Gematria is an Assyro-Babylonian system of numerology later adopted by Jews that assigns numerical value to a word or phrase in the belief that words or phrases with identical numerical values bear some relation to each other or bear some relation to the number itself as it may apply to a person's age, the calendar year, or the like. The best-known example of Gematria is the Hebrew word Chai ("alive"), which is composed of two letters that (using the assignments in the Mispar gadol table shown below) add up to 18. This has made 18 a "lucky number" among Jews, and gifts in multiples of 18 are very popular.
Although the term is Hebrew, it most likely derives from Greek geōmetriā, "geometry", which was used as a translation of gēmaṭriyā, though some scholars believe it to derive from Greek grammateia, rather; it's possible that both words had an influence on the formation of the Hebrew word. (Some also hold it to derive from the order of the Greek alphabet, gamma being the third letter of the Greek alphabet (gamma + tria).) The word has been extant in English since the 17th century from translations of works by Giovanni Pico della Mirandola. Although ostensibly derived from Greek, it is largely used in Jewish texts, notably in those associated with the Kabbalah.
- Mispar Hechrachi (absolute value) that uses full numerical value of the twenty-two letters. Sometimes it is also called Mispar ha-Panim (face number), as opposed to the more complicated Mispar ha-Akhor (back number).
- Mispar Gadol counts the final forms (sofit) of the Hebrew letters as a continuation of the numerical sequence for the alphabet, with the final letters assigned values from 500 to 900.
- The same name, Mispar ha-Gadol, is also used for another method, which spells the name of each letter and adds the standard values of the resulting string.
- Mispar Katan calculates the value of each letter, but truncates all of the zeros. It is also sometimes called Mispar Me'ugal.
- Mispar Siduri (ordinal value) with each of the twenty-two letters given a value from one to twenty-two.
- Mispar Bone'eh (building value, also Revu'a, square) is calculated by walking over each letter from the beginning to the end, adding the value of all previous letters and the value of the current letter to the running total. Therefore, the value of the word achad (one) is 1 + (1 + 8) + (1 + 8 + 4) = 23.
- Mispar Kidmi (triangular value) uses each letter as the sum of all the standard gematria letter values preceding it. Therefore, the value of Aleph is 1, the value of Bet is 1 + 2 = 3, the value of Gimmel is 1+2+3=6, etc. It's also known as Mispar Meshulash (triangular or tripled number).
- Mispar P'rati calculates the value of each letter as the square of its standard gematria value. Therefore, the value of Aleph is 1 × 1 = 1, the value of Bet is 2 × 2 = 4, the value of gimmel is 3 × 3 = 9, etc. It's also known as Mispar ha-Merubah ha-Prati'.
- Mispar ha-Merubah ha-Klali is the square of the standard absolute value of each word.
- Mispar Meshulash calculates the value of each letter as the cube of their standard value. The same term is more often used for Mispar Kidmi.
- Mispar ha-Akhor – The value of each letter is its standard value multiplied by the position of the letter in a word or a phrase in either ascending or descending order. This method is particularly interesting, because the result is sensitive to the order of letters. It is also sometimes called Mispar Meshulash (triangular number).
- Mispar Mispari spells out the standard values of each letter by their Hebrew names ("Achad" (one) is 1+8+4=13 etc.), and then adds up the standard values of the resulting string.
- Mispar Shemi (also Millui letter "filling"), uses the value of each letter as equal to the value of its name. For example, the value of the letter Aleph is (1 + 30 + 80) = 111, Bet is (2 + 10 + 400) = 412, etc. Sometimes the same operation is applied two or more times recursively.
- Mispar Ne'elam (hidden number) spells out the name of each letter without the letter itself (e.g. "Leph" for "Aleph") and adds up the value of the resulting string.
- Mispar Katan Mispari (integral reduced value) is used where the total numerical value of a word is reduced to a single digit. If the sum of the value exceeds 9, the integer values of the total are repeatedly added to produce a single-digit number. The same value will be arrived at regardless of whether it is the absolute values, the ordinal values, or the reduced values that are being counted by methods above.
- Mispar Misafi adds the number of the letters in the word or phrase to their gematria.
- Kolel is the number of words, which is often added to the gematria. In case of one word, the standard value is incremented by one.
- Atbash exchanges each letter in a word or a phrase by opposite letters. Opposite letters are determined by substituting the first letter of the Hebrew alphabet (Aleph) with the last letter (Tav), the second letter (Bet) with the next to last (Shin), etc. The result can be interpreted as a secret message or calculated by the standard gematria methods. A few instances of Atbash are found already in the Hebrew Bible. For example, see Jeremiah 25:26, and 51:41, with Targum and Rashi.
- Albam – the alphabet is divided in half, eleven letters in each section. The first letter of the first series is exchanged for the first letter of the second series, the second letter of the first series for the second letter of the second series and so forth.
- Achbi divides the alphabet into two equal groups of eleven letters. Within each group, the first letter is replaced by the last, the second by the tenth, etc.
- Ayak Bakar replaces each letter by another one that has a 10-times-greater value. The final letters usually signify the numbers from 500 to 900. Thousands is reduced to ones (1000 becomes 1, 2000 becomes 2 etc.)
- Ofanim replaces each letter by the last letter of its name (e.g. "Fe" for "Aleph").
- Akhas Beta divides the alphabet into three groups of 7, 7 and 8 letters. Each letter is replaced cyclically by the corresponding letter of the next group. The letter Tav remains the same.
- Avgad replaces each letter by the next one. Tav becomes Aleph. The opposite operation is also used.