The seven methods of gematria

Seven gematria methods, one at a time: the rule, where the tradition itself uses it, a worked example, and when a learner should reach for it.

Ask what a Hebrew word is worth and the honest answer starts with another question: counted how? The gematria methods are the rules for turning a word’s letters into a number, and they do not agree. This site computes seven of them over every word, phrase and verse of the Tanakh. This page takes them one at a time: what each rule is, where the tradition itself uses it, quoted from texts this site holds and said plainly where it holds none, one worked example computed by the engine, and when a learner should reach for it. The letter chart is in how to calculate gematria, and all seven worked side by side on a single word are in what gematria is, and what it is not.

Seven gematria methods, and one old word for all of them

The word itself is old. When the Gemara in Sukkah lists everything Rabban Yochanan ben Zakkai never left unlearned, from Scripture and Mishnah down to the talk of the palm trees, gematriot stand in the list beside the calculations of the seasons, one more discipline a master of the Torah did not leave aside. And the Talmud’s word covers more than addition. In Sanhedrin, Rav says that the writing on Belshazzar’s wall was written for them in gematria, and the letters he then gives are not a sum of anything; they are a letter-for-letter exchange, the one now called atbash. The neat division of the subject into separate named reckonings belongs to later centuries. What follows uses the names this site uses and is careful about which of them the older texts actually show at work.

Standard: mispar hechrachi

The rule. Alef is one, up to yod at ten, then by tens to kuf at a hundred, then by hundreds to tav at four hundred. A final letter counts as its ordinary form.

Where the tradition uses it. Almost everywhere. Nearly every gematria the Talmud makes is in the standard count, and the one worth studying first is unusual, because it carries a law rather than a homily. The Mishnah in Nazir rules that a vow of nezirut with no term named lasts thirty days. The Gemara asks where that comes from, and Rav Matna answers from the Torah’s own words, he shall be holy:

יהיה, he shall be, is thirty in gematria.

יהיה=30

Even here the number rides on a tradition rather than creating one. Bar Pada, on the same daf, counts something else: the words nazir and nezer are said in the Torah thirty times less one, and he reads the term from that. The Gemara then spends the next page testing the two derivations against the wording of the Mishnah. The Mishnah’s thirty was fixed before either of them spoke.

When to use it. First, and by default. When a source says a word comes to a number and does not say how, this is how. The search on this site starts from it for the same reason.

Gadol: mispar gadol, the great number

The rule. The same as the standard count, except that the five final forms carry on the hundreds where tav stops: final kaf five hundred, final mem six hundred, final nun seven hundred, final pe eight hundred, final tzadi nine hundred. A word with no final letter has the same value either way. A word that ends in one can jump a long way. אדם, man:

אדם=45אדם=605 Gadol

Where the tradition uses it. The final forms themselves are ancient; the Gemara in Shabbat says the seers established them, and the article on calculating gives that passage. Counting them as five hundred to nine hundred is another matter. No text in this site’s library computes a word that way, so this page credits the great number to no particular book; it belongs to the later literature of the reckonings.

When to use it. Only when the source in front of you is using it. A result under gadol and a result under the standard count are different claims, and the commonest mistake in this whole subject is to pick whichever of the two makes the match.

Katan: mispar katan, the small number

The rule. Drop the zeros. Each letter keeps only its digit: yod, which is ten, counts one; shin, three hundred, counts three. Every letter is worth between one and nine, and the value of a word is small. This site adds the digits once and stops there. Some calculators go on to reduce the total itself to a single digit; that is a different rule, and it is not what is computed here. A word from the second verse of the Torah:

תהו, formless, is four hundred, five and six in the standard count, and four, five and six in the small one. תהו=411תהו=15 Katan

Where the tradition uses it. By name, in a note printed among the Zohar’s addenda, where Rabbi Binyamin Levi records readings he says he found written. It reckons this very word in the small number, then its neighbours in the verse, and then the earthquake and the still small voice of Eliyahu’s vision at Chorev, several of them with the kolel, one added for the word as a whole. This site does not add the kolel, and the equations the note draws between those words and the Divine Names are its own; they are not reproduced here.

When to use it. When a source uses it, and as a way of seeing the alphabet’s structure: alef, yod and kuf all count one in the small number, bet, kaf and resh all count two, and so on down the three runs of nine. Because the values are small, many words share each one, so a match under katan is worth even less on its own than a match under the standard count.

Ordinal: mispar siduri

The rule. Each letter is worth its place in the alphabet: alef one, bet two, and so on to tav at twenty-two. The final forms take their ordinary letter’s place.

Where the tradition uses it. In the Gemara in Shabbat, in a lesson it puts in the mouths of schoolchildren who came to the house of study and said things not said even in the days of Yehoshua bin Nun. Why, they ask, are the letters of שקר, falsehood, close together, and the letters of אמת, truth, far apart? Because falsehood is common and truth is rare. The argument is about places in the alphabet, which is exactly what the ordinal count measures. Truth takes its letters from the start, the middle and the end, places 1, 13, 22. Falsehood takes three neighbours near the end, places 21, 19, 20.

אמת=36 Siduri (ordinal)שקר=60 Siduri (ordinal)

The totals are the site’s arithmetic, not the Gemara’s. The children did not add the places; they looked at how far apart they stand. That is a fair picture of how the ordinal count is best used.

When to use it. When position matters more than size, and when a source says it is counting by order. With every letter worth twenty-two at most, the values crowd together even more than under katan.

