What's the formula?
It used to be that you could find your normal ELO by looking in the Logs folder of League of Legends (along with the ELOs of everyone you played with in the last game) but sadly Riot decided that this fostered too much competition in the casual gaming mode and removed it.
Can you still figure out your normal game ELO? While there are a couple calculators such as http://lolcave.com/ec/, sadly enough they're not terribly accurate since it's only based off of your win/loss ratios.
Generally your normal game ELO will be higher than your ranked game elos by a large amount since that's the way it works, but Riot has also publicly stated that there are many top level ranked players whose normal game ELO is ridiculously high with win ratios of 85% or more.
On the other hand, for us normal people, we'll generally reach a point where we win approximately 50% of the time in normals and lose 50% of the time in normals. It's not because we all got worse and worse, but just because we've reached our proper ELO.
Riot's official page: http://na.leagueoflegends.com/learn/gameplay/matchmaking
TLDR; You can't find your normal game ELO anymore, but http://lolcave.com/ec/ made a calculator they use to bring in web traffic.