The Hebrew Numbering System

Contents:

Introduction

The Hebrew Alphabet

The Hebrew alphabet has 22 characters, as shown in the following table. Each letter is considered to have a numerical value which is used in writing numbers and for numerological interpretations of words.

Sequence order Numerical value Character Unicode code point Unicode character name
1 1 U05D0 HEBREW LETTER ALEF
2 2 U05D1 HEBREW LETTER BET
3 3 U05D2 HEBREW LETTER GIMEL
4 4 U05D3 HEBREW LETTER DALET
5 5 U05D4 HEBREW LETTER HE
6 6 U05D5 HEBREW LETTER VAV
7 7 U05D6 HEBREW LETTER ZAYIN
8 8 U05D7 HEBREW LETTER HET
9 9 U05D8 HEBREW LETTER TET
10 10 U05D9 HEBREW LETTER YOD
11 20 U05DB HEBREW LETTER KAF
12 30 U05DC HEBREW LETTER LAMED
13 40 U05DE HEBREW LETTER MEM
14 50 U05E0 HEBREW LETTER NUN
15 60 U05E1 HEBREW LETTER SAMEKH
16 70 U05E2 HEBREW LETTER AYIN
17 80 U05E4 HEBREW LETTER PE
18 90 U05E6 HEBREW LETTER TSADI
19 100 U05E7 HEBREW LETTER QOF
20 200 U05E8 HEBREW LETTER RESH
21 300 U05E9 HEBREW LETTER SHIN
22 400 U05EA HEBREW LETTER TAV

Five letters have alternative glyphs when they occur at the end of words. These are encoded in Unicode as separate code points before the respective base characters, as follows:

Numerical value Character Unicode code point Unicode character name
500 U05DA HEBREW LETTER FINAL KAF
600 U05DD HEBREW LETTER FINAL MEM
700 U05DF HEBREW LETTER FINAL NUN
800 U05E3 HEBREW LETTER FINAL PE
900 U05E5 HEBREW LETTER FINAL TSADI

As the table shows, the final letters are sometimes assigned numerical values of their own which can be used in numerology, but they are rarely if ever used to express numbers so they will not concern us here.

There are also two punctuation marks which we will be referring to:

Character Unicode code point Unicode character name
U05F3 HEBREW PUNCTUATION GERESH
U05F4 HEBREW PUNCTUATION GERSHAYIM

These punctuation marks may not be available in all fonts (and legacy encodings), so an implementation should be prepared to degrade gracefully. U0027 APOSTROPHE for GERESH and U0022 QUOTATION MARK for GERSHAYIM are acceptable fallbacks.

Numbers in Hebrew

Classical Hebrew has no numerals. The letters of the alphabet are used to express numbers and to index lists of items. For indexing there are two possible systems, the alphabetical system and the numerical system. To express numbers, only the numerical system is relevant. Both systems are written from right to left, like other Hebrew text.

Writing conventions

This section applies to both systems, but I use the term number for the sake of simplicity.

When numbers appear in isolation, e.g. as page numbers or as list indexes, they should be written with the letters alone. If they appear embedded in other text, punctuation marks are added to clarify that they are numbers and not words. The most common convention is as follows:

If a number is written as a single character, add GERESH after this character:

(Day 1, i.e. Sunday)

If a number is written as more than one character, insert GERSHAYIM before the last character:

(22 letters)

" (Page 176)

Speech conventions

The expression of numerals in speech is rather inconsistent. Sometimes they are spelt out letter by letter, sometimes pronounced as if they were words, and sometimes as the number they represent.

Lamed Vav Tzaddikim (36 righteous ones)

Tu Bishvat (The date 15th of Shevat)

Arba amot (four cubits)

A text-to-speech implementation should use the first possibility and spell numbers out letter-by-letter. This may not always be the most natural option to a native speaker, but it will never sound as wrong as the other options will if misplaced.

The alphabetical system

This simply uses the 22 letters of the alphabet in sequence:

This can be extended to arbitrary length by chaining:

The numerical system

Basic rules

The basis of the numerical system is quite simple, at least for numbers less than 1,000. Numbers are expressed using the numerical values in the table, written from greatest to least. For numbers greater than 499, the letter TAV is repeated as necessary.

1
2
3
9
10
11
19
20
21
99
100
101
499
500
501
997
998
999

Exceptions: substitution

If the last two digits of a number are 15 or 16, they should be expressed not as YUD HE (10+5) and YUD VAV (10+6), but as TET VAV (9+6) and TET ZAYIN (9+7). This is done to avoid a close resemblance to the Tetragrammaton (four-letter name of God) YUD HE VAV HE. Although this convention is originally derived from religious practice, it is universally used even in completely secular contexts.

Exceptions: reordering

The numerical value of each letter is fixed and not determined by position, so reordering a number will not change its value. This may be done when a number spells out a word with negative connotations (e.g. 298: RESH TSADI HET is the Hebrew for murder so it is sometimes written as RESH HET TSADI), or when the reordered form has especially positive connotations (e.g 18: YUD HET is often written as HET YUD, the Hebrew for alive). Unlike the previous exception, using the regular form in these cases is not considered an error.

Larger numbers

To extend the numerical system to numbers above 1,000, the same numerical values are used multiplied by 1,000, 1,000,000 etc.

5,763

‎1,234,567

Or with the GERESH and GERSHAYIM where appropriate:

The year 5,763

1,234,567 fish

Because there is no symbol for zero, this will cause ambiguity in some cases.

Is this 3? 3,000? 3,000,000?

Possible solutions to this problem:

Adding the word for thousands. This will need special handling for 1,000 and 2,000 because of grammatical considerations.

1000
2000 or
3000
4000
1000000 or
2000000 or
3000000 or
3000000123 " or "

Many reference books (e.g. Even Shoshan's Hebrew Dictionary and "A Universal History of Numbers" by Georges Ifrah) prescribe two dots above the letters to represent thousands, but I have never seen this usage in print and I doubt if it would be widely understood unless the context made it very clear.

It could also cause problems for implementation. I'm not sure if it's a limitation in fonts or a bug in browsers, but the character I have tried to use for this in the follwing examples, U0308 COMBINING DIAERESIS, doesn't combine well with right-to-left characters, so I have had to use <bdo dir="ltr"> to make them align correctly.

1000̈
2000̈
3000̈

This convention suggests a possible extension to three dots over the letters to represent millions, etc., which is worth considering, though all the previous caveats would apply with no less force.

At some order of magnitude this numbering system just becomes too clumsy, and one should be prepared to bail out to another system when the numbers get too large.

References

TODO: Add references

Updated October 2005, with thanks to Jacob Wexler