If you're just starting up the website then the cost to startup the website can be very cheap.
Web hosting $4.00 per month Domain $11.00 per year.
So with those costs the cost to run a website averages $60.00 per year.
If you use an ssl the cost goes up a little but you're likely to spend less than $100.00 per year to run a website in the beginning.
When you're website starts growing and you require a vps or dedicated hosting then your cost will get higher maybe into the thousands per year.
But if you have that amount of website traffic you should be able to more than cover your costs through Adsense or other ad networks.