Things You Didn’t Know About D&D 5e: Calculating AC

Calculating Armour Class (AC) is actually quite easy once you know how it works. Unfortunately, the key rules seem to be fairly easy to overlook, and therefore many players get confused about how to calculate their Armour Class when they have multiple bonuses from multiple sources. This post will endeavour to explain how AC is properly calculated to help dispel the confusion. 


Chapter 1, “Step-by-Step Characters” of the Player’s Handbook discusses what your Armour Class (AC) is and how to calculate it, but the many options that players are presented with to modify their Armour Class can cause some confusion. Below is an in-depth look into the intricacies of this very important feature.

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There Are Two Kinds of AC Bonuses

The first and foremost thing that you have to remember about Armour Class is that there are two kinds of Armour Class bonuses in 5th edition. The first kind is not so much a bonus as it is a formula to calculate your Armour Class, and the other kind is a flat AC bonus that you can apply to any formula you have used to calculate your AC. Generally, features granted by your race or class (such as Unarmoured Defence or natural armour) will give you a formula, as will the kind of armour your wear. These features say “your AC equals”. Sundry items such as shields or rings of protection, on the other hand, simply say that you add whatever number to your Armour Class.

Formulas for calculating AC do not stack. If you have a natural armour formula and don a suit of armour, you can’t benefit from both at the same time. Likewise (and is an exceptionally common question), a tortle monk does not get to add their Dexterity and Wisdom modifier to their race’s natural armour.

The flat bonuses from sundry items do stack, with the principal exception that no item stacks with itself (yes, this includes shields, so dual wielding shields is silly unless you plan to use one to shield bash every turn). For example, a barbarian wearing bracers of defence would add the +2 from the bracers to his or her armour class (stacking with unarmoured defence) because the bracers are not a separate formula, they simply add a flat bonus.

Therefore, a barbarian with Dexterity 14 and Constitution 14, and wearing a ring of protection and bracers of defence, would have an AC of  17 (10 + 2 Dex + 2 Con + 1 ring + 2 bracers). If the barbarian somehow found a second ring of protection, though, he may as well give it to the wizard because he can’t benefit from two of the same item (in this case, though, it’s primarily because he can’t attune to a second item of the same name as one he already has). But, if the barbarian found a cloak of protection, then he could wear that as well and have an AC of 18.

Each Armour Class Formula is Mutually Exclusive

The second thing to remember is that any formula for calculating your Armour Class is its own, discrete calculation that is mutually exclusive to every other Armour Class formula. In other words, whenever you encounter a calculation method that states “your AC equals”, such as the monk or barbarian’s Unarmoured Defence, the Draconic Bloodline (sorcerer)’s Draconic Resilience, or your shiny suit of full plate armour, you cannot stick them all together.

For example, if you are a sorcerer/monk/barbarian multiclassed character, your AC does not become 13 + your Dexterity modifier + your Constitution modifier + your Wisdom modifier. You can only gain the benefit of one of the following:

  • (a) the sorcerer option
  • (b) the barbarian option or  the monk option (whichever class you went into first, as per PHB 164)

Likewise, and to address a specific question that many shameless power-gaming munchkins often ask (and the reason why this article uses the header image that it does), a lizardfolk barbarian with Dexterity 10 and Constitution 18 (or a lizardfolk monk with Wisdom 18) who is not wearing any armour would have an AC of either 13 (from natural armour)[1] or 14 (10 + 4 from their ability), but not 17. This is because the natural armour bonus a lizardfolk receives does not stack with the barbarian’s (or monk’s) Unarmoured Defence; they are separate formulas. And if someone cast mage armour on the lizardfolk barbarian, the creature would have to choose between using this new Armour Class calculation or one of the other two options.

As an important side note here: even though the Armour Class formula for armour and the Armour Class formula for natural armour are mutually exclusive, you aren’t considered to be wearing armour with natural armour. This is important because it means that if the lizardfolk barbarian described above picked up a pair of bracers of defence, the creature could still benefit from wearing them because it is not considered to be wearing armour.

You Pick The Best Option

If you have access to several methods of calculating your AC, such as is the case for a lizardfolk barbarian, you pick the option that you want to use. If you are a lizardfolk barbarian and your Constitution modifier is higher than +3, you may wish to use the barbarian’s Unarmoured Defence option. However, if you are subsequently affected by an effect that reduces your Constitution score (and, therefore, your modifier), you can still choose to benefit from the lizardfolk’s natural armour.  Likewise, if you take a level of fighter and decide to don a suit of mail[2] armour, you can then decide that the AC provided by the suit of armour is superior to the barbarian Unarmoured Defence ability, and take that AC calculation.

I’ll also take this opportunity to include a special reminder about Unarmoured Defence. If you gain the Unarmoured Defence feature from one class and later would gain it from another (for example, if you started as a barbarian and then took a level of monk), you do not gain this feature again from multiclassing (see PHB 164). In other words, the first time you gain the Unarmoured Defence option, that is the only version of that option that you can ever benefit from.

Step By Step

Now that we understand the various components of Armour Class, let’s look at how simple it is to calculate your AC.

