In most cases, there is no set distance between the barrels. This is because the size of the barrel pattern depends on the size of the arena they are being run in. A large arena will have a large pattern. Likewise, a small arena will have a smaller pattern.
However, there is a standard barrel racing pattern designated by the WPRA. It is a fairly large pattern so it usually isn't found at more barrel races (or even rodeos), but this is considered "standard".
90 feet between barrel 1 and barrel 2
105 feet between barrel 3 and barrel 1 or 2
60 feet from barrel 1 or 2 to the start line
At least 20 feet from any barrel to the fence
So just set up your barrel pattern based on what you have room for in your practice area. The most important thing is making sure you have plenty of room for the start line, and plenty of room between your barrels and the fence. This is just for safety purposes so have adequate room.