What's the best way to determine what you can afford to buy?

I feel like those online calculators are too generic and honestly, the amounts they are giving me just don't seem right.

For example, we want to keep our mortgage costs the same. We do have the cheapest mortgage possible on our place here-- so I guess that does factor into things. I guess we'd look for a 30 yr fixed unless there is something else that's a better option. But on our next place we plan to put a lot down-- something like 30% to 40%, but the online calculators tell us we can basically spend the value of our current home which seems crazy to me.

So our mortgage would be a lot less, but our payments seem to be the same.