So I am fixing to start a “slouch hat”. The pattern says size 8 & 9, 16 inch circular. Does that length include the cable plus the interchangeable needles. I have a 14inch cable but with 10 more inches for 5 inch needles that’s now 24 inches. I think I have an 8 inch cable but that’s still 18 inches. Am I going to have to get 4 inch needles to make it work. Also with chiaogoo up to size 8 is “s” cables and 9 and above is “L” cables. So the cast on and ribbing is on size 8 needles then switch to the 9 and eventually to size 9 DPN. Depending on the answers I receive will help decide what I need to purchase. I don’t have any 4 inch needles and my 8 inch cable is a “s”.
Cable length
Circulars are measured tip to tip so you’re right that a 14" cable makes a 24" needle. If you have a longer cable you can use traveling loop, magic loop, two circulars or double pointed needles. Personally I find the shorter tips for 16" circulars too short to use because of how I knit. They hurt my hands and cause cramping. My usual choice is magic loop. Before spending money on more needles you might want to try other methods for knitting in the round.
I recently succumbed to dpns and bought a set for cheap. I decided they’re the best method for glove fingers. I can use them but I’ll never love them.

One more thing, the yarn I am using is Cascade eco alpaca weight “4” and for adult size medium cast on 100.
I have 108 stitches in fingering on a circ for magic loop. I can’t measure it accurately while in use but I think it’s over 40". I could use a shorter one but it’s a fixed circ I bought for socks and don’t have a lot of length options. I wouldn’t go any shorter than 32" for magic loop and might decide to use traveling loop. I think the only way to know what works well for you is to try it. If you’re using interchangeables it’s pretty easy to change cable length if one isn’t working well.
Haven’t done magic loop before but I guess maybe I’ll give it a shot. After watching the videos you sent (thanks so much for sending them) I realized that I used a modified traveling loop to do the armhole border on a jumper(dress) I just finished. Who knew! So I have a 30 inch cable and with 5 inch needles. will that be enough for traveling loop?
Don’t you love it when you find out something you already do has a name? Half of my 108 st (54) fit on the 5" tip of my needle. I expect yours might too. All you need is a cable long enough to loop twice. 30"ish could work fine.
Are you aware that with interchangeables you can use tips of different sizes? The one that has to be the right size is the one you knit with. The other can be smaller, not larger, and often makes difficult decreases easier to manage. If you have two tips of the right size you can make two needles for using two circulars in the round. I thought I’d mention it in case you find out you’re not a fan of magic loop or traveling loop.