Gemara

(Mishnah - R. Shimon) Chachamim taught that one can immerse in 40 Sa'im, but not in a drop less than 40 Sa'im!

98a (Mishnah): There were two rods for measuring an Amah in the Mikdash. One was half an Etzba (finger) bigger than the (six Tefachim) Amah of Moshe. The other was one Etzba bigger.

98b - Suggestion: Perhaps the staves go along the length of the Aron!

Rejection (Rav Yehudah): (Two men stand side by side between the staves and carry the Aron.) Two men cannot fit in one and a half Amos (the Aron's width)!

41b (Rav Papa): Whenever the Torah requires a Tefach, this is the width of four thumbs, which equals the width of six pinkies or five intermediate (index) fingers.

Pesachim 109a (Rav Chisda): The Revi'is of the Torah is the volume of a box two thumbs by two thumbs by two and seven tenths thumbs:

Eruvin 3b (Rava): All Amos are six Tefachim. Those (of Kil'ayim) are smiling (the hand-width is measured with space between the fingers, like one who smiles separates his lips). Those (of Mavoy and Sukah) are sad (without spaces between the fingers).

(Beraisa): "Kol Besaro" - the Mikveh must contain the entire body (of an average size person), i.e. an Amah by an Amah and three Amos tall. Chachamim calculated that this is 40 Sa'im.

Rishonim

Rambam (Hilchos Bikurim 6:15): A Revi'is is the volume of a box two fingers by two fingers and 2.7 fingers tall. The Shi'ur Chalah is about a cube six and seven ninths fingers on each side. This is 43.2 eggs. This amount of wheat flour of Mitzrayim is the weight of 520 Mitzri Zuz nowadays.

Rambam (Hilchos Sefer Torah 9:9): The thickness of a thumb for all Shi'urei Torah is an average finger. We found that it is seven barley seeds pressed next to each other, which is like the length of two barley seeds with space.

Tashbatz (3:33): It is best to measure for a Mikveh based on fingers of average sized people. Eggs vary more from place to place. When we gauge the size based on eggs, it is much smaller than based on fingers. If there are two different Shi'urim, it is proper to be stringent about Torah laws. A Tosefta (Mikva'os 5:4) teaches that for anything mid'Oraisa with a Shi'ur mid'Rabanan, we are stringent about a Safek, and all the more so if the Shi'ur is mid'Oraisa.

Rivash (295): Do not say that nowadays people are smaller due to our sins. We rely on the measures of earlier generations. Mishnayos Mikva'os (which give the Shi'ur for Mikva'os) was taught that nowadays (i.e. after the Churban), just like the Mishnah which gives dimensions of burial caves (which are appropriate for people nowadays).

Poskim

Shulchan Aruch (YD 201:1): The Shi'ur Mikveh is 40 Sa'im, which is one Amah by one Amah by three Amos. The Amah is six Tefachim and half a finger. The Mikveh must be 44,118 and a half cubic fingers.

Beis Yosef (DH Tzerichah and DH v'Chosav Od): The Mikveh must be 41,472 cubic fingers. The Ra'avad (Ba'alei ha'Nefesh, Sha'ar ha'Mayim) says that we use an Amah Sochekes (with spaces between the fingers), for we are stringent about all Shi'urim of the Torah (Eruvin 3b). The Rashba says that it is a half finger more than Moshe's Amah (Menachos 98a).

Divrei Chamudos (Nidah 10:45): Here, the Beis Yosef's calculation overlooked the extra half finger. Also Rashi, the Rashbam, Tosfos and the Rif overlooked it regarding a Revi'is. However, they discussed a Kos Shel Berachah, which is mid'Rabanan, for which we are not stringent to require the extra half finger!

Rebuttal (Shach 6): The Beis Yosef wrote that it is 41,472 cubic fingers, i.e. based on Amos of six Tefachim. Those are Amos (and fingers) Sochakos; each is half a finger more than a regular Amah. It equals the Shi'ur he wrote in the Shulchan Aruch. Also Pesachim discusses 'the Revi'is of the Torah'! According to Divrei Chamudos, a Mikveh is 42 Sa'im and half a Lug. The Gemara and Poskim always say only 40 Sa'im. All measures they gave regarding Mikveh are Sochakos.