Step 1: Figure out what AC formulas you can use.
Are you wearing armour? Do you have a class feature that offers you a way to calculate your AC? Make a list of the options. If you only have one option, skip to step 3.
Step 2: Figure out which AC formula is best for you.
Figure out which option gives you the best AC. If you are a mountain dwarf Draconic Origin sorcerer, for example,  you may wish to wear a medium armour option instead of relying on Draconic Resilience.
Step 3: Add in your miscellaneous bonuses.
Are you using a shield? Are you wearing a ring of protection? Tally them up and add it to your AC.

Example: Giovanni the Tortle Monk/Barbarian

Giovanni is a tortle who grew up in the sewers beneath a metropolitan city, learning the secrets of martial arts from a great master who had been afflicted with lycanthropy by a wererat. He has a Dexterity 17, a Constitution 17, and Wisdom 14. His player wants to determine what Giovanni’s armour class is.

A tortle’s Natural Armour gives them a base AC of 17. Their Dexterity modifier does not apply to this. A monk’s Unarmoured Defence feature gives them a base AC of 10 + their Dexterity modifier + their Wisdom modifier. Giovanni therefore has two base AC calculations: the tortle’s and the monk’s. Each calculation is its own discrete entity; Giovanni can either take it or leave it, he can’t take a part of it here or there. Because the Unarmoured Defence calculation comes in at only AC 15 (+3 Dex, +2 Wisdom), the player opts to have Giovanni rely on his armoured hide in battle.

When Giovanni gains his next level, his player decides that the tortle has been learning to embrace his inner fury with his fighting style and so will take a level of barbarian. As barbarians also have an Unarmoured Defence feature, he once again considers Giovanni’s AC. Page 164 of the Player’s Handbook tells him that because Giovanni had Unarmoured Defence from the monk class already, he does not gain it from the barbarian class, and so even though that option would yield a higher bonus than the monk’s Unarmoured Defence (AC 16 to the monk’s AC 15), it is not an option for Giovanni. However, that’s ultimately a moot point because the tortle’s Natural Armour feature is still better than either of them, as it gives a base AC of 17. Therefore, there is no change to Giovanni’s AC.

Giovanni does not end up with an AC of 25 (17 + 3 Dex + 3 Con + 2 Wis). If that is what Giovanni’s player comes up with, then Giovanni’s player needs to read this article again.

Putting It All Together

Calculating AC in Fifth Edition is, more often than not, a matter of picking the better formula. While you can’t stack a barbarian’s Unarmoured Defence with a sorcerer’s Draconic Resilience, you can pick which one you wish to use. Separate AC formulas don’t stack, so a lizardfolk who is a draconic bloodline sorcerer/monk/barbarian with Dex 14, Con 14, and Wis 14 doesn’t automatically have AC 21; you would have to pick which method of calculating AC you wish to use: the lizardfolk’s natural armour (AC 15), the sorcerer’s Draconic Resilience (AC 15), or the monk’s or the barbarian’s Unarmoured Defence (AC 14). Once you have done that, you can look at the flat AC bonuses from other features or items, such as a shield (or the shield spell), which stack with everything else (except themselves). Remember to read your class features carefully to be sure that you are adding the correct bonuses.


Footnotes:

¹ Many people read “+3 natural armour” on page 282 of the DMG and assume that they can apply this to their lizardfolk player character. In fact, that chapter of the DMG is written specifically for creating NPCs, not player characters, and so this is inappropriate. To see how you should actually be calculating your lizardfolk PC’s Armour Class, consult page 113 of Volo’s Guide to Monsters, as Volo’s is a player resource. There you will find that the natural armour bonus is written as “your AC is 13 + your Dexterity modifier”. So no, you cannot be a plate-armour-wearing lizardfolk with AC 21 at 1st level. 
² Also known as ‘chain mail’. Minor annoyance: ‘mail’  already means chain, as opposed to ‘plate’, which refers to a drastically different type of armour made with metal plates (as opposed to interlocking links). ‘Chain mail’  is a redundancy and ‘plate mail’  is an oxymoron.  Not only that, it also makes the terminology more cumbersome.  Please consider this the next time you talk about armour. 


Special Note:

Dungeon Master’s Workshop is a Canadian publishing operation. This is reflected in how we spell armour (armor), defence (defense), and several other words—these are not typos, they are how these words are actually spelled. If your country spells them differently, that’s really not our problem. When Wizards of the Coast hires us to write “armor”, we’ll write it that way. Until then, God Save the Queen.


Changelog:

—Edit 2018/01/31: Clarified the first section due to misunderstanding about “bonus types”. This term, borrowed from a previous edition, was meant to demonstrate that different armour calculations (as well as two shields/rings) don’t stack. The plain language of 5th Edition can sometimes cause people to overlook the subtle nuances, and we thought applying a label to bring peoples’ attention to it would help clarify things. We got the point across for 99.9% of readers using that description, but we aim for 100% and so we’ve adjusted the section.—


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13 thoughts on “Things You Didn’t Know About D&D 5e: Calculating AC”

    1. As a medieval historian, I can assure you that “plate mail” is a neologism with no basis in historