Is there an unspoken rule against waiting up to one week to call someone whose number you've taken?

I think about one week is max if you are actually interested in the person and want to plan something with them. If you wait longer than that after striking up an acquaintance, they might just think you are looking for a booty call or something. That’s how it would seem to me at least.

I think it depends on the circumstances and the reason for the follow-up call. Are we talking about a potential romantic relationship and calling to set up a date? I think it’s polite to call or send a quick text the next day just to say thank-you for the other person spending time with you (and maybe remind them who you are if they were drunk!). But I would think it’s too soon to try setting up another date that quickly, and I would wait a few more days.

If you meet someone and take their number and then don’t call for a week or longer, they may forget who you were. Then you’d be in the embarassing situation of having to remind them and describe the circumstances (“Remember? We met on the bus going to work last Wednesday? I was reading the book you said you were interested in? I had brown hair? You told me you were excited about vacation and I told you I just had vacationn? Remember?”)

relevant

If I give my number I would expect some sort of contact within a day, 2 max. If someone is truly interested then they would txt the next day to show seriousness.
Waiting for specified amount of time as to not to look “too eager” is just gameplay.

Why wait? If you were interested enough to ask for a number, call the person when you want to talk to them. If you play these dating games, you might lose someone that could have been very special to you. If someone waited that long to call me, I would assume they didn’t think enough of me to make time for me, so why should I make time for them?

It’s all circumstantial.

If you met her on the bus on the way to work, call that evening. You need to call her before you’d see her on the way to work the next day.

If you met on the way home from work, call the next day, no earlier than 10 a.m., no later than 4. You need to call her before you might run into her on the way home.

If you met her on a Friday night, call Sunday afternoon. You can’t give her the impression she’d be home on a Saturday. Call after she’d be home after Sunday brunch.

If you met her on a Saturday, call her Sunday night, or, better, Monday early evening.

To summarize: Call before you might run into her again. And treat her as if she has an active, popular, social life.

If you want to meet a person again, call them. Don’t buy into “rules” and game-playing.

Screw the rules, screw the dating advice and dating ‘experts’. If you can’t develope a comfort zone with a person you’ve met, or at least enough to make this decision on your own without resorting to the advice of others, then why bother with them at all then?

In some circumstances though a week might be pushing it, unless you’ve brought up the potential delay to the other person, and have given them a viable reason for this. Outside of basic common sense I say just do your own thing.

As a practical matter, unless you had a very memorable meeting, if you want more than a few days after getting a number, the person will forget you. There’s no rule against it, though. At least, not in any rule book I know of.