I have a raspberry pi that is running a node server (that receives maybe 10 requests a day) that is running constantly. I am wondering if anyone know about how much bandwidth this will take up or how I could go about calculating the amount of bandwidth it is using.
That's kind of like asking, "How much gas will this car use?". It depends entirely what you do with it and how you use it. Sitting in the garage, it doesn't use any gas. Racing on the autobahn at 200km/hr, it uses a lot.
A server all by itself barely uses any bandwidth. The Raspberry Pi has a deamon that checks with an external ntp server to keep the local clock accurately synced with the outside world, but other than that, it likely uses no bandwidth by itself.
So, any other bandwidth comes entirely from the requests that are sent to it and the responses that you send back. If you measure those and then multiply by how many times per day you make those requests, you will pretty much have the bandwidth consumed. If there are just regular http requests returning a small amount of data, then the total bandwidth is probably less than browsing a few web pages with big images on them or certainly less than watching a few YouTube videos.
You should also be aware that if your server is discoverable on the internet, you may also get some requests from unsolicited sources, either search crawlers or bots looking to do some mischief.
If you want to just measure what your Raspberry Pi is using, there are a wide range of tools for doing that on Linux and you'd have to investigate which ones are already available for the Pi or which you could recompile to work on the Pi's ARM chip.