To get the highest ac in the game possible we will assume 20 in all stats, so with those being our stats we will need 2 Levels in Wizard (Bladesinger), 3 Levels in Monk (Kensei), 10 Levels in Bard (Swords), 3 Levels in Fighter (Battle Master), and 2 Levels in Sorcerer (Wild Magic) Though that last one is a bit iffy depending on how you want to calculate the ac. So based on all of this here is the math.

BASE - 61
10 Base
+5 Dex
+5 Wis (Unarmored Def - Monk 1st Level)
+5 Int (Bladesinging - Bladesinger Wizard 2nd Level)
+2 (Agile Parry - Kensi Monk 3rd Level)
+2 (Haste)
+6 (Defensive Duelist)
+1d8 (Evasive Footwork - Battle Master Fighter 3rd Level)
+1d10 (Defensive Duelist - Sword Bard 10th Level)
+1 (Dual Wielder)
= 54
+5 (Shield Spell - iffy ruling)
+2 (Wild Magic surge - only on 51-52)
=61
MAGIC ITEMS - 7
+3 Defender Sword
+2 Bracers of Defence
+2 Staff of Power
= 68
OTHER/SITUATIONAL - 12
+5 ¾ Cover
+2 (Ceremony of Marriage)
+1 (Blessings)
+3 (Boon of Dreadnaut)
+1 (Wyrm Knight Boon)
= 80
ALLIES - 41
+12 (Valor bard - 15th level)
+8 (Cavalier Fighter - 7th level)
+1 (2nd level Cleric Spell - Warding Bond)
+5 (Glory Paladin - 15th level)
+2 (Shield of Faith)
+12 (Battle Master Fighter - 18th level - Bait and Switch)
+1 (Rod of Alertness - Ally needs attunement)
= 121

So yeah that is the highest I believe without using any single ability more than once, however I only consider the 54 to be the true highest ac, but I know you guys want more than just that since that would be boring.

88

I know this question is over 5 years old and that it specifically asks for AC without allies' buffs, but I know I was curious enough to look for it with allies' buffs, so I'm sure someone else is as well.

I found a way for an AC of 88 with the support of 4 allies and without using any ability score raising items or stacking any bonus from the same source. This build was created just after the release of Tasha's Cauldron of Everything.

Character Build (receiver of AC)

Race: Warforged. This is to receive a +1 bonus while wearing armor thanks to the Integrated Protection racial trait.

Class 1: Alchemist Artificer (10 Levels). With 10 levels in Artificer, you gain access to the Magic Item Adept feature which allows you to have 4 items attuned at once. Additionally, the Alchemist subclass gives the Expiremental Elixir feature which, when an Elixir of Resilience is created and consumed, gives you +1 AC.

Class 2: Forge Domain Cleric (6 Levels). With 6 levels in the Forge Domain, you have the Soul of the Forge feature which gives you +1 AC when wearing heavy armor. Use the ASI at 4th level to take the Fighting Initiative feat and select Defense to earn another +1 AC when wearing armor. This will also give us access to the spell Shield of Faith buffing our AC by +2.

Class 3: Wild Magic Sorcerer (2 Levels). This one is a bit of a stretch, but we are looking for the highest AC possible in DnD not the highest realistic AC. With 2 levels in the Wild Magic subclass, you gain access to the Wild Magic Surge feature which allows the DM to ask for a 1d20 roll after you cast a spell, and on a natural 1, you roll on the Surge Table. If you roll a 51 or 52 on the Surge Table, you gain +2 AC.

If you've been keeping track, with just Race and Class, we are currently at an AC bonus of +8 so long as we include heavy armor below.

Magic Items:

Plate, +3. This gives us a bases AC of 21.

Shield, +3. This gives us a total additional AC of +5.

Defender Sword. Attunement Slot 1. While wielding this weapon, we can have another +3 AC if we convert it's magic bonus to AC on our previous turn. (Be sure to use a one-handed sword for this to be able to wield our shield.)

Cloak of Protection. Attunement Slot 2. This gives us +1 AC.

Ring of Protection. Attunement Slot 3. This gives us +1 AC.

Ioun Stone of Protection. Attunement Slot 4. This uses our additional attunement slot earned earlier and gives us +1 AC.

So Far, we have a total AC of 40.

