Abjad numerals

The Abjad numerals, also called Hisab al-Jummal, are a decimal alphabetic [numeral system]/alphanumeric code, in which the 28 letters of the Arabic alphabet are assigned numerical values. They have been used in the Arabic-speaking world since before the eighth century when positional Arabic numerals were adopted. In modern Arabic, the word means 'alphabet' in general.
In the Abjad system, the first letter of the Arabic alphabet, ʾalif, is used to represent 1; the second letter, bāʾ, 2, up to 9. Letters then represent the first nine intervals of 10s and those of the 100s: yāʾ for 10, kāf for 20, qāf for 100, ending with 1000.
The word ʾabjad itself derives from the first four letters of the Semitic alphabet, including the Aramaic alphabet, Hebrew alphabet, Phoenician alphabet, and other scripts for Semitic languages. These alphabets contained only 22 letters, stopping at taw, numerically equivalent to 400. The Arabic Abjad system continues at this point with letters not found in other alphabets: thāʾ = 500, khāʾ = 600, dhāl = 700, etc. Abjad numerals in Arabic are similar to the alphanumeric codes of Hebrew gematria and Greek isopsephy.

Abjad order

The Abjad order of the Arabic alphabet has two slightly different variants. The Arabic abjad order is not a simple historical continuation of the earlier north Semitic alphabetic order, since it has a position corresponding to the Aramaic letter samekh / semkat ס, yet no letter of the Arabic alphabet historically derives from that letter.
In the most common Mashriqi abjad sequence, loss of ' was compensated for by the split of ' ש into two independent Arabic letters, ش and ﺱ, which moved up to take the place of '.
The Mashriqi abjad sequence, read from right to left, is:
غ ظ ض ذ خ ث ت ش ر ق ص ف ع س ن م ل ك ي ط ح ز و ه د ج ب ا
ʿ / ʾ

This is commonly vocalized as follows:
Another vocalization is:
In the Maghrebian abjad sequence, loss of ' was compensated for by the split of ' צ into two independent Arabic letters, ض and ص, which moved up to take the place of '.
The Maghrebian abjad sequence, read from right to left, is:

which can be vocalized as:
Another vocalization is:
;Competing order
Modern dictionaries and other reference books use the newer ' / ' and more common order, which partially groups letters together by similarity of shape, and is never used as numerals.
The common ' sequence, read from right to left, is:
ي و ه ن م ل ك ق ف غ ع ظ ط ض ص ش س ز ر ذ د خ ح ج ث ت ب ا
/ ʿ ʾ

Persian uses a slightly different order, in which و comes before ه instead of after it.
In the Maghrebian ' / order, the sequence is:

In Abu Muhammad al-Hasan al-Hamdani's encyclopædia Kitāb al-Iklīl min akhbār al-Yaman wa-ansāb Ḥimyar, the letter sequence is:

Uses of the Abjad system

Before the Hindu–Arabic numeral system, the abjad as numbers were used for all mathematical purposes. In modern Arabic, they are primarily used for numbering outlines, items in lists, and points of information. Equivalent to English, "A.", "B.", and "C.", in Arabic, thus "أ", then "ب", then "ج", not the first three letters of the modern ' order.
Like Roman numerals, there is no representation of zero and there are no fractions. By convention, the numbers are written largest first. Reversing the order indicates multiplication, so for example is 2000 while is 1002.
The abjad numbers are also used to assign numerical values to Arabic words for purposes of numerology. The common Islamic phrase بسم الله الرحمن الرحيم ' has a numeric value of 786. The name Allāh الله by itself has the value 66.

Letter values

In common abjad order:
Notice that some letters appear in their initial form and others in a riqaa-like form, with the alif having a different shape.

In Maghrebian Abjad order:

For four Persian letters these values are used:

Value	Letter	Name	Trans- literation	Has numerical value of
2	2=پ			ب
3	2=چـ		or	جـ
7	2=ژ		or	ز
20	گ			ک

Similar systems

The Abjad numerals are equivalent to the earlier Hebrew numerals up to 400. The Hebrew numeral system is known as Gematria and is used in Kabbalistic texts and numerology. Like the Abjad order, it is used in modern times for numbering outlines and points of information, including the first six days of the week. The Greek numerals differ in a number of ways from the Abjad ones. The Greek language system of letters-as-numbers is called isopsephy. In modern times the old 27-letter alphabet of this system also continues to be used for numbering lists.