Gematria Methods: 26 Systems with Examples

Mispar Hechrachi מספר הכרחי Sum

Also known as: absolute, standard, ragil

Standard absolute value; every letter (incl. finals) by its base value.

The foundational method used in classical rabbinic literature: each letter carries its conventional numeric value (א=1, ב=2, … ת=400), ignoring vowel marks. Also called Mispar Ragil or simply "standard gematria."

Mispar Gadol מספר גדול Sum

Also known as: large, sofit

Like hechrachi but final forms (ך ם ן ף ץ) carry 500–900.

Extends standard gematria by assigning large values (500–900) to the five letters that have a final form (כ מ נ פ צ when written at end of a word). This doubles the numeric range and allows more discriminating comparisons.

Mispar Siduri מספר סידורי Sum

Also known as: ordinal

Ordinal position 1–22; finals share their base letter's position.

Each letter is counted by its position in the Hebrew alphabet (alef=1 through tav=22) rather than its conventional weight. Final forms share the ordinal of their base letter. This method compresses the value range and links letters by sequential proximity.

Mispar Katan מספר קטן Sum

Also known as: small, reduced

Per-letter significant digit (10→1, 20→2, …, 300→3).

Strips trailing zeros from each letter's standard value before summing: mem (40) counts as 4, shin (300) as 3, qof (100) as 1. This changes which words share a numeric value. A match between unrelated roots does not establish a linguistic or historical relationship.

Mispar Katan Mispari מספר קטן מספרי Derived

Also known as: integral reduced, digital root

Digital root of the hechrachi total (reduced to 1–9).

First computes the standard Hechrachi value, then repeatedly sums its digits until a single digit (1–9) remains — the "digital root." Two words with identical digital roots share this reduced equivalence, regardless of their full values.

Mispar Perati מספר פרטי Sum

Also known as: squared, bonaeh

Sum of the square of each letter's standard value.

Each letter's standard value is squared before summing. Also called Mispar Meruba Pratit ("individual squared"). Squaring amplifies differences between letters — a large letter such as shin (300² = 90,000) dominates heavily, making this method sensitive to which heavy letters appear.

Mispar Milui / Shemi מספר מילוי Sum

Also known as: full, name-filling

Sum of the standard value of each letter's full-name spelling (canonical spellings).

Instead of counting the letter itself, you spell out its full name (e.g., Alef → א-ל-פ) and sum those letters' standard values. Also called Mispar Shemi ("name gematria"). This method is frequently used in Kabbalistic literature for analyzing Divine Names.

Mispar Ne'elam מספר נעלם Sum

Also known as: hidden

Milui minus the letter itself: value of the name's 'hidden' part.

The "hidden" or "concealed" value: take each letter's full-name spelling (as in Milui), then subtract the letter itself, keeping only the letters that come after it in the name. This isolates what is "hidden inside" each letter's name.

Mispar Musafi מספר מוספי Derived

Also known as: added

Hechrachi total plus the number of letters in the text.

Adds the count of letters in the word to the standard Hechrachi value. This is a form of the "Im HaOtiyot" (with the letters) convention, which compensates for the fact that a single letter has a positive presence beyond its numeric weight.

Mispar im ha-Kolel מספר עם הכולל Derived

Also known as: with the kolel

Hechrachi total plus the number of words in the text (the kolel, +1 per word).

A classic rabbinic adjustment: adds the number of words to the Hechrachi total. The "kolel" (כולל, "totality") convention allows a numeric match to stand even when it is off by one, because each word as a whole also contributes a single unit.

Mispar Kidmi מספר קדמי Sum

Also known as: triangular, meshulash kidmi, cumulative

Each letter valued as the sum of all standard values from alef up to it.

Also called Mispar Meshulash Kidmi ("triangular-cumulative"). Each letter's value is the running sum of standard values from alef up to and including that letter. This produces a triangular-number sequence; the effect is that later letters in the alphabet carry much higher weights.

Mispar Meshulash מספר משולש Sum

Also known as: cubed

Sum of the cube of each letter's standard value.

Each letter's standard value is cubed before summing. The exponential amplification makes this method highly discriminating: shin (300³ = 27,000,000) dominates any word it appears in. Useful for finding structural equivalences between short words and phrases.

Mispar Meruba Klali מספר מרובע כללי Derived

Also known as: squared total

Square of the hechrachi total.

Squares the overall Hechrachi total rather than individual letter values. Unlike Mispar Perati (which squares per-letter), this method is order-independent and treats the word as a single unit, then raises that unit to the second power.

Atbash אתב״ש Substitution

Reflect the alphabet (א↔ת, ב↔ש, …), then sum standard values.

The oldest and most famous Hebrew substitution cipher: letter 1 (alef) swaps with letter 22 (tav), letter 2 (bet) swaps with letter 21 (shin), and so on. Atbash appears explicitly in the book of Jeremiah (Jer 25:26 "Sheshach" = Babylon). After substitution the standard values of the new letters are summed.

Albam אלב״ם Substitution

Swap the two halves of 11 letters (א↔ל, ב↔מ, …), then sum standard values.

Divides the 22-letter alphabet into two halves of 11, then swaps letters between the halves: alef↔lamed, bet↔mem, gimel↔nun, and so on. The name "Albam" encodes the first two pairs (א-ל, ב-מ). Used in biblical exegesis and Kabbalistic commentary.

Achbi אכב״י Substitution

Swap adjacent pairs (א↔ב, ג↔ד, …), then sum standard values.

