an egg’s bulk. MB 486:1 states that when it comes to reciting a berakha aĥarona, which is only required if one eats a kezayit, one must follow Tosafot, since we are lenient whenever there is uncertainty in the laws of berakhot. Thus, one is only required to recite a berakha aĥarona if he eats at least half an egg’s bulk, not less. Le-khatĥila one should not invite an ambiguous situation, and should eat either less than one third of an egg’s bulk, in which case he would be exempt from a berakha aĥarona according to everyone, or more than half an egg’s bulk, in which case he would be required to recite a berakha aĥarona according to everyone. Regarding matza, one must be stringent and follow the opinion of Tosafot. Similarly, one must follow the opinion of Tosafot vis-à-vis maror, since we recite a berakha on it. On the other hand, when it comes to the requirement to eat a kezayit of korekh and the requirement to eat a kezayit of afikoman, one may be lenient and follow Rambam.
BHL on 271 explains the opinion of Noda Bi-Yehuda. MB (486:1) quotes Sha’arei Teshuva that regarding Torah commandments, including mitzvot like kiddush with a biblical basis, one should be stringent and follow Noda Bi-Yehuda. On the other hand, vis-à-vis rabbinic mitzvot like the four cups of wine, one need not follow Noda Bi-Yehuda. MB (ibid.) also states that regarding berakha aĥarona one need not follow Noda Bi-Yehuda; rather, he should recite a berakha aĥarona after eating the amount of half an egg, as per Tosafot. Sephardim do not show any concern for Noda Bi-Yehuda’s measurements, since the tradition regarding halakhic measurements was passed down, uninterrupted, in the regions near Eretz Yisrael, and every time the sizes were recalculated, the same results were found.
It should also be noted that there are two opinions within the view of Noda Bi-Yehuda that the kezayit of Tosafot is the size of a modern-day egg: according to MB this means an egg with its shell, and according to Ĥazon Ish this means an egg without its shell; the difference between these two opinions is about ten percent.
MB 486:3 states that one must realize that all of these measurements are based on volume, and only when there are large air pockets is one required to compress the food. The food’s natural texture does not need to be compressed. Therefore, the weight of a kezayit often varies, depending on the density of the food.
After measuring, it emerges that a kezayit according to Tosafot, which is the size of half a modern-day egg, is at most a third of a machine-made matza. If we multiply this shi’ur based on MB’s stringent explanation of Noda Bi-Yehuda, namely, that a kezayit is the size of a whole egg with its shell, a kezayit is approximately two-thirds of a machine-made matza. According to Ĥazon Ish’s understanding of Noda Bi-Yehuda, roughly half of a machine-made matza is sufficient, or, according to some, slightly more than half. In any case, one who eats two-thirds of a machine-made matza fulfills his obligation according to even the most stringent opinions (the weight of a machine-made matza is approximately 33 grams). See Sidur Pesaĥ Ke-hilkhato 2:8:4, which explains the calculations practically.
After reciting the berakha, one must eat two kezeytim (SA 475:1 citing Rosh and Mordechai). One kezayit is taken from the top, whole matza for the berakha of “ha-motzi,” and one kezayit is taken from the middle, broken matza for the berakha of “al akhilat matza.” BHL questions this ruling, since it does not seem that any other Rishonim require eating two kezayit-sized pieces. Nevertheless, the custom is to follow SA. However, one certainly does not need to be stringent in measuring the two pieces; therefore, if he ate a kezayit according to the measurement of Noda Bi-Yehuda, he has already fulfilled the obligation to eat two kezayit-sized pieces according to the accepted measurement (that of Tosafot) and has eaten more than three kezayit sizes according to the measurement of Rambam.
One who has difficulty eating two-thirds of a machine-made matza may eat one third and may recite the berakha of “al akhilat matza,” since, as we already mentioned, technically the halakha follows the accepted measurement (Tosafot), and even regarding berakha aĥarona one need not follow Ĥazon Ish (with the exception of his students and followers). Regarding the practice to eat two kezeytim, we have already mentioned that not all Rishonim agree that this is a requirement; moreover, one third of a machine-made matza likely contains two kezayit sizes according to Rambam. Therefore, one who eats one third altogether should eat a small piece from the whole matza and a small piece from the broken matza.