How to avoid ambiguity when referring to a 24-hour period?

Suppose I want to refer to a 24-hour period (from midnight till midnight). The word "day" can in fact mean "24 hours" (as in here), however it's somewhat ambiguous. I believe that if I say something like "just wait a day", most people will understand it in a common meaning. I could also say "just wait 24 hours", but that sounds a little weird to me, about as much as saying "I want 127.5 grams of cheese, please" in a store.

So how would a native speaker refer to the 24-hour period to avoid ambiguity (and being concise in the same time)? Maybe there is a fancy scientific word for it?

Solution 1:

There's nothing weird about saying 24 hours, but if you want to avoid it you can say until / at / by this time tomorrow.

Solution 2:

First off, make up your mind if you are looking at day or 24 hours — they are not quite the same thing! The first, Nychthemeron, is I feel not very relevant here.

Rather, the OP means a period of 24 hours from a reference point.

Considering this, (and in order not to sound weird), I'd actually just say, "Same time, tomorrow."