If I understand your question correctly, that characteristic (range of vocabulary) is often implicitly calculated when tagging a text corpus. So some tools/services working with text corpora may provide such information.
The Ukrainian language corpus of Laboratory of Computer Linguistics of Institute of Philology of Taras Shevchenko National University of Kyiv has the “Статистика текстів” (statistic of texts) subsection. It allows to see lexeme statistic of different works by expanding a category (▹) at the left, choosing a work and clicking “Частотний словник лексем” (frequency dictionary of lexemes):
I suppose that “всього лексем” (number of lexemes) may be a value you need.
Still, it can only show you statistics of already pre-analyzed texts, without possibility to "feed" the tool with an arbitrary text for getting its (text) statistics.
Some other services for Ukrainian corpora are listed on the online sources meta page. Still, I don't know whether they can work with an arbitrary text and whether they provide such information at all.
There are tools that allow you to tag an arbitrary text corpus yourself. For example, one of them is LanguageTool (e.g. tagging a corpus using LanguageTool; for example, Leipzig Corpora Collection uses LanguageTool as part-of-speech tagger). Still, doing that maybe uneasy for unexperienced user and, besides this, the value you need may not come immediately from manipulations with LanguageTool themselves.
P.S.: However, I may misunderstand you; please notify me in that case.