Avkas Rochel (53): We do not rely on the weight of the water for the Shi'ur of a Mikveh if this contradicts the volume. The volume is primary.

Tzlach (Pesachim 116b DH v'Ho'il): The Shi'ur for Chalah is 43.2 eggs. The Tosfos Yom Tov measured that this is the old pint of Prague. I made a Kli seven thumbs less two ninths long in each dimension, which is the Shi'ur for Chalah. This Kli holds two pints! This is a contradiction in the Shi'ur for Chalah. This Shi'ur and for Mikveh are both traditions from Sinai. We must say that either thumbs became bigger than they were in the days of the Tana'im, or eggs became smaller. It is known that the generations are getting smaller; we cannot say that our thumbs are bigger than those in the days of the Gemara, so we must say that the eggs are smaller. A k'Zayis is like an egg nowadays. One should use this for Matzah, Maror and all Shi'urei Torah.

Chasam Sofer (1:127): I measured and found like the Tzlach. The fingers did not change. In another Teshuvah (181) I wrote that even though Chachamim knew that the generations are changing, every generation gauges according to thumbs at the time. Presumably, everything else will change correspondingly, e.g. the Amah.

Kaf ha'Chayim (456:11): When measuring thumbs, one should not press it down, for this makes it wider.

Yismach Levav (OC 8 DH v'Hinei): Pesach ha'Dvir says that the Tzlach's measurement was based on a large man, pressing the thumb. If we average the size of the thumbs of a big and small man, without pressing, there is no discrepancy.

Chazon Ish (OC 39:12): Also R. Akiva Eiger measured and confirmed the Shi'ur of the Tzelach and Chasam Sofer. In pressed circumstances, one may rely on 648 liters for a Mikveh. L'Chatchilah, it should be significantly more than the minimal Shi'ur. If it is too small, a Nidah did not immerse, and there is a Chiyuv Kares.

Igros Moshe (YD 3:66): I do not understand what the Acharonim delved into. Surely, all measurements were given in fingers are based on people nowadays! If not, there is no limit. Perhaps in the days of Chazal, people were twice or three times our height! Chazal should have fixed a Shi'ur also for our generations. If sizes would change, they knew this through Ru'ach ha'Kodesh! One opinion in Shabbos holds that people in the days of the Gemara were the same size as in the days of Moshe. If so, we need not be concerned that afterwards they became smaller! Rav holds that the Leviyim, and surely all of Yisrael, were 10 Amos tall (and two or three times wider than people today). In the Gemara, all agree about the size of a Mikveh. It is one Amah by one Amah by three Amos. This sufficed for Yisre'elim in Moshe's Dor to immerse in, for it was based on their Amos! The Rishonim assumed that they (in their Dor) were the same size as people in the Gemara. Presumably, people were always the same size; only the Dor that received the Torah were bigger. Therefore, the Midos of the Mishkan and its Kelim were based on standard Amos. The same applies to all other laws, e.g. four Amos for Shabbos.

Note: If so, what was his proof from Mikveh? A Mikveh of one by one by three Amos suffices, for this is based on normal people, even though adults of Moshe's Dor could not fit inside! Also, even though the staves of the Aron were along its width, there were only two and a half Amos in between them. How could two people fit inside if they were twice as wide as people today?

Igros Moshe: Surely, we follow the size of people nowadays. It is not clear who is called average, therefore, we must be stringent. I measured average people, and found that the Amah is 21 and a quarter inches (about 53 centimeters). For a Mikveh, I suggest using 24 inches. This is a stringency. I did not find anyone average with an Amah more than 23 inches. In general, the Mikveh should be much more than the minimal size. Indeed, our eggs are smaller. We do not rely on the size of eggs, rather, the size of fingers. We do not follow the Rambam's Shi'ur based on barley; perhaps it became bigger or smaller!

Ohr l'Tziyon (3, Introduction, Shi'urei Mitzvos 2): Sefardim follow our tradition, that the measures did not change. However, some Sefardi Gedolim were stringent for the larger Shi'ur (and consider a Tefach to be 10 centimeters) for Torah Mitzvos such as Mikveh, the four Minim and Sukah.