How to calculate gematria, step by step

Twenty-two letters that were always numbers: the chart, the addition, the three things that change an answer, and how to check every sum against the text itself.

Learning to calculate gematria takes about ten minutes, and all of it rests on one fact about Hebrew: the language never had a separate set of numerals. Each of its twenty-two letters is also a number, so the value of a word is simply the sum of its letters. This page is the practical half of the subject. It sets out the gematria chart, shows how to calculate gematria for a single word, a phrase and a whole verse, names the three things that change an answer, and ends with the way to check any result against this site’s index of the whole Tanakh. What gematria is for, and what it cannot be asked to prove, is the subject of a companion piece.

The gematria chart

The alphabet counts in three runs of nine. Alef to tet are the units, one to nine. Yod to tzadi are the tens, ten to ninety. Kuf to tav are the hundreds, and there the alphabet runs out: tav is four hundred and no letter stands for five hundred. Every number in the chart below is computed by the same engine that values every word on this site, and each letter’s name opens its own page in the letters census. The last column is the letter’s place in the alphabet, which one of the other reckonings uses; the value column is the one you need.

The five final forms

Five letters take a different shape at the end of a word: kaf, mem, nun, pe and tzadi. They are the second form beside each of those letters in the chart. In the standard reckoning, which is the one nearly every classical source means when it says a word comes to a number, a final letter is worth exactly what its ordinary form is worth. Final mem is forty, as mem is.

The forms themselves are old enough that the Gemara in Shabbat has to explain where they came from. Rabbi Yirmiyahu, or as some say Rabbi Chiya bar Abba, says the seers instituted them. The Gemara objects that no prophet may introduce anything new. Its first answer is that both forms were already in use and what nobody knew was which of each pair belonged in the middle of a word and which at its end, until the seers settled it. Pressed again with the same objection, it answers that the forms had been forgotten, and the seers established them once more.

One reckoning does count them differently. Mispar gadol, the great number, lets the final forms carry on the hundreds where tav stops:

Unless a source says it is using the great number, it is not, and a beginner should leave the finals at their ordinary values. The article on the seven methods covers gadol and the others one at a time.

Adding up a word

Three steps. Take the letters only: the vowel points under and over them, and the cantillation marks, are not letters and add nothing. Look each letter up in the chart. Add. Here is שלום, peace, done by hand:

ש 300 + ל 30 + ו 6 + ם 40 = 376

שלום=376

Two short words show the thing that makes gematria interesting in the first place, which is that different words can come to the same total. אחד, one, and אהבה, love:

א 1 + ח 8 + ד 4 = 13

א 1 + ה 5 + ב 2 + ה 5 = 13

אחד=13אהבה=13

That pair is famous, and the article on thirteen explains why the usual way of telling it is slightly wrong. The first word of the Torah is worked the same way:

ב 2 + ר 200 + א 1 + ש 300 + י 10 + ת 400 = 913

בראשית=913

Phrases and whole verses

A phrase is added exactly like a word. The space between two words is worth nothing, so a phrase is the sum of its words and a verse is a longer phrase. Here is the Torah’s first verse, and below it the same words one at a time, each read out of this site’s index and valued by its engine.

The verse has 7 words and 28 letters, and it comes to 2,701. Nobody needs to do that sum by hand twice: this site has already added up every verse in the twenty-four books, and every run of adjacent words inside each verse, so a phrase of any length can be looked up rather than computed.

Three things that change the answer

The vowels never do. Every verse on this site is shown fully pointed, and every value on it is computed on the consonants alone, which is how the reckoning has always been done. If a result seems to depend on a vowel, a letter has been miscounted somewhere.

The spelling always does. Hebrew can write a vowel sound with a letter, a vav or a yod, or leave the letter out, and the letter it adds is value it adds. The standing example is the name of Jerusalem. Written the way it is written today, with a yod before the final mem, and the way the Tanakh nearly always writes it, without one:

ירושלים=596ירושלם=586

Ten apart, because a yod is ten. Our index says the short spelling stands on its own 349 times in the twenty-four books, and that the long one, the spelling everyone types, does not stand on its own anywhere in them. With a letter fused to its front the long spelling does appear, four times in all, once each in Yirmiyahu and Esther and twice in Divrei HaYamim. Here is one of them.

Those are counts of a spelling, not of the city, which is named a great many more times with a prefix on the short form. The lesson is the practical one: a calculator that quietly modernises the spelling gives you the value of a word the text does not write. This site counts the letters on the page, and where the written form of a word and the way it is read aloud differ, it counts the written one.

The reckoning does. Everything on this page uses the standard method, which is the one a source means unless it says otherwise. There are six others, and each gives a different answer for the same word; the article on the methods takes them one at a time.

From a number back to letters

The chart works in both directions, and the reverse is how Hebrew writes a date, a chapter or a page. Take the largest letter that fits, subtract it, and repeat. Six hundred and thirteen is tav, four hundred; resh, two hundred; yod, ten; gimel, three. Written together, they are also read as a word, taryag, the traditional name for the count of the commandments, which has an article of its own.

תריג=613

Two numbers break the rule. Fifteen is written tet and vav, nine and six, rather than yod and heh, ten and five, and sixteen is written tet and zayin rather than yod and vav. The reason usually given is reverence. Yod and heh together are a Divine Name in their own right: the Rambam, setting out what may not be erased, says of those two letters that they are a Name by themselves, being part of the four-letter Name. He says nothing there about writing numbers, though, and yod and vav are not a Name at all, only the four-letter Name’s first two letters. So the custom is universal, but its reason, for sixteen especially, is the one usually given rather than a ruling this site can show you.

טו=15טז=16

And a year leaves out its thousands, so the year 5787 is written with the letters of 787, as the article on Elul and the new year works out in full.

תשפז=787

How to check any word on this site

Everything above can be done with a pencil, and it is worth doing a few times by hand, because the chart is small enough to learn and once it is learned every Hebrew word becomes a sum you can see. After that, let the engine do it. Type a Hebrew word or phrase into the search box, or into the gematria calculator, and it answers with the value under all seven methods and with every word, phrase and verse in the twenty-four books that carries the same number, in the order the text stands, from Bereshit forward. Type a number and it lists the places that carry it. Every number also has a page of its own; here is the page for 913. And the letters census counts every letter of the chart across the whole Tanakh, with its final form counted separately.

The one thing the engine cannot tell you is what a shared number means. That question belongs to the sources, and the honest answer is usually that a match on its own means very little. The arithmetic is yours in ten minutes; the learning takes longer.