Embarrassing Question: What size of case will actually hold these bulky components?

Here's the build, lacking only a Case:


My main concern centers around the Hyper 212 EVO cpu cooler and the HIS IceQ Radeon 7870. They seem rather bulky and I'm concerned about what measurements I actually need to get a Case that will hold them.

This is my first build so I'm uncertain what sorts of clearances/measurements one needs to be concerned with when trying to stick (seemingly large) objects on your motherboard. Basically I am imaging this scenario in my head where I purchase everything, snap that Hyper 212 EVO onto the CPU and then find out the hard way that they aren't going to fit in the tower.

Here are the dimensions for the Hyper 212 EVO:

source: http://www.coolermaster-usa.com/product.php?product_id=3053 (has pictures/diagrams)

So I guess it sticks 6.3 inches up off the motherboard. So, if stacked on top of my Phenom 965 in my ASRock 970 Extreme3 mobo, how wide of a Case will I actually need to have sufficient clearance to actually fit this thing in there?

Further, what sort of clearances (if any) do I need to stress about in regards to fitting in my HIS IceQ Radeon 7870, which seems to have a sort of bulbous fan assembly hanging off the end of it?

Any advice on what sort of Case dimensions I need to hunt for would be extremely appreciated.

Pretty much any mainstream mid-tower case (and bigger) would house your setup and since you've picked an ATX board, the cases that could be giving you troubles are a non-issue

um i have that GPU & CPU cooler they both fit in this case http://www.newegg.com/Product/Product.aspx?Item=N82E16811147160&Tpk=rosewill%20redbone%20u3

i recommend a  case with good cable routing like http://www.newegg.com/Product/Product.aspx?Item=N82E16811352020 any 1 will do 

I just picked up an Antec P280 XL-ATX case on sale for $70, right now it's about $90-100 http://www.ncix.ca/products/?sku=65170&vpn=P280&manufacture=Antec&promoid=1310

I have a Maximus V Formula (E-ATX board), Hyper 212 heatsink, 660 ti, there is tons of room for whatever you could ever want to put into a case.