I'm not sure what you are asking when you say days of years. Re: calendars, there is not a calculation aspect to it that I'm aware of. Regarding
days of years, are you looking for the number of days since Jan 1, on that year, e.g., Dec 31 would generally equal 365?
Regarding days of the week, I'm aware of a "stupid human trick" technique for quickly figuring out what day of the week a given year-month-day date would fall on. I don't have to do this often enough to keep the technique in my memory, but I could probably dig it up if that would help.
Other than that, I have an Excel template that's really simple. It has 13 sheets, one for each month and a settings page. In the first page, you would plug in the year and what day of week to start the week on, e.g., sunday as opposed to monday. Entering this updates the 12 monthly sheets to make a nice wall-calendar planner type view that can be printed off. I use this to track things that I don't do too often, e.g., the last time I had a haircut or cleaned the bathroom. J/K I clean my bathroom twice weekly so that doesn't need to be tracked.

The other thing I use it for is to keep track of what meds need to be refilled when. I had them all on the same day at one time, but then they got all out of sync again. First world problem, but I'm OCD so that matters to me, lol.
Not sure if that's your use case but I could share that, or probably port it to Google sheets. But you said you don't want a calculator, which this arguably is. That is why I stated first that I'm not clear on the goal here. I'm guessing that after writing all this, you've already solved it, though. I'm probably going to port the Excel stuff to Google sheets just for giggles anyway.