Well, to answer that question there are a couple factors that need to be discussed first, because it depends. It depends on the thickness and weight of the rib-eye steak, temperature of the fire, and how you like your steak cooked. Lets first go over the "doneness" of a steak.

There are two standards that you can base your opinion off of. There is a Chef Standard and a USDA Standard. I personally like the Chef's Standards, you will probably have more chances of food borne illnesses, but that is a risk I am willing to take.

So here is the Chef Standards:

Doneness ------------------Temp.

Rare ----------------------120 - 125 F.

Medium Rare -----------125 - 135 F.

Medium ------------------135 - 145 F.

Medium Well ------------145 - 155 F.

Well -----------------------155 F. +

Here are the USDA Standards:

Doneness ------------------Temp.

Rare --------------------------n/a

Medium Rare --------------145 F.

Medium ---------------------160 F.

Medium Well ----------------n/a

Well --------------------------170 F.

I really like my steak at the Chef Standard Medium Rare. The USDA recommends cooking red meat to 145 degrees, if you are working with ground beef, then they recommend 160 degrees.  When you are cooking your Rib-eye Steak, make sure you take into account for carryover heat.  Steak usually cooks 10 degrees more even after you take it off of the grill.  There are a few ways you can determine the doneness of your steak.  You can use a thermometer and stick it into the thickest part of the meat, personally I do not do this.  You can peek at your doneness, just flip the steak and cut a little into it, to check it out.  Make sure you do not cut the good looking (presentation) side of the steak.  Or you can do the touch test, press your first finger and thumb together, that firmness is like a rare steak.  If you press your middle finger and thumb together, that is more like the doneness of a medium rare steak.  The steak will get more firm the longer you cook it.

I usually only cook my 1 1/4 inch steaks for around 10 minutes, for medium rareness.  I do not like using a thermometer or a knife to cut into my rib-eye steaks, because I feel that too many juices are lost in that process.

So now that you know the temps, it is time to discuss how much time you should have your steak on a grill. Thickness is what determines how long you should cook your steak.  All the following times are based off of a medium rare steak. Always sear your steaks first in direct heat.

DH= direct heat; IDH = In-direct heat

Thickness-------------------------Grill Time

3/4 inch ------------------------ 4 to 6 min. (DH)

1 inch -------------------------- 5 to 8 min. (DH for 4-6 minutes, IDH for 1-2 min.)

1 1/4 inch --------------------- 8 to 10 min. (DH for 6 minutes, IDH for  2-4 min.)

1 1/2 inch --------------------- 10 to 14 min. (DH for 6-8 minutes, IDH for 4-6 min.)

2 inch -------------------------- 14 to 18 min. (DH for 6-8 minutes, IDH for 8 to 10 min.)

Always make sure that your rib-eye steak is at room temperature before you put it on the grill to endure even cooking.