A statistical atlas of gematriya

The Numbers of Tanach in 305,507 words

Every figure on this page is counted directly from the Leningrad Codex: each word, each verse, and every run of one to six consecutive words. Explore how values are distributed, which letters carry the weight, how the books compare, and how the traditional counting methods differ.

78,091,408

Total gematriya of all Tanach

Torah alone: 21,010,192

255.6

Average word value

Median 204; 80% of words fall between 31 and 541

1,053,799

Distinct phrases of 1–6 words

39,615 distinct word forms

1,190

Different values taken by single words

Highest: 1640

I. Distribution

How phrases spread across the numbers

Choose a phrase length to see how the distribution shifts and widens. Place any word or number to see where it falls.

Words per phrase

Log scale1,053,799 phrases · peak at 550–559 · mean 1004

Place a word or number702 sits at the 34th percentile · 7,334 phrases in its bin

Distinct sequences of 1–6 consecutive words within a verse, grouped into bins of 10. A phrase that occurs many times counts once.

II. The landscape

Average word value, chapter by chapter

From Bereishit to Divrei HaYamim, all 929 chapters. Lists of names and numbers, Aramaic passages and poetry each leave their mark.

TorahNevi'imKetuvimAverage word value (5-chapter smoothing)

Dashed line: the average across all of Tanach (255.6).

Each point is one of the 929 chapters; the line is smoothed over five chapters. Highest chapter average: Exodus 26 (393.8); lowest: Psalms 117 (134.9).

III. The books

Average word value by book

Colored by section. Switch to “highest first” to rank them.

TorahNevi'imKetuvim

Hover or tap a bar for details

150

225

300

Average standard value of every word in the book. Hover or tap a bar for its totals.

IV. The letters

Which letters carry the weight

The light letters י, ו and ה are the most frequent, while the heavy final hundreds carry far more of the total than their frequency suggests.

Share of all lettersShare of total gematriya

Counted over every letter of every word (6.38% of letters are final forms, counted with their base letter). Yud is the most common letter (11.52%) but carries only 1.77% of the total; Tav carries the most (32.38%).

V. Word length

Longer words, larger values

Values rise steadily with length, but the spread at each length is wide: a three-letter word can be worth 9 or 1,000.

Median valueMiddle 50% / 80% of words

Distinct word forms grouped by number of letters. Shaded bands: the middle 80% and middle 50% of values.

VI. The methods

How the counting methods compare

Methods with fewer possible values (katan, ordinal) gather many more phrases under each number; milui and gadol spread them most thinly.

Method	Distinct values	Phrases per value (average, log scale)	Chance two share a value	Words for even odds
Standard Mispar Hechrachi	3,780	278.8	1 in 1,936	31
Gadol Mispar Gadol	5,583	188.8	1 in 3,017	37
Katan Mispar Katan	179	5,887.1	1 in 85	6
Ordinal Mispar Siduri	480	2,195.4	1 in 246	9
Atbash	3,872	272.2	1 in 2,190	28
Albam	4,077	258.5	1 in 2,141	31
Milui Mispar HaMilui	7,013	150.3	1 in 4,049	38
Chaser Chaser (defective spelling)	3,758	280.4	1 in 1,916	30
No Aleph Chaser Aleph	3,775	279.2	1 in 1,906	30

“Chance two share a value” is the probability that two phrases picked at random from Tanach have the same total (the sum of each value's squared share). “Words for even odds” is how many random distinct words it takes before two sharing a value becomes more likely than not.

VII. The birthday problem

How quickly do two words share a value?

In a room of 23 people, two probably share a birthday. The same mathematics applies to gematriya values.

Katan: 6 words for even oddsOrdinal: 9 words for even oddsStandard: 31 words for even odds

Words picked31

With 31 random words: Katan 100.0% · Ordinal 99.9% · Standard 48.9%

Like the classic birthday problem (23 people for even odds of a shared birthday): each method's values are drawn with the frequencies they actually have among Tanach's distinct words. Poisson approximation.

