Angle Time

Times where the hour and minute hands form an angle of ° are:

has an angle of .

Other times with that angle are:

What

I’ve been known to answer really stupid questions with math. So in that spirit, what is the angle between the hour and minute hands of a clock?

I worked it out on a whiteboard in 2022, but basically you get the angle of each hand relative to 12 o’clock, subtract them from each other, and set that equal to the angle you want to find. From there it’s just algebra.

A whiteboarding showing math. The hour hand’s angle is a funciton of total time in minutes; the minute hand’s angle is a function of the time in minutes modulo 60.

My purpose here isn’t to go through the math, mainly because I’m lazy, have a baby, and just want to get this thing out there. But there are plenty of walk-throughs elsewhere on this World Wide Web. Sorry!

Why??

Some time in 2022 I was staring a clock and a random question popped into my head: what are all the times where the hands are at 90° to each other? I did some math, came up with the list, posted it on Mastodon, and forgot about it.

Fast forward several years. I’m walking around the living room with a crying baby in the middle of the night looking at the clock. “I should make a little web app for this,” my brain said. Well, now that the baby is sleeping through the night, here’s a web app.

In the spirit of less thinkering, more tinkering, I decided to stop worrying so much about code quality and consistency. This is a sketch; I did it for fun.

How

I wrote this all by hand like some kind of Luddite (complimentary). No LLMs, zero dependencies, and doesn’t need a build tool. Just plain old HTML, CSS, and JavaScript like we used to do in the ’90s.

Who

I’m Noah Liebman. You can find me on the socials (by which I mean just Mastodon).