Allies

Valor Bard (15 Levels): This ally will give you a die of Bardic Inspiration which, thanks to Combat Inspiration, allows you to add 1d12 to your AC as a reaction. Like with Wild Surge earlier, we will assume the best roll possible which in this case, adds +12 to your AC.

Cavalier Fighter (7 Levels) and Cleric (3 Levels): With 7 levels in Cavalier, this ally can buff your AC by 1d8 with it's Warding Maneuver feature. Again, we'll use the highest roll possible meaning +8 AC. Additionally 3 levels in Cleric gives access to the spell Warding Bond which will increase your AC by another +1.

Oath of Glory Paladin (15 Levels): A Glory Paladin gets the feature Glorious Defense which can raise your AC by it's CHA Modifier which we will assume to be +5. This Paladin is also capable of casting Haste for another +2 AC.

Battle Master Fighter (18 Levels): Using the Bait and Switch combat maneuver, this ally can raise your AC by 1d12, so for our sake, +12 AC.

Thanks to our allies, we now have an AC of 80.

Other

Cover: With 3/4 cover, we gain another 5 AC bringing us to 85.

Marriage: If either you, the Paladin, or the Fighter/Cleric cast the spell Ceremony and held a wedding within the last 7 days between you and another ally listed above, you gain +2 AC. This brings us to an AC of 87.

Rod of Alertness: If one of your allies has attuned to and placed this magic item, you gain your final AC bonus of +1 for a grand total of 88 AC.

tl;dr

With a specific AC build for yourself, specific support builds for 4 allies, 7 magical items, 4 spells, a wedding, and 3/4 cover, there is a 1 in 3,456,000 chance that one can achieve an AC of 88 without stacking sources.

Class level: Artificer 20 Race: Warforged

Artificers at high level have 6 atunment slots and the only rules preventing people using multiple copies of a magic item are exclusive to Adventurers League

Total Walking around Armor Class : 37 (only aplicable in game if you are suprised or out of spell slots)

• 18 Armor(Half Plate, +3)

• +3 Dex bonus (Medium armor Master)

• +1 Armored Bonus(Fighting Initiate - Defense (UA)) UA feat (only bit of UA in this build)

• +1 Misc Bonus(Integrated Protection) - Warforged racial Feat

• +1 Atuned Item 1 (Cloak of Protection)

• +1 Atuned Item 2 (Ring of Protection)

• +1 Atuned Item 3 (Ring of Protection)

• +1 Atuned Item 4 (Ring of Protection)

• +1 Atuned Item 5 (Ring of Protection)

• +2 Atuned Item 6 (Staff of Power)

• +5 Shield(Shield, +3)

• +1 Blessing of protection

In combat spells/ magic items AC + 9

• +2 Spell(Shield of Faith) - Magic Initiate Feat Bonus action
• +5 Spell(Shield Spell) - Reaction Cast
• +2 Potion of Speed(Haste) Action

Total is now 46

3/4 cover would add another +5 to make it 51.

A CR 30 Monster (proficiency +9) With a Dex score of 30 (+10), a +3 magic bow, +3 magic ammo, and wearing bracer of archery(+2) would have a +27 to hit meaning a roll of 19 (20 auto hit) would be a total of 46 so even without cover only a 19 or 20 would hit. This creature would be a homebrew thing however as the highest to hit RAW is +19.

I like this build because it also gives you a +13 to all saving throws, if you have a paladin on your team it increases it to +18, with proficiency in a save you'd have +24 and the highest save DC in the game is a 27 so as well as never being able to be hit you can dodge/avoid almost any spell. Dex saves are +27 with Resistance(Dexterity) able to auto dodge even Tiamat's breath weapons. Highest player spell DC is 26 (warlock cha 22, robe of the archmage, +3 rod of the pact keeper, Ioun Stone of Mastery)

Character Example: https://www.dndbeyond.com/characters/32499716

I see a lot about Barbarians being used for high AC but you could do the same with a wizard. If you go wizard and pick Bladesinger as your school you can add your intelligence modifier to your ac. If you cast mage armor on yourself, and have an 20 in both int and dex, your AC will be equal to 23. Depending on dice rolls and race you can achieve this fairly early on. If your just trying to be hard to hit you can cast blur on yourself, granting disadvantage on attack rolls against you. Then use Move Earth to make a wall before you. This wall can grant you cover, boosting your AC further. So very early on you could have an AC of 27 without any magic items. If you want to go higher you can, but I've always preferred casters to melee classes. So this is just my findings.

