This is not a complete discography.
Complete discographies can contain unreleased and unissued recordings, lost recordings, private tapes, radio broadcasts, TV and movie appearances, re-issues, remasters, compilation albums, and more! If you're looking for a complete discography, get The John Coltrane Reference.
This selected discography details basic information of approximately 105 releases that feature Coltrane as either a leader or sideman that are easily found and accessible via Amazon.com, iTunes, Spotify, etc. The items here can be searched using the search bar above, sorted by earliest session date, and filtered to display only the leader albums personally approved by Coltrane (not the many albums compiled by record labels after Coltrane left the label).
Again, to see items not listed here (there are many...), and for the most accurate John Coltrane discography and chronology, refer to The John Coltrane Reference, by Chris DeVito, Yasuhiro Fujioka, Wolf Schmaler, David Wild, and Dr. Lewis Poter (Ed.). It's one of the most incredible examples of jazz research I've ever seen -- highly recomended.