These Halachot were summerized from Rav Bodner's Sefer "Halachos of K’zayis"
1. Shiur K’zayis
The Torah commands us to make a brocha after eating bread (and being satiated), and defines for us what is meant by “eating”. “Eating” means that a person ate 1 k’zayis and if someone ate less then a k’zayis of bread he is not required, nor PERMITED to bentch.
When Chazal instituted the requirement to make a brocha achrona for foods other then bread they used the same criteria that the torah uses for bentching. Therefore, with regards to brocha achrona, if one ate less then a k’zayis of food he is not required, nor PERMITED to make a brocha achrona.
Knowing how much food equals k’zayis is not an easy matter. A k’zayis is a measure of volume. (Volume – the amount of space the item occupies). Two items which when measured have the same volume; will often not be perceived as such.
For example, a cube of chocolate measuring 1.2” x 1.2” x 1.2” high, is a k’zayis. That same amount of chocolate can be melted and poured into a bar shaped mold measuring 3.7” x 3.7” x 1/8” high. The resulting products, a small cube or a big bar appear as two very different shapes, yet both hold the same amount of chocolate and the same volume. The same k’zayis of chocolate can then be poured into ball shaped molds having a ¾ inch diameter. It will fill 8 balls. The same k’zayis can then be poured into slightly smaller ball shaped molds having a ½ inch diameter. It will fill 27 Balls! An insignificant quarter of an inch difference in diameter makes a significant difference when computing cubic volume.
2. How much is a Shiur K’zayis
K’zayis means that the item is the size of an olive. The Shulchan Aruch states that this shiur is a measurement of cubic volume, and explains that volume is measured by submerging an item in water and measuring the amount of water that it displaces.
Some Poskim are of the opinion that the shiur of k’zayis is based on the actual size of an average contemporary olive. Olives are graded into seven sizes from “Small” (.10 of one fluid once) to “Super Colossal” (.50 of one once). The middle size, “Extra Large”, has a volume of .20 of one fluid once. According to this view, the shiur is quite small, the displacement of about 1/5 of one fl. oz.
The Shulchan Aruch gives the shiur in relation to the size of an average egg. The average egg will displace slightly less then 2 fluid ounces. The Shulchan Aruch states that, in view of some rishonim, a k’zayis is equal to approximately one third of an average egg while other rishonim say the shiur k’zayis is equal to half an egg.
The Mishna Berura and most Poskim rule that with regard to brocha achrona we adopt the most stringent view, not to make a brocha achrona unless one ate an amount equal to ½ an egg.
The shiur k’zayis is defined as an item containing slightly less then one fluid once (more precisely .96 of fl. oz.) It could also be measured as 28.8 cubic centimeters.
IMPORTANT NOTE: The Mishna Berura recommends that one should avoid eating an amount for which the brocha achrona requirement is questionable. He may eat the volume of a once or more and unquestionably make a brocha achrona. He may eat the volume of less then half a fl. oz. and not make a brocha achrona. However, he should try to avoid eating between a half fl. oz and one fl. oz., because the brocha achrona requirement for that in-between amount is questionable.
3. How Much Counts
Small air holes within the food item, like sponge cake, all contribute towards the calclated volume. Additionally, one shouldn't sqeeze the cake to make it smaller, we measure based on how the item stands at the moment, despite that we know it rose from baking.
However, large air bubbles can not count the kazayit shiur and in a case where there is a large air bubble in the food item, one would need to take extra to compensate for the loss.
There are opinions that a whole item (beria), such as a grape, would receive a bracha achrona even if it were less than a kezayis. However, Halacha L'Maseh, due to our doubt, we take the lenient position and require a full kezayis of volume (safek brachot le'hakel).
That being said, one should avoid the situation in the first place. If for whatever reason, one only has a single grape - then divide it into two pieces and problem solved!
5. How to calculate the Shiur K’zayis
CUBE – Measure one side of the cube in centimeters. (If your ruler only shows inches, convert the inches into centimeters. One inch equals 2.54 centimeters.) Cube that number to determine the volume. (The mathematical formula is: Volume = S3.)