The Highest Possible AC is 69

• Permanent AC: 34
• Combat AC: 41
• One-attack AC with the same build: 58 (63 max)
• One-attack AC with specialized build: 63 (69 max)

Permanent AC with no Magic Items: 23

• Werebear/Werewolf/Wereboar [for natural armor]
• Fighter 1 [for Defense Fighting Style]
• Cleric 6 [for heavy armor proficiency and Soul of the Forge]

18: Plate Armor
+2: Shield
+1: Defense Fighting Style
+1: Soul of the Forge
+1: Natural Armor (see below)

+1 bonus to AC while in bear or hybrid form (from natural armor)

Adding Magic Items and Other Rewards: 34

• Wizard 1 [for magic item prerequisites]

+3: Magic Armor
+3: Magic Shield
+2: Staff of Power
+2: Choose two out of Ring of Protection, Cloak of Protection, Ioun Stone - Protection
+1: Blessing of Protection

Adding Temporary Magic Items, Spells, and other Abilities: 41

• has Cleric (Forge) 1 [for Shield of Faith]
• Wizard (War Magic 10) [for Durable Magic]
• has Piety of at least 3 with Karametra

+2: Potion of Speed
+2: Shield of Faith
+2: Durable Magic
+1: Karametra’s Devotee

Expected AC for One Attack: 57 (min), 63 (avg), 69 (max)

• replace one of the +1 AC magic items with a defender
• has Wizard (War Magic) 2 [for shield and Arcane Deflection]
• has Cleric 6 [for 1 feat, and to keep Soul of the Forge]
• Martial Adept [for Evasive Footwork]
• replace Wizard 3-10 and Fighter 1 with Ranger (Hunter) 7 [for Defense Fighting Style and Multiattack Defense]
• Bard (College of Swords) 5 [for Defensive Flourish and Bardic Inspiration (d8)]

+5: 3/4 cover
+5: shield
+3: defender [replaces a +1 Magic Item]
+2: Arcane Deflection
+2: Multiattack Defense [replaced Durable Magic]
+1d8: Defensive Flourish
+1d6: Evasive Footwork

Note: without replacing the Wizard and Fighter levels (if you want the same build as highest combat-ready AC) you will only have a d6 Defensive Flourish and miss out on Multiattack Defense resulting in an Expected -3 AC (-4 max)

Note 2: after attacking to activate Defensive Flourish, the PC must drop his finesse weapon and draw the Staff of Power with his/her free object interaction. If your GM rules that dropping the finesse weapon serves as your free object interaction (a ruling I haven't seen before, but is possible), then you will lose +2 AC for the purposes of one-attack AC

What about Manuals and Tomes?

I assumed a maximum of 20 for each ability score because the number of magic items and other rewards is already very restrictive. This clause from the question prompted this:

Time and magic items are limited to practical use

Collecting a bunch of Very Rare magical books on top of the items already needed is impractical (as is waiting for them to refresh their magic). If you want to include them, you will have to change the entire build to account for Unarmored Defense, Bladesong, and the Dual Wielder feat

• (Barbarian OR Monk 1/Wizard 2/Ranger 7/[Bard 10/Martial Adept OR Bard 5/Fighter 3])

which gives you these numbers before tomes and manuals:

• Permanent AC: 32
• Combat AC: 37
• One-attack AC: ~60 (69 max)

Then just add 1 to each metric for each book read (up to a maximum of 5 each) among:

• Manual of Quickness of Action
• Tome of Clear Thought
• Manual of Bodily Health OR Tome of Understanding

This brings the theoretical maximum to:

• Permanent AC: 47
• Combat AC: 52
• One-attack AC: ~75 (84 max)

Most games allow you to have equipped 2 magical items, 2 attunement slots and as many not attuning magical items as you want, most DM's allow you to carry a bag of holding as well. So you are stuck with a lot of physical weaknesses right off the bat.

The max bonus to AC on armor is +3, and no unarmored defenses don't stack. Reading a book won't necessarily work as most DM's don't even know what that is or how it functions.

Waiting out the period to increase your AC is pointless as then you would have to drop that character and watch the DM make him a god over time since you need to continue with the campaign.

The next biggest weakness is AOE spells, all you guys are talking about is increasing your AC, and yes this question is about what is the highest AC you can reach but that's the least conventional way to do things.

But sure, let's make a max AC character.

