How formal is the Spanish word cuán? When is it appropriate to use, and when does it seem out of place? How are sentences using cuán normally expressed in informal speech?
In Spain, cuán is rarely used in normal, informal speech, though I think it would generally be understood.
To express the same, you can use qué, or lo ... que:
In questions, in Spain, it is often replaced by cómo de:
But this usage is probably incorrect.
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Although this isn't really what you were asking about, maybe it's worth mentioning that it would be somewhat out of place to use cuán when you're in Mexico, where it is far more common to say qué tan. For example,
In questions, "cuán" is equivalent to "qué tan":
In exclamations, "cuán" is equivalent to "qué":
"Cómo de" is a regionalism. I think outside of Spain it sounds very bad. In general, if you can use "qué", this will be the preferred form in the informal and formal speech. "Cuán" is more common in writing, especially in literature. I think using "cuán" is not formal; it's just not usual. My hypothesis is educated people use "cuán" more frequently, but it isn't related to a formality issue.