What is the minimum size that my tortoise's enclosure has to be? I have a 4 year old Hermann tortoise whose shell measures about 6 inches long and 5 inches wide. ( Not including the head or tail)
The bigger the better. I keep my tortoise indoors, so I got a 48" by 18" cage (75 gallons), because I want a cage that I can keep even when she grows to her full size. If you keep your enclosure outside, however, I would recommend much bigger since there is more room! At first I kept my tortoise in a 55 gallon tank but she became so dissatisfied (clunking, scraping, climbing) that I had to get a bigger one.
4x8 feet is the minimum typically recommend here for an adult Testudo. Some say 3x6 is sufficient. Others say 4 shell lengths by 8 shell lengths (in your case, that would only be 2x4 feet, which is quite a small space that won't allow a lot of room for activity - and would only be temporary since your tortoise isn't full sized yet).
There is no scientifically set minimum. There are just people's varying opinions. A tortoise is not going to suddenly drop dead in a 2x4' enclosure, but this is too small and not "good" for a tortoise. I think 4x8' is a good minimum size for an adult tortoise the size of yours, but most people argue that they don't have that much space. I argue back that if you don't have room for a large enough enclosure to meet your animals needs, then you don't have room for that animal and you should give it to someone who does have enough room. My answer is not based on what is cheap, easy and convenient for the human. My answer is based on what is best for the tortoise.
I also think tortoises should have an even larger, safe, outdoor enclosure for nicer weather. I like the big indoor enclosure for whenever weather is too hot or too cold, but outdoors most of the time is best for adults in most instances.