First off, shields don't require attunement and stack with everything, even spells as long as you have war caster. that's +10AC right off the bat.

Finding the highest base armor rating is difficult, however it's the barb 20, paladin 3 and fighter 1 that end up tying at a total of 21 AC. Cleric's can go there as well but why i said paladin 3 is because of the fighting style making the fighter the cheapest and most effective high AC at 22. That takes up your first equipped magical item with your armor, the second strongest is the defense sword, however that's a legendary and you are already wielding a shield with the same bonus as it so we will stick with the shield for math calculations to get the cheapest AC build possible.

Right now we sit at 32 AC base.

• Drinking a potion of speed adds +2 AC,
• Shield grants +5 AC for one turn only,
• Shield of faith adds an additional +2 and so does another cleric spell.
• Since we can only get a +3 AC gauntlet with our final attunement slot we will get just that.

35 AC standard with two shields. Stack Haste spell, Speed Potion, Shield spell, Shield of Faith and the final spell of which i am too lazy to look up the name of, you gain the final and MAX AC within a legit campaign at drumrolls 48 AC without situations.

Stack on 3/4 cover you reach 53 AC. Being prone against rangers is helpful since that's automatic 1/2 cover if they are on the same ground level or 3/4 if slightly below along with their disadvantage on attacks. However under no circumstance can this number be modified which is what the other people tried to fix with adding barbs and those filthy books.

We can reach a permanent AC of 36.

As a barbarian lvl 8, monk 1, dragon bloodline sorcerer 1, my ac would be 13+dex+con+wis.

By level 8, it is possible (albeit unlikely) to have 20 in 3 stats. We'll assume we've reached that point. That puts us at 28 AC.

We use the manuals for Wis, Con and Dex, which brings us to 31 AC.

Ring of protection +1 and cloak of protection +1 gives us 33 AC. Defensive Sword with all bonus to AC puts us at walking around with 36 AC.

Under unusual circumstances, it is possible to get an AC of 49

• Highest permanent AC: 31
• Highest combat-ready AC: 35
• Highest the-stars-aligned AC: 49

Permanent AC with Magic Armor, no other Magic Items: 27

There are actually several ways to achieve this.

• Barbarian 20
  • 22: Unarmored Defense = 10 + 5 (20 DEX) + 7 (24 CON)
  • +5: +3 Shield

    NOTE: Barbarian 20 precludes several options that require levels in other classes

• Heavy Armor
  • 21: +3 Plate Mail
  • +1: Defense Fighting Style (Fighter 1 or Ranger 2 or Paladin 2)
  • +5: +3 Shield
• Medium Armor
  • 18: +3 Half-Plate
  • +3: 16 DEX or better and Medium Armor Master Feat
  • +1: Defense Fighting Style (Fighter 1 or Ranger 2 or Paladin 2)
  • +5: +3 Shield

Things that don't work:

• Light Armor: 26
  • 15: +3 Studded Leather
  • +5: 20 DEX
  • +1: Defense Fighting Style (Fighter 1 or Ranger 2 or Paladin 2)
  • +5: +3 Shield
• Robe of the Archmagi: 25
  • 15: Robe of the Archmagi (Wizard, Sorcerer, or Warlock 1)
  • +5: 20 DEX
  • +5: +3 Shield
• Monk: 20
  • 20: Unarmored Defense = 10 + 5 (20 DEX) + 5 (20 WIS)
  • +0: Precludes shield

Adding Magic Items with Ongoing Effects (Except ones that permanently raise ability scores): 31

• +2: Staff of Power (Wizard, Sorcerer, or Warlock 1)
• +2: Choose two out of Ring of Protection, Cloak of Protection, Ioun Stone - Protection

NOTE: The Defender, because of the way it works, is considered (and rejected) as a Situational AC Boost.

Adding Combat Buffs - Consumable Magic Items and Spells: 35

• +2: Potion of Speed (effect of Haste spell, no Concentration)
• +2: Shield of Faith (Cleric 1 or Paladin 2, Concentration)

Adding Situational AC Boosts: 49

• +5: 3/4 Cover
• +4: Multiattack Defense (Ranger 7, triggered by getting hit, active for rest of attacking creature's turn)
• +5: Shield (Wizard 1, reaction to being hit, active until your next turn)

A note on the Defender: The Defender and Staff of Power are both weapons that can provide a significant AC boost. I think most characters with the choice would choose the Staff of Power. In hand it is always on and also has a +2 attack or spell DC bonus. The Defender is not in effect during any round you do not attack, including a surprise round or a round in which you Disengage or Dodge, and going max AC leaves no bonus for the attack roll. Importantly for this question, hiding behind 3/4 cover pretty much means you are not attacking, and therefore cannot shift +3 to AC. If the Defender replaced the Staff of Power and chose not to hide behind 3/4 cover, the highest AC would be 45.