For example, a typical cube measures 1.4 centimeters on all sides. Multiply 1.4 by 1.4 and you get 1.96. Multiply that by 1.4 and you get 2.74. So the volume of that sugar cube is 2.74 cubic centimeters. You need 28.8 cc for one k’zayis. Since each cube is 2.74 cc, you need 10 and a half of them to make one k’zayis.
RECTANGLE – Measure the length and the width and the height in centimeters. (If your ruler only shows inches, convert the inches into centimeters. One inch equals 2.54 centimeters.) Multiply the length by the width by the height. (The mathematical formula for a rectangle is: Volume = L x W x H.)
For example, a typical piece of potato kugel measure 6 centimeters long, 5 centimeters wide and 3 centimeters high. Multiply the 3 together and you get 90. The piece of kugel has 90 cc and since you need 28.8 cc for one k’zayis, then there are slightly more then 3 k’zayisim in that piece of kugel. (90 divided by 28.8 gives you 3.12)
SPHERE – Cut the ball in half and measure the radius in centimeters. (If your ruler only shows inches, convert the inches into centimeters. One inch equals 2.54 centimeters.) Cube the radius and then multiply the resulting number by this special π-based number – 4.186 (The special number is based on π, 3.14, plus one third of π) (The mathematical formula for a sphere is: (4/3) π x r3).
For example, a typical chic pea has the radius of 0.62 centimeters. Multiply .62 x .62 to get 0.384 and multiply again by .62 to get .238. Multiply .238 by the special π number, 4.186 and you get 0.996. A typical chic pea has the volume of .996 cc. You need 28.8 cc for one k’zayis and therefore you would need 29 chic peas for one k’zayis.
CYLINDER – Measure the radius and height in centimeters. (If your ruler only shows inches, convert the inches into centimeters. One inch equals 2.54 centimeters.) Square the radius and multiply that number by the height of the cylinder. Now multiply that by π, 3.14. (The mathematical formula for a cylinder is: π r2h).
For example, a typical slice of kishke has the radius of 3.5 cm and is 2.2 cm high. Square the radius and you get 12.2. Multiply that by 2.2 and you get 26.8. Multiply that by π, 3.14, and you get 84.1. That slice of kishke has a volume of 84.1 cc and since you need 28.8 cc for one k’zayis – there are almost 3 k’zayisim in that slice of kishke. (84.1 divided by 28.8 equals 2.92 k’zayisim)
Doughnut-shaped Items (Torus)
For example, a typical bagel has BIG R of 3.5 and small r of 2.1. Multiply 3.5 (BIG R) by
6. Shiur for Sephardim
The Kaf Hachaim writes that the minhag is to use weight rather then volume to determine how much food is needed for a brocha achrona. According to this minhag, one may not make a brocha achrona unless the items weighs one once. Some S’fardic Poskim rule that one should follow this minhag. They explain that it is more practical and less confusing to set the shiur according to its weight. The reason that since most foods weigh less than the amount it displaces, if it weighs one once, it will almost always have enough volume to meet the volume requirement. According to this minhag the weight requirement is 29 grams.
For example, a typical machine matzah weighs slightly more then one once (33 grams) by it displaces 2 fl. oz. Thus when measured by weight we will need one whole matzah for a k’zayis, but in reality, when measured by volume half of a matzah is enough for a k’zayis.
Other S’fardic Poskim (Haham Ben Zion Abah Shaul and Rav Mansour of Brooklyn) rule that the shiur of a k’zayis should be measured by volume since this is the opinion of the Rambam and the Shulchan Aruch. According to this view, S’fardim should not make a brocha achrona unless the food item has a cubic volume of one fluid once, regardless of its weight, just like the Ashkenazim.
RAV OVADIA YOSEF says that S’fardim should follow this minhag and calculate the k’zayis by weight. According to this minhag, calculating the amount of food needed for a requirement is very simple. You can either weigh the item yourself on a scale, or since all packaged goods come with the weight information on the box calculate it yourself. It should say the weight in grams on the nutrition facts but if not you will need to convert the ounces to grams:
Ounces (oz) to grams = multiply by 28.35