Depends heavily on the size of said stallion (mini, or full-size etc), as well as your region and how you plan to do this. Also what you want to calculate into this (like the car able to pull a horse trailer, is that a horse- or a your-life expense?).
But if you are in the US near a middle-sized city, and it's a middle-sized stallion, you keep it at a professional facility, expect 500 to 800 USD/month absolutely all in all. But there is no upper limit, really. Could as well be 1500 USD. Insurance is gonna be high for stallions, and general breakage of things should be double to triple of what my mare breaks.
Of course you can keep that guy in your backyard, but then you need two horses because you can't keep a horse alone. Except this is a stallion, then again....
Coarsely, you can approach this another way: Do you life on your own? Just double the money you spend on your life at the moment. That's probably at least what you will need (this way we integrate the cost of everything at your place, clever, eh...). If you life with a spouse or children, only deduct what those eat (and similar) from the total household expenses, then use that as the base for doubling.
There are example budgets what horses cost on google, just go through these and construct a theoretical way you wanna do this, than add up the single items from those example lists to estimate where you will end up. Cross-check in the end that you have enough reserve in addition and that your constructed way of life is animal-friendly for the animal, too.
Also; If this is your first horse, rather don't get a stallion. Like - seriously. If they notice that you only wear the drill-instructor hat but nothing else is behind this, then you are fucked. Can you ride and/or do you have horsecare/horsemanship knowledge? If not, then rather don't get a horse. Rather first take riding lessons, take classes in horsekeeping, maybe start easy with a riding-share and after one or two years of building up to it, buy your own horse. Cause if you don't know what you are doing, you really can screw up badly here.