What is the largest size a gzip (say 10kb for the sake of an example) can be decompressed to?
Update 2020-02-06: As mentioned in the comments, I have been unable to reproduce the original result with gzip. Working on the assumption that I accidentally used a different compression format in that original quick test I've repeated with gzip and updated the figures below accordingly. This new result agrees with the theoretical maximum compression stated in other answers/comments.
It very much depends on the data being compressed. A quick test with a 1Gb file full of zeros using a standard version of gzip (with default options or specifying -9) gives a compressed size of ~1018Kb, so your 10Kb file could potentially expand into ~10Mbytes.
If the data has low redundancy to start with, for instance, the archive contains images files in a format that is compressed natively (gif, jpg, png, ...), then gzip may add not further compression at all. For binary files like program executables you might see up to 2:1 compression, for plain text, HTML or other markups 3:1 or 4:1 or more is not unlikely. You might see 10:1 in some cases but the ~1030:1 seen with a file filled with a single symbol is something you are not going to see outside similarly artificial circumstances.
You can check how much data would result from unpacking a gzip file, without actually writing its uncompressed content to disk, with
gunzip -c file.gz | wc --bytes - this will uncompress the file but not store the results, instead passing them to
wc which will count the number of bytes as they pass then discard them. If compressed content is a tar file containing many many small files you might find that noticeably more disk space is required to unpack the full archive, but in most circumstances, the count returned from piping
gunzip output through
wc is going to be as accurate as you need.
Quoted verbatim from https://stackoverflow.com/a/16794960/293815
The maximum compression ratio of the deflate format is 1032:1. This is because the longest run that can be encoded is 258 bytes. At least two bits are required for each such run (one bit for the length code and one bit for the distance code), hence 4*258 = 1032 uncompressed bytes can be encoded per one compressed byte.
You can get more compression by gzipping the result of gzip. Normally that doesn't improve compression, but for very long runs it can.
By the way, the LZ77 approach used by deflate is more general than run-length encoding. Instead of just a length, a length/distance pair is used. This allows copying a string from some distance back, or replicating a byte as in run-length for a distance of one, or replicating triples of bytes with a distance of three, etc.
The compression ratio of any compression algorithm will be a function of the data being compressed (besides the length of that data).
Here is an analysis at MaximumCompression,
Look at one of the samples like,
File type : Multiple file types (46 in total) # of files to compress in this test : 510 Total File Size (bytes) : 316.355.757 Average File Size (bytes) : 620,305 Largest File (bytes) : 18,403,071 Smallest File (bytes) : 3,554
The answer to your question, depends the input. To give you an idea how compression is done watch this six minutes videos.
What you should get from it is that the compression rate depends on the frequency of each character, thus there is no generel max rate, it depends on the input, for english text it is about 65 percent.