Base64 will inflate a list of bytes by 33%. For every three bytes that go in, 4 bytes are returned. Wikipedia has a very good explanation of why this is:

http://en.wikipedia.org/wiki/Base64

While we're on the subject, Ascii85 is kind of a cool alternative. By increasing the number of characters used for the encoded string and breaking a 32 bit integer apart in an interesting way, it is able to reduce the expansion down to 25%. For every 4 characters in, 5 come out. Again, more info is available on Wikipedia:

http://en.wikipedia.org/wiki/Ascii85