I need to replace some bass strings. I keep hearing about calculating tensions. What exactly is that? Besides the obvious supplies and tools, what other instruments or tools do I need?

This is too big a subject for a forum like this. You need to work with someone knowledgeable.

If it's just a few bass strings you can send the old ones to the bass string company and they'll send you back new ones that are custom made to the same specifications. Then you don't need to worry about tension changes. You only need to worry about calculating tensions if you're thinking about redesigning the scale, which I don't think is typically done except if you're re-stringing the whole piano. Apart from that the topic is out of my depth.

If it is an emergency fix,one can use a universal temporarily but if there are a few, you change them all in that they're all history. You make a pattern and get the complete set. Exception wise you might change a few brand new bass strings if they are dead or defective or ? from the get go but even still a new double won't match up with the previous new paired string.

Just don't bin the old ones! Label them up note and number for a pattern made replacement