12:30 – when it’s a.m. and p.m.

Here’s my answer to this interesting question:

First of all, you have to decide whether to use the 24-hour or the 12-hour clock. If you choose the 24-hour clock, 30 minutes after midnight is 00:30, without a.m. or p.m. If you choose the 12-hour clock, 30 minutes after midnight is 12:30 a.m. and 30 minutes after midday is 12:30 p.m.

30 minutes after midnight:

00:30 or 12:30 a.m.

30 minutes after midday:

12:30 or 12:30 p.m.

You might find this site interesting: wwp.greenwichmeantime.com/gmt-converter.htm

By the way, you can write am/pm or a.m./p.m. I prefer a.m./p.m., because I want to avoid confusion with the German word ‘am’. They are also preferred by American style manuals.