Swaps adjacent letter pairs across two groups of 11: alef↔kaf, bet↔yod, gimel↔tet, and so on within each half. The name "Achbi" encodes the first swap (א↔כ, ב↔י). Like Atbash and Albam, it is applied by substituting letters then summing their standard values.

Mispar Bone'eh מספר בונה Sum

Also known as: building, cumulative-positional

Running cumulative within the word: each letter's standard value is multiplied by the number of letters from it to the end (inclusive). Σ vᵢ·(n−i) over 0-based position i, n = total letters.

Mispar Bone'eh ("building value") weights each letter by how many letters remain from it to the end of the word (inclusive). The first letter carries the heaviest multiplier, the last carries ×1. An equivalent formulation: sum the word's running left-to-right partial-sums.

Mispar Ha'achor מספר האחור Sum

Also known as: positional, reverse-positional

Each letter's standard value multiplied by its 1-based position in the word. Σ vᵢ·(i+1) (0-based i).

Mispar Ha'achor ("backward/positional value") multiplies each letter's standard value by its 1-based position from the left. This is the positional complement to Bone'eh: where Bone'eh weights letters by distance to the end, Ha'achor weights them by distance from the start.

Mispar Mispari מספר מספרי Sum

Also known as: number-name, numeric-name

Each letter is replaced by the gematria (Hechrachi) of the spelled-out Hebrew name of its numeric value (e.g. alef=1 → the word אחד = 13), then those values are summed. Number-name spellings follow TorahCalc's convention.

Mispar Mispari ("numeric gematria") replaces each letter with the Hechrachi value of the Hebrew name of that letter's numeric value — a second-order substitution. Alef=1, whose Hebrew name is אחד (= 13); Het=8, whose name is שמונה (= 401); and so on. The spellings used follow the TorahCalc convention.

Atbach אטב״ח Substitution

Decade-complement substitution: each letter is replaced by the letter whose value completes its "decade" — units complete to 10 (א↔ט), tens to 100 (י↔צ), hundreds to 1000 (ק↔ץ, with final forms carrying 500–900). Sum the substituted values.

Atbach (אטב"ח) is a decade-complement cipher: units (1–9) pair with the letter that brings them to 10 (א↔ט, ב↔ח, ג↔ז, ד↔ו — ה is self-complementing at 5+5); tens (10–90) pair to 100 (י↔צ, כ↔פ, ל↔ע, מ↔ס, נ↔נ); hundreds (100–400/900) pair to 1000. The name encodes the first two pairs (א-ט, ב-ח). After substitution the standard values of the resulting letters are summed.

Ayak Bachar אי״ק בכ״ר Substitution

Also known as: aiq bekar, theosophic substitution

The 27 letters (including finals) are arranged in a 3×9 grid; each letter cycles within its column (units→tens→hundreds→units, i.e. ×10 modulo the row). Sum the substituted values.

Ayak Bachar (אי"ק בכ"ר) — also spelled Aiq Bekar — arranges the 27 letters (22 base + 5 finals) into a 3×9 grid by value magnitude: row 1 = units (א–ט), row 2 = tens (י–צ), row 3 = hundreds (ק–ץ). Each letter substitutes the letter directly below it in the same column (wrapping from row 3 back to row 1). The name encodes the first column: alef(1)→yod(10)→qof(100) = אי"ק.

Ofanim אופנים Substitution

Also known as: wheels, last-letter name

Each letter is replaced by the LAST letter of its own spelled-out Hebrew name (e.g. alef = אלף → ף), then those values are summed.

Ofanim ("wheels") is an unusual substitution: each letter is replaced not by a fixed partner but by the last letter of its own spelled-out name. Alef (א-ל-פ) ends in pe (ף=80); Bet (ב-י-ת) ends in tav (ת=400); and so on. The method's name alludes to the wheels (אופנים) of Ezekiel's vision — the letters cycle through their own spellings.

Achas Beta אח״ס בט״ע Substitution

Also known as: achas bta, plus-7 shift

Substitution by a +7 shift through the first 21 letters of the alphabet (wrapping within those 21); tav (ת, the 22nd letter) is left unchanged. Sum the substituted values.

Achas Beta (אח"ס בט"ע) shifts each letter +7 positions in the alphabet (positions 1–21 wrapping cyclically); tav, the 22nd letter, is unchanged. The name encodes the first pairs of the cipher: alef(1)→het(8) = א-ח, bet(2)→tet(9) = ב-ט, gimel(3)→samekh(15) = ג-ס. After substitution the standard values of the resulting letters are summed.

Avgad אבג״ד Substitution

Also known as: next-letter

Each letter is replaced by the NEXT letter in the alphabet (tav wraps to alef). Sum the standard values of the substituted letters.

Avgad advances each letter one step forward in the Hebrew alphabet: alef→bet, bet→gimel, …, shin→tav, tav→alef (wrap). The name itself illustrates the cipher: א-ב-ג-ד (alef→bet, bet→gimel, etc.). The substituted letters' standard values are then summed.

Reverse Avgad אבג״ד הפוך Substitution

Also known as: previous-letter, avgad reverse

Each letter is replaced by the PREVIOUS letter in the alphabet (alef wraps to tav). Sum the standard values of the substituted letters.

Reverse Avgad is the mirror of Avgad: each letter steps one position backward in the Hebrew alphabet (alef wraps to tav). It is also called Avgad Hafuch (הפוך = reversed). The substituted letters' standard values are summed.