Today means "the current day", so if you're asking what day of the week it is, it can only be in present tense, since it's still that day for the whole 24 hours. In other contexts, it's okay to say, for example, "Today has been a nice day" nearer the end of the day, when the events that made it a nice day are finished (or at least, nearly so).
tenses - Today Was vs Today Is - English Language & Usage Stack Exchange
Neither are clauses, but "today in the afternoon" is grammatical (adverbial phrase of time), while "today afternoon" is not. I would also suggest "this afternoon" as a more succinct and idiomatic alternative to "today in the afternoon".
word choice - 'Today afternoon' vs 'Today in the afternoon'? - English ...
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Two other options (in addition to "as from today," "from today," and "effective today") are "beginning today" and "as of today." These may be more U.S.-idiomatic forms than British-idiomatic forms (the two "from" options have a British English sound to me, although "effective today" does not); but all five options are grammatically faultless, I believe.
In my town, people with PhD's in education use the terms, "on today" and "on tomorrow." I have never heard this usage before. Every time I hear them say it, I wonder if it is correct to use the wor...