Do you need a caliper? I'd say no straight-off. Comparative measurements will often get you far enough. Like any tool, you can always find other solutions.
There are two types of measurement and which one you need depends on your personality, what you're trying to achieve, and how your mind learns.
- ABSOLUTE which results in numbers. This is rulers and calipers and tapes and protractors.
- RELATIVE or Comparative, where you're checking two things against each other. Gauges and existing parts would go here.
However as your tool collection grows over your life, each subsequent tool generally does a more specialised task and has a narrower range of uses. We start with a hammer and two screwdrivers and a knife, and that set can probably do 30% of all tasks you face.
Comparative measurements (ie holding a piece of wood up to another) can do a lot, but a ruler should be an early purchase.
Calipers can be had cheaply, which is a great thing for expanding tool collections. Try ebay and garage sales and so on. You do not need new tools. If one comes up at a good price, snag it.
For measuring seatpost holes in frames I have a go/no-go gauge which measures standard sizes.
But once printed I measured its accuracy using both a set of calipers and a micrometer and I test-fitted it to a couple of frames where I know the seatpost size already.
This gauge is no-use for measuring seatposts themselves though, and also can't do handlebars.
I stumbled across this today - the documentation archive at wolf tooth has some phenomenally-useful PDFs at https://www.wolftoothcomponents.com/pages/tech-docs including
This seatpost specific page-click for full sized PDF
Print that at 100% scaling, check with a ruler that the dimensions are right, and then cut out the ribbon. Figure where it overlaps and you have an answer. Note not all the sizes are listed.
To measure seat tubes, put the printout over the top of the hole in the frame and press down with a thumb. You should be able to get a visible crease matching one of the common sizes shown.
Personally, yeah I own multiple calipers and micrometers, and I use them at least weekly. As funds permit, more-specialised tools become achievable.