VIII. Exploring a list

How many phrases in a list share your number?

Choose a value and a number of phrases to explore, and see how likely it is that at least one of them shares it.

Your number289Phrases you explore300Counting methods allowed1Allow kolel (±1)

Chance that at least one shares your number

10%

On average you'd find 0.1 of them.

Rough model: each candidate phrase is treated as a random draw from Tanach's phrase-value distribution (376 of 1,050,775 phrases equal 289), and each extra method or kolel offset as another independent shot.

IX. Benford's law

Do gematriya values follow Benford's law?

Many natural datasets start with 1 about 30% of the time. Tanach's word values tell a different story.

Tanach (every word occurrence)Benford's law

Benford's law describes data spread across many orders of magnitude, like populations or prices. Word values mostly sit between 30 and 600, so leading 1s are far rarer than the law predicts and 3s, 4s and 5s more common.

X. Divisibility

Verse totals and their remainders

Each of the 23,213 verses has a total. Choose a divisor to see how the remainders are spread, with a statistical test of evenness.

Divide verse totals by7

Divisible by 7: 14.22% of verses (even split: 14.3%) · χ² = 3.5, p ≈ 0.75

Hover or tap a bar for details

10%

15%

20%

Remainder · dashed line: a perfectly even split

χ² goodness-of-fit test against an even split across the 7 remainders (6 degrees of freedom). A large p-value means the remainders are as evenly spread as chance alone would make them.

XI. Notable numbers

Records and curiosities

The most shared values

Values claimed by the most distinct single words.

140123 wordsפְּנֵי · מֵעַל · עֵינֵי · לְעַם
146121 wordsעוֹלָם · פָּנָיו · הַצֹּאן · עֵינָיו
120117 wordsעַמִּי · לְמֶלֶךְ · מוֹעֵד · מַדּוּעַ
136113 wordsמִמֶּנּוּ · קוֹל · וַיַּעַן · חִזְקִיָּהוּ
150110 wordsמֵעִם · מֵעָלָי · עִמָּם · כָּנָף
156109 wordsיוֹסֵף · וַיָּקָם · צִיּוֹן · יָקוּם

Nearly every number has a word

Every value from 3 to 968 is the value of at least one word in Tanach. Up to 1,000, only 9 values have no single word: 1, 2, 969, 979, 983, 987, 989, 993, 999.

The heaviest words

1640to Artaxerxesלְאַרְתַּחְשַׁשְׂתְּא
1616and Artaxerxesוְאַרְתַּחְשַׁשְׂתְּא
1610Artaxerxesאַרְתַּחְשַׁשְׂתָּא

Verse totals

The average verse totals 3,364. The highest is 2 Chronicles 22:11 at 13,639 (37 words); the lowest is Ezra 10:35 at 153. The 23,213 verses take 6,520 different totals, and 21,564 verses share their total with at least one other verse.

Primes

14.5% of distinct words have a prime value, a little below the 18.5% you would expect from numbers of the same size, since so many letter values are even.

Famous verses

The first verse Genesis 1:12,701
= 37 × 73 · the 73th triangular number (1 + 2 + … + 73) · 7 words
Shema Yisrael Deuteronomy 6:41,118
= 2 × 13 × 43 · 6 words
Love your neighbor Leviticus 19:182,717
= 11 × 13 × 19 · 12 words
The Priestly Blessing (first line) Numbers 6:24854
= 2 × 7 × 61 · 3 words
The Lord is my shepherd Psalms 23:1943
= 23 × 41 · 6 words
The first of the Ten Commandments Exodus 20:22,495
= 5 × 499 · 9 words

Method: standard values (mispar hechrachi) unless noted, computed over the written text (ketiv) of the Westminster Leningrad Codex. Phrases are runs of 1–6 consecutive words within a verse, each distinct phrase counted once. Source data and code are linked in the footer.