The Nine Systems of Gematria: A Complete Guide with Calculations
Gematria assigns numerical values to Hebrew letters. The same word yields different numbers depending on which system you apply, and the choice of system is not arbitrary — each was developed for a different purpose. This guide gives the exact rule and a worked example for all nine.
The nine systems, with rules and examples
| System | Rule | Example: חי (chai) |
|---|---|---|
| Mispar hechrachi absolute value | א=1 … ת=400; final forms count as regular | 8 + 10 = 18 |
| Mispar gadol large number | Final letters take 500–900: ך=500, ם=600, ן=700, ף=800, ץ=900 | ארץ 291 → 1101 |
| Mispar katan small number | Zeros dropped: י=1, ק=1, ת=4 | 8 + 1 = 9 |
| Mispar siduri ordinal | Position in the alphabet, 1 to 22 | תורה 611 → 53 |
| Mispar shemi filling (milui) | Each letter spelled out in full, then summed | א → אלף = 111 |
| Mispar kolel | Sum plus the number of letters (or plus one) | allows a match to be closed by 1–2 |
| Atbash | Mirror alphabet: א↔ת, ב↔ש | ששך → בבל (Jeremiah 25:26) |
| Mispar prati | Sum of the squares of letter values | חי = 64 + 100 = 164 |
| Mispar meshulash | Sum of the cubes of letter values | חי = 512 + 1000 = 1512 |
Where does gematria come from?
The word derives from the Greek geōmetría. The practice of assigning numerical values to letters was known to Babylonians and Greeks before it entered Jewish use.
The oldest documented instance is not Jewish at all. An Assyrian inscription of Sargon II (727–707 BCE) records that the king built the wall of Khorsabad 16,283 cubits long, so that it would match the numerical value of his name.
In rabbinic literature gematria appears with the Tannaim of the second century CE. The Baraita of 32 Rules attributed to Rabbi Eliezer lists it as rule 29. The classic worked example: Abraham's 318 men (Genesis 14:14) are read as a reference to one man, Eliezer — because אליעזר equals 318.
Classical identities of the tradition
| Words | Value | Traditional reading |
|---|---|---|
| אחד "one" = אהבה "love" | 13 | Together they make 26, the value of the Name |
| יין "wine" = סוד "secret" | 70 | "Wine goes in, a secret comes out" — Eruvin 65a |
| אלהים "Elohim" = הטבע "nature" | 86 | God acting through nature |
| נחש "serpent" = משיח "messiah" | 358 | The repair of the sin of Eden |
The limit the tradition set on itself
Gematria has a boundary, and it was drawn by a kabbalist. Nachmanides (Rambán, 1194–1270) ruled that gematria is admissible only as asmakhta — a support and a mnemonic for meaning already received through tradition — and never as a mechanism that generates meaning.
No one has the right to compute a gematria in order to derive from it something that came into his own mind. Nachmanides, rendered in sense
The Vilna Gaon worked the same way: in his hands gematria confirms a meaning established from other sources. Abraham ibn Ezra (1089–1167) had objected earlier and more bluntly to using gematria to derive the content of a text.
This is the single most useful methodological statement in the field, and it is routinely ignored by people selling numerological readings.
What about "Torah codes"?
Equidistant letter sequences are a separate matter and they do not survive scrutiny. Witztum, Rips and Rosenberg published their study in Statistical Science in 1994; the journal's editor framed it explicitly as a "challenging puzzle" rather than an accepted result.
In 1999 McKay, Bar-Natan, Bar-Hillel and Kalai published a refutation in the same journal. They showed the result reflects choices made in constructing the experiment: rabbis' names have many valid spellings, and minor permissible changes to the list destroy the effect. Control tests found equally striking "codes" in War and Peace and Moby-Dick.
Ordinary gematria is a different thing entirely: it is plain addition, fully deterministic, and anyone can verify it on paper in under a minute.
Frequently asked questions
How many systems of gematria are there?
More than twenty are documented; nine are used in practice. The list above covers all nine.
Which system should I use?
Mispar hechrachi is the default and the one meant when a source says "gematria" without qualification. The others add layers rather than replace it.
Do final letters change the number?
In mispar hechrachi, no — a final mem counts as 40, the same as a regular mem. In mispar gadol, yes — final letters take values from 500 to 900.
What are master numbers?
When a total is reduced to a single digit by summing its digits, the values 11, 22 and 33 are conventionally left unreduced. This is a numerological convention, not a talmudic rule.
Can gematria predict the future?
No, and the tradition itself says so. Nachmanides restricted gematria to confirming meaning already received, never to generating new claims.
Is gematria the same as numerology?
They overlap but differ in source. Gematria works with the Hebrew alphabet and Jewish textual tradition. Western numerology usually applies a 1–9 scheme to Latin letters, a Pythagorean framework with no connection to Hebrew.
