Starting from nothing, without building a whole system
Almost every household starts with a spreadsheet, and there is nothing wrong with that. A spreadsheet is free, it does exactly what you tell it, and for the first two months it is genuinely the fastest way to see what is going on.
What tends to happen next is not that it stops working. It is that one person becomes the person who maintains it β and the other one stops looking, because it is easier to ask than to open. That is the failure worth planning around, and it is a people problem rather than a tooling one.
These posts cover both routes honestly: how to build the spreadsheet properly if that is what you want, including the formula for splitting by income, and how to tell when the maintenance has quietly become one person's job.
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Or see it on your own numbers
Pairly holds the rent, the bills and the subscriptions for two people, splits them the way you agreed, and shows the same picture to both of you. No bank connection, no card to start.