There are multiple ways to say “to convert something into something”, but which verb is specifically used when I talk “I need to convert 1 kg into grams” or “Exchange 1000 yen into british pounds”. Basicly what is used for matimatical unit conversions?
The word for unit conversion is 単位変換 that brings up the unit conversion on google.jp . 両替 is the noun for currency exchange. So it may vary on what conversion you’re talking about in the end.
I can’t give you specifics on which is the best as that I haven’t been corrected when I’ve used some of these, but perhaps this corpus could help you narrow your choices?