Question 1: How many words are minimal for a naturalistic conlang? (1000, 1500, 3000 or even more)
Question 2: How many words do the conlangers usually create?
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Let's start with some numbers: Esperanto started with 900 radicals (which is different from the number of words that can be formed from that radicals) while Interlingua debuted with a dictionary containing the impressive number of 27000 words. The last number is surely very much on the upper end for a conlang creation, one tenth of it is more realistic.
So a realistic starting number for a not too schematic language (e.g., avoiding something like the Esperanto prefix mal- as an obligatory tool to construct an antonym) would lie in the region of 2000 words including some derivational morphology.
I don't have statistics on how many words conlangers create on average, but there are certainly some conlang enthusiasts out there who just love to create words and to give them etymologies (based on the real world or fictional ones). Those enthusiasts may create very rich constructed vocabularies.
The answer to both of these questions lies somewhere between "it depends" and "let's speculate a little".
The act of inventing a naturalistic language does not necessarily mean that you must also create a naturalistically large lexicon. After all, it's the grammar, the syntax, the usability in a wide variety of normal contexts that determines naturalism. A natural language might have anywhere between 15000 and 1,000,000 words. And as you can see from the several English entries, there's not even a consensus as to how many words there are in a language. The number of words you should create is entirely up to you. A more interesting question, interesting in the broad sense of course!, is how many words is enough words to create? This is not only more interesting to consider, but also harder to answer because there is no pat response and any answer given will be purely opinion.
I'd argue that 2000 is a bare bones lower estimation, given that this is the lexicon size for Basic English. But B.E. isn't exactly "naturalistic", so that figure is undoubtedly low. Somewhere between 3000 and 6000 gives you a little more than dry bones to gnaw on!, but still hardly approaches the naturalism of a natural language, to say nothing of the works of the more gung ho kind of lexicophilic glossopoets!
As for the second question, we do have some recent figures. The results of a recent survey of language inventors determined a spread of approximately 500 (+/-) to >5,000 over 246 respondents. Of note are the lowest and highest categories, with about 70% of respondents falling into the <500 & >5000 categories. The remaining 30% fall between 500 and 5000 words.
Information on a minimum useful vocabulary size appears within this answer to a question on Worldbuilding SE.
I don't have a reference but some philologists and linguists have speculated that you could survive (explain who you are, ask for employment and food, etc.) in a foreign land with as few as 500 words. Henry C. Fenn, author of several language texts, felt that a vocabulary of 5000 words was sufficient to support learning new words by context, e.g. by conversing with natives and reading newspapers. In my own experience as a linguist and translator I found 5000 generic words plus about 2000 topical words (those popular for only a few years) sufficient for keeping up with current events. This gives you some idea of the vocabulary size you should be considering.
It depends on the type of conlang you are creating.
I have read, for example, that certain highly polysynthetic languages such as those Eskimo-Aleut, Salishan, and Wakashan stock tend to have only a couple to a few thousand roots, while analytic and fusional languages such as the Austroasiatic Aslian languages, such as Semai and Jahut, have thousands of roots in a category completely lacking in SAE languages, namely "expressives" or ideophones.
Now, obviously roots are not identical to words, but I recall reading in a grammar Inuktitut that there are hundreds of "postbases"—suffixes with often highly salient meaning such as "to help" or "to hunt"—, while likewise the Northwest Coast Wakashan and Salishan languages have hundreds lexical affixes with similarly or even more precise and concrete meanings, such as body parts, common spatial relations, and the like. If I am correct, however, though extremely morphologically complicated, remarkably regular rules apply to these affixes; if your conlang was to adopt say a hundred lexical affixes, it could cut down on the need for separate lexical stems quite significantly.
On the other hand, if you opt for sound symbolism and a fusional and/or isolating route, you probably need at least 3,500-8,000 lexical items; I say 3,500-8,000 because that is the range I regularly run across as between the number of Chinese Characters in common usage and the number of characters the average, college-educated Chinese adult knows. I am aware that Chinese Characters and words or even morphemes do not have a 1-to-1 mapping, but nonetheless I see that as a reasonable range for an isolating language.
This I cannot answer very well, but I can say that I would assume it is significantly lower than a thousand, because so many conlangs are never fully able to be usable or are just naming languages. But for usable conlangs, I would guess around 3,000 or a little more, excluding naming languages and highly developed conlangs.
As the other comments have said, this number can vary drastically depending on how in-depth you want to go. To get literally every concept that exists in say, English, you'd need tens of thousands. However, as Zipfian laws have shown, 20% of words receive 80% of the use, and the most common words are used exponentially more than the less common. I tend to strive for 1000 words as a start; the top 207 of which can essentially be a Swadesh list. When going for larger sums of words you can use lexicon generators like Awkwords. This could be used to create phonologies, or even morphologies if you use the formatting correctly.
I think, it depends on
First, language type plays an important role in determining the number of words in that language. i.e., Let us take English as an example. English mostly do not create words from the root, rather it kind of borrows from other languages. Languages like Chinese and Tamil do not borrow words, it creates new words from the existing words. So, if a conlang you are going to create is like English, it might need more words.
Secondly, where and how this conlang is going to be used plays an major role too. For example, take Dovah language, a conlang. This language does not need words related to technology and science as this language is not going to be used in modern timeline, but an ancient timeline. So if the conlang is going to be made for a specific purpose, it is not necessary to add unrelated words.
So, number of words could be even 340 words(Taki Taki (also called Sranan), 340 words. Taki Taki is an English-based Creole spoken by 120,000 in the South American country of Suriname.) to 250,000 words(English) and it has to be noted that Taki Taki is not a full-fledged language and English is one of the most spoken language.
And as a personal advice, before creating a conlang, please refer to the grammar and phonology of other language families other than your mother tongue language family, it would help you to make a unique conlang easily.
The number of words in a conlang is up to you- you can start small, then add on layers and layers of vocabulary.
For example- Toki Pona started with just 120 words, but added on a few extra words.
Remember that you can never stop adding words. Whenever you find that you need to add words, just add them.