Actually, I don’t think that anybody has ever counted them.Mathematically: 21,952 roots. Practically, you get 6,332 roots.

There are many Arabic dictionaries. *Hans Wehr**‘**s **A**rabisches Wörterbuch für die Schriftsprache der Gegenwart* (named after a German scholar, published in 1952) is the most complete dictionary of __Standard Arabic__ ever published in the West. It contains **2967** roots (جِذْر) with 3 letters and 362 with 4 letters.

The most famous dictionary of __Classical Arabic__ is *Lisān al-‘Arab* (لِسان الْعَرَب), compiled by Ibn Manzūr (ابْن مَنْظُور) in the early 14^{th} century (711 AH). It contains around 80,000 entries and in total (3 + 4 letters + foreign words) **9273** roots.

Since the Arabic alphabet consists of 28 letters (consonant phonemes) there are **21,952** theoretical combinations (=28^{3}) of roots with __three__ radicals. However, certain combinations are impossible (with few exceptions):

There is

__no__Arabic root which consists of**three identical**consonants.There are

__no__Arabic roots with**identical**consonants in the**first**and**second**position.There are

__no__Arabic roots with identical consonants in the**first**and**third**position.However, there

__are__roots whose**second**and**third**letter are**identical**, for example,*to pass*(م–ر–ر).

Taking into account all possible restrictions, the theoretical number of all possible combinations of roots (morphemes) with three letters is **6332.**

**Remark: What are the most common root letters?** In *Hans Wehr*, the most common root letter is ر (722 times). The ظ is the least common: only 42 times (1.4 %). The ن is the most common first radical (235 times).

I would like to see details of how you arrived at 6332.

If I adjust for the limitations you mention I get:

28 x 27 x 27 = 20,412.

There are 28 possible 1st letters, the second letter cannot be the same, so there are only 27 possible letters. The third letter cannot be the same as the first letter, so there are only 27 possible third letters. The fact that all 3 letters cannot be the same is already included in this calculation, and although interesting, does not affect the number of roots.

That’s a long way from 6332. What other restrictions have you included?

Taking into account the glottal stop (hamza), should it not be said that there are 29 letters in the Arabic alphabet? At the same, alif being only a vowel cannot be part of a radical, so this first comment is uneffective…

Second comment: a theoretical value of 28^3 assumes that we accept combination R1=R2=R3, which I understand is forbidden. I was wondering whether other combinations are forbidden too.

Thank you for your comment. It is only a theoretical number. There are many restrictions as some letters do not like having certain neighbors (for reasons of pronunciation). If you calculate or find a realistic number, please let me know. I would appreciate it.