Atbash

The rule. Fold the alphabet in half, so that the first letter pairs with the last, the second with the second-last, and so on inward: alef with tav, bet with shin, gimel with resh, dalet with kuf. Swap every letter of a word for its partner. What the tradition does with the result is read the new word; what this site then does is take the new word’s standard value, which is what the atbash column in the search means.

Where the tradition uses it. In several places this site can open, and the first is the scheme itself. The same page of Shabbat on which the children read truth and falsehood runs through all eleven pairs, alef-tav, bet-shin, gimel-resh, dalet-kuf, down to kaf-lamed at the middle of the alphabet, and reads the pairs as sentences, first about the wicked and then about the righteous. It then goes on to two other ways of pairing the alphabet, one of them the scheme called albam, which this site does not compute.

The second is Yirmiyahu’s name for Babylon. Bamidbar Rabbah says it outright: Sheshach, in atbash, is Bavel. The prophet uses the name twice, and in the second the verse itself sets the two names in parallel halves.

Swap the letters of בבל and the engine returns ששך. So the atbash value of the one is the standard value of the other. בבל=620 Atbashששך=620

The third is the writing on the wall, which Daniel read and the king’s wise men could not.

The Gemara in Sanhedrin asks why they could not read it, and Rav answers that it was written in gematria. The letters he gives for the first word are yod, tet, tav, and the engine’s atbash of מנא is יטת, letter for letter. His letters for the last word match the engine’s exchange of ופרסין just as closely, פוגחמט. Rashi uses the same exchange on a single letter when he finds the six hundred and thirteen commandments in the incense of the princes’ offerings, and the article on 613 works that one through.

When to use it. When a text is hiding one name inside another, which is what it is for, and when a source writes the pairs themselves. As a value to search by, it is a curiosity: the atbash value of a word is simply the standard value of its exchanged letters.

Perati: the squares

The rule. Square each letter’s standard value, then add the squares. Values grow quickly, because tav alone is a hundred and sixty thousand. אחד, one, is a single, a sixty-four and a sixteen:

אחד=81 Perati

Where the tradition uses it. Nowhere this site can show you. It is the least attested of the seven, no text in our library computes with it, and the names of the minor reckonings are not used the same way by every writer. On this site perati means the squares, and every value in its column follows that rule.

When to use it. Rarely: chiefly to check a figure someone else has published. Nothing should be built on a match found here.

Milui: mispar shemi, the letters named in full

The rule. Each letter is worth the standard value of its own name written out. Alef is not one but אלף, a hundred and eleven. A final form takes its ordinary letter’s name, since a final mem is still a mem. Here is אדם again, now with its letters named:

אלף 111 + דלת 434 + מם 80 = 625

אדם=625 Milui

Why it is the one method with a choice in it. Several letter names have more than one authentic spelling, and the tradition keeps them all. The standing proof is the four fillings of the Divine Name in the kabbalistic literature, each a named value, and each the same four letters with heh and vav spelled differently. This site’s default is the filling with alef, the milui alfin, in which heh is spelled heh-alef and vav is spelled vav-alef-vav. Under it the Name comes to 45, the value called mah, and the other three fillings, 72, 63 and 52, are each one choice away in the calculator. Tav is תיו, four hundred and sixteen, its name in rabbinic Hebrew, rather than the two-letter spelling, which is the biblical word for a mark.

Where the tradition uses it. The letter names themselves are Talmudic. The same page of Shabbat reads the alphabet name by name, alef-bet as learn wisdom, gimel-dalet as be kind to the poor, and it spells a dozen of the names out as it goes. Every one of them, tav with its yod among them, is spelled exactly as this site’s default table spells it. The fillings themselves are all in our library. A passage of the Zohar Chadash on Ruth names the four together, ע״ב, ס״ג, מ״ה and ב״ן. Two passages printed among the Zohar’s addenda spell two of them out: one gives the filling with yods and calls it ע״ב, seventy-two; the other calls the Name in its filling mah, spells it out with alefs, and says it is the number of אדם. And another passage of the Zohar Chadash spells the filling that mixes yods with an alef in the vav and gives its reckoning as ס״ג.

אדם=45

A Tosafist commentary on the Torah that this site does not hold, the Paaneach Raza, works the milui of בראשית with tav spelled in two letters, tav and vav, and reaches 1,819; set tav that way in the calculator and the engine agrees, while the default table gives 1,829.

How this site keeps it honest. The default table is the only one the search answers under, and every milui value in the index is built on it. The alternatives, the other spellings of dalet, heh, vav, zayin, ayin, pe, tzadi, shin and tav, are computed live in the calculator and never indexed, and a reading that departs from the default rides in the page address so that anyone can reproduce it. Three of the alternatives, פי, שן, תאו, have no classical attestation at all. They are kept only so that a result can be reconciled with another calculator that uses them, and the calculator groups and labels them as modern conventions.

When to use it. When reading the kabbalistic literature, where milui is at home, and always with the table stated. Two people computing milui on different tables are not disagreeing about a word; they are using two different alphabets.

Which method should you use?

Start with the standard count, because that is what a source means unless it says otherwise. Use another method when the text in front of you uses it, and then use exactly the table it uses. And never choose a method after seeing which one makes two words match: with seven methods and a whole Tanakh to search, one of them nearly always will, which is why the question worth asking is never whether the numbers work out but who says so.