This question really depends on what you label as a capital ship, because the size matters a lot when it comes to armor thickness, along with intended role.
I personally have not seen the use of much other than advanced armor as effective as you can almost always efficiently overcome the weight added by using it. Those uses are only for smaller ships though so it doesn't come into view here.
The question you
should be asking is how much advanced armor are you to use.
I use at least a single layer of advanced armor on all parts of my combat ships, the frontal plates are also thicker in large margins than the rest of the ship. Angling is also something to be taken into account if you are worried about damage tanking, though it is slightly specific in usage which I will expound upon later. Back to the original premise: On larger ships 500+ in max dimension the frontal plate thickness I aim for can be anywhere from 10 meters of advanced armor to 50 meters depending on the role, 10 meters being the minimum.
For the skin of a fighter being one thick advanced armor in order for a capital ship to have the same proportion of armor the thickness must increase. If you have a fighter that is 50m L, 30m W, 25 H then going off of the easiest to hit side which would be the top or the bottom, the relative thickness is 1/25 for each individual side which would be 2/25 overall. This is about the ratio I use for my fighters, normally one thick everywhere with around a 3 thick frontal plate in front of the cockpits. If you have a capital ship that is 500 meters long then its thinnest piece of armor is to be (1/25)*500=20. Now you can also take into account growing surface area and how the damage will be spread across it a little more than a tiny ship, so we can slim that armor down to half which would be 10. Depending on the role you may slim it down more in specific areas of the ship, but at minimum I would say keep it 5 thick.
There are ways for armor to be fit into smaller volumes that will save space but not mass. This includes double wedging to apply twice the health of a block in one block space and quad tetra-ing to fit four times the health in one block space. Wedging being used for anti-cannon and tetra-ing being use for anti-missile as they have different mitigation characteristics.
For sloping which is kinda finicky, you need to pick ships that will most likely be facing the enemy at all times. I have a 233 meter long light frigate that has 4 meters of armor on all sides except for the front which has equivalent of between 10-18 depending on the weapon used because of the mitigation characteristics of the composites I put in. However, because of the sloping on the side armor, if I am facing the enemy the sides will approach 30+ meters of armor with glancing shots. I can bank on this happening because I tailor made the ship to be able to fire all weapons forward which means that I will most likely be facing the enemy at all times.
The ship: Xerxes Class Light Frigate
Though I don't consider anything smaller than a cruiser a capital ship, cruisers start at 400 meters for me, I do think that the armoring of ships 100+ should take the proportioning I outlined in to account with some fudge room of course.
Long story short though, on anything "capital ship" sized the question should stop being about what
type of armor you should use and instead be
how much advanced armor you should use.