Bonus Questions: What's the lowest level at which I could achieve this?

Because this doesn't rely on crazy stats, it can be achieved at a fairly low level. We have a choice between a Heavy and a Medium Armor build. Using the Medium Armor build obviates the need for Heavy Armor Proficiency (which would require a feat or 1st level in Fighter or Paladin).

Minimum Stats (easily achievable at 1st level using the default array with any PH race):

• DEX 16
• INT 13 (Wizard multiclass)
• WIS 13 (Ranger and Cleric multiclass)

Feat:

• Medium Armor Master - taken at Ranger 4, or at 1st level as a Variant Human

Minimum class level requirements:

• Ranger 7 / Wizard 1 / Cleric 1

Important Caveats

I have assumed that ability scores max out at 20 unless a class feature says otherwise. If abilities go above 20, where do they stop? I have chosen to disregard two possible ways in which characters can get ability scores over 20:

1. Even without magic items, Epic Boons can be used to continue to improve abilities to 30 (DMG 230), while the characters remain "20th level" characters. Given enough time, assume all 30s.
2. There are several magic items that give permanent ability boosts. The only ones worth considering here are the Tomes and Manuals which give +2 to the relevant ability but also increase the ability maximum by 2. Although, once used, they become blank for a century, there is nothing in these manuals that suggest they are unique or that they can't benefit a character multiple times. How high can your ability scores go? Per RAW and RAI, the answer to Can I increase an ability score above 30? is NO.

In either case, we no longer need Barbarian 20 for CON 24. Barbarian 1 gets access to Unarmored Defense, time/magic gets us DEX 30, CON 30, and multiclassing is possible. Highest the-stars-aligned AC becomes 57. I think this violates the spirit of the question however.

The highest AC I've had for a character (without going so overboard as to be ridiculous) is AC31 the character is a goblin paladin wearing +3 mithril plate and a +3 shield with a Dex of 20...going overboard its possible to hit AC41 (Dex of 30, cloak of protection, ring of protection, Defender +3, +3 mithril plate, +3 shield...This assumes alot of exp past lv.20 to get Dex 30 (DMG states at lv.20 characters can go up to 30 but not higher than that using the attribute increases given for every 30k exp above 355,000exp)

1 cleric 19 Wizard . Plate +3 armor +11 (can have resistance or immune to critical hits), Shield magic +3 =+5, Shield of faith spell +2, Shield spell +5, Ring of defense +1, Staff of Power +2 (or Defender weapon +3), Cloak of Displacement (basically a +2) all attacks are disadvantage Ion stone of protection +1: Total= 38 (40) attacks disadvantage

OR...1 Barbarian, 19 Wizard, Robe of Magi 15+ dex, 22 dex +6, 22 Con +6, Magic Shield +3 = +5, Shield of faith spell +2, Shield spell +5, Ring of defense +1, Staff of Power +2 (or Defender weapon +3), Mage Armor +3, Cloak of Displacement (basically a +2) all attacks are disadvantage, Ion stone of protection +1: TOTAL = 47 (49) attacks have disadvantage and no special circumstances

You could potentially duel wield two defender weapons (+3 each) and use bracers of defense so that the bonus is equal to a magic +3 shield...then take defense duelist for an additional +1ac.

Alright. Let's work this out, since my friends and I have as well.

High Elf Barbarian 1 (Let's assume, for all intents and purposes, you started with maxed stats, 18s in all (DEX to 20 and 19 INT due to High Elf).

Level 1 has you sitting at a 10+5+4 Nekkid AC of 19. Throw in a +3 Shield, and you're at 24. I have a good reason for going Elf instead of where many do.

Next, go Wizard for 2 levels to get the Blade Dancer Arcane Tradition to add your INT Modifier too, as it isn't an "Unarmored Defense" equivalent. So you can get another +4 to that AC, but you lose the Shield at this point. Make sure one spell you do take is "Mage Armor" to increase your Base AC to a 13.

So for Level 3 (Barbarian 1 / Wizard 2) you'd have 13(Mage Armor)+5(Dex)+4(Con)+4(Int) = 26 AC with NO MAGIC ITEMS.

For the next 5 levels, we'd work on leveling those two classes to 4 so you get the Ability Score Increase. Improving Constitution or Intelligence each time since an ASI from this ability can't improve it beyond 20. This would raise it up two more points by 8th level to a 28 AC.

At this point, additional levels don't REALLY matter since you can't improve Base Scores through ASI, and since wearing armor is going to lose you 3 or more points from the AC score, you're not going to want to mess that up. And wearing a shield, will get you no net gain (+3 shield give +5 AC, which loses the Blade Singing bonus which is your INT modifier, also a +5 at this point).

From here on out, any and all improvements will be gained via Magic Items or through playing with RAW.

One way, as has been said, is to get the Ability Score improving books. As a High Elf, you're likely to "live well over 700 years" which, for sake of argument, we'll say you started adventuring as an elf at the child-like age of 50. We'll say you stole these books from the library of your starting city, not realizing what they were. The ones that would benefit you most as a Barbarian 4 / Wizard 16 (Since for some of this, I need access to 7th+ level spells) would be: Manual of Bodily Health (Constitution), Manual of Quickness of Action, and the Tome of Clear Thought. Assume you read each of these which increase the scores by 2. The first time reading these gets you a +3 to that already large AC, a 31. Then, let's attune our first magic item, Bracers of Defense, this raises it to a 33 since we're not wearing armor, or using a shield, throw in a Ring of Protection, and an Ioun Stone of Protection, and we're at a 35 (+1 AC from both). Next, we'll assume we use a full "Deck of Many Things" and get REALLY lucky with our draws and get the Star and boost our INT up and raise it to a 36. We'll also assume we get the Moon and max our "Wish" number (These come into play later) at 3.

Alright, as it stands we're at a whopping 36 AC. Let's progress the clock until you're 150 years old. You've just gained another +3 and you're now at 39. Lather, Rinse, Repeat. 250: 42 AC, 350: 45 AC, 450: 48 AC, 550: 51 AC, 650: 54 AC, 750: 57 AC. By this time, you're getting up in years, despite it saying "Well Over 700" we're unsure how old they actually intent to allow you to get. So we'll assume you won't make it to 850... naturally...

Now we're messing with the RAW. By this point you've probably got a well established family and are well on your way to becoming a legend. You know that you can tell your family to leave your three books alone, and they would.

So you go ahead, and use a spell slot and cast "Sequester" on yourself with the set rule to not be awakened for 100 years. You'll be left there, perfectly fine, unless someone finds and dispels the magic before the 100 years. You can use this method, basically indefinitely to raise it well beyond the 57 AC we're sitting at before that.

You could also use your ability from the "Wish" spells you technically gained through the Moon card to wish to be able to lower the age of your physical body to a point such as 50 (Where you started), but to retain all the improvements and mental advantages you had gained through your years of experience... Basically, this one works BEST if you are a lawyer and can actually prevent any and every loophole possible to keep your skills and scores where they were to get you that 57 AC as a 50 year old elf, and possibly start your career anew and start using the books again. Or use a new set that you could have made during your wait since you'd have had the, well over 6,000 days to make a new set (2,000 each since they're each 50,000 and divide that by 25 to make to determine the days required). From that point on, you could go through that process two more times without having to worry about needing to find a new way to get "Wish."

tl;dr End Tally is a 57 AC without hitting a ceiling for the age of a High Elf.

Well, manuals allowed, you could use them an infinite number of times if you had a mirror of life trapping. Thus, you could have a nearly infinite AC.

Well you can actually get to 40.

First you need to be a werebear or a warforged; both grant +1 to AC. Then you need a level in Sorcerer with dragon origin base, making your base AC 13, and a level in Barbarian to add your Con and Dex to AC. Then you can get Wis and Dex to 24 using a Deck of Many Things and then use Manual of Bodily Health and Quickness that can give you another +2 to each Con and Dex making each 26. Then you need bracers of defense for a +2, a ring of protection, a cloak of protection, and ioun stone of protection — which all give a +1 — and finally a shield +3.

13+1+8+8+2+3+5=40

Now you still have 18 levels to play with and it is still possible to use a shield spell on yourself using Sorcerer.

Potentially Highest Achievable Armor Class

Character Class: Barbarian using Unarmored Defense & some magic items

• AC 30(33) appears to be a theoretical max for "walking around" AC¹

• AC 42(45) appears to be a theoretical max for a brief duration¹

+1 Ring of Protection (1)(attuned)¹
+1 Cloak of Protection(attuned)¹
Dexterity = 22²
Constitution = 24³
Magical shield: +3(attunement not required)
Defender sword(Legendary)⁴
Feat: Defensive Duelist ⁵

¹ You need to attune the cloak and the ring. Based on Sage Advice from Jeremy Crawford, 21 Sept 2015, you can't attune two Rings of Protection.
² Max Dex is 20, 22 with a Manual of Quickness in Action
³ the +4 added to the usual cap of 20 is unique to lvl 20 Barbarians; the 4 extra points come with the capstone "Primal Champion" feature
⁴ Defender sword requires attunement; you have to be in combat and choose on the first attack of your turn to get the sword bonus
⁵ If using a finesse weapon (a match with high dexterity on this character) add the proficiency bonus (+6) to AC for one attack against you (p. 165 PHB). This is treated separately in calculations.

Calculation

Permanent/walking around armor class = 30(33)⁴ begin{array}{rl} 10 & text{(base)}\ +13 &text{(+6 Dex, +7 Con)}\ +5 &text{(+2 shield, +3 magic)}\ +2 &text{(ring and cloak)}\ hline = 30\ +3 &text{(when using all bonuses on sword for defense)}\ hline = 33 end{array}

Temporary #1: If you are behind Half Cover: +2 bonus to the above 32(35)⁴
Temporary #2: If you are behind Three-Quarters Cover, +5 bonus to the above. 35(38)⁴

• Note, you are either behind 1/2 or 3/4 cover; you can't stack those.

Temporary #3: Magic

• If the Barbarian can read a magical scroll (For the duration of the spell)

  • Cast from a scroll "Shield of Faith spell" add +2 bonus to the above.

  • Cast from a scroll "Shield" spell, you'd add +5 bonus to the above.

These spells should stack. From @Ethan's suggestion: the Magic Initiate Feat could supply the Shield Spell once per day and avoid having to use a scroll in combat.

The effects of different spells add together while the durations of those spells overlap. The effects of the same spell cast multiple times don’t combine, however. Instead, the most potent effect—such as the highest bonus—from those castings applies while their durations overlap. (Basic Rules p. 81)

It looks like the max with 3/4 cover and a shield spell is 42(45)⁴

---

Multi Classing: Barbarian MC loses the Constitution boost to 24 (Capstone).

If the Barbarian multi-classes, subtract 1 from his Constitution bonus; we'll assume a manual of Bodily Health (22 Con). He could take 1 level in Wizard and cast the Shield spell.

The "walking around" AC would drop to 29(32)⁴, his temporary could add +5 from that spell 35(37)⁴ and get could as high as 41(44)⁴ if all of the necessary conditions noted above are met.

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Defensive Duelist Feat

With three creatures attacking you, you only get this +6 boost for one attack, but if you are fighting just one creature, this provides an AC boost of 6 from that feat. (Occasional 39/51 AC is thus possible if all other conditions are met). How to combine that with 3/4 cover becomes a tactical question; most of the time won't apply. The more likely benefit of this feat is a 33/46 theoretical max.

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**Influence of a hard cap on ability scores, and multiple magical manuals that allow a PC to raise an ability score above 20.

• A practical hard cap for a PC of 24 is implied by the descriptions of two artifacts

  The Book of Exalted Deeds and The Book of Vile Darkness, both of which allow ability increases beyond 20 but with a cap at 24. (DMG p. 222 and 223).

• An absolute Hard Cap is found in Chapter 7 (p. 60, Basic Rules) in the Ability Score discussion. The highest score listed is 30 (+10 mod bonus) - which is also the highest score for any ability in the Monster Manual. This puts the highest theoretical Constitution or Dexterity at 30 each but that would take numerous instances of each magical book to achieve (as discussed in other answers). If that extreme is reached, it would add a total of +7 to all of the above (yielding 38, 42, and 56 respectively) but manipulating the centuries in order to get multiple instances of those books is beyond the scope of this answer.

With the conditions you've set, you can have infinite AC. Just buy an infinite number of Manuals of Quickness of Action, and your AC will be limited only by the time it takes to use them.