I clicked on the site without reading your opening comments. It took me a couple of minutes to understand what the purpose is. I think I would not have given it that much time if it was not a Show HN. But then again its such a specialized tool that if someone finds it they will perhaps know how to use it. I don't know, maybe add a button somewhere for a simple explanation?

Also the title says "What time today?" but actually the default calendar which shows up is the work week. That seems like mixed messages. Here is something I think will be cool, make the "What time ______?" as a drop down. So it goes "what time this week/day/work week?" etc. Some people might find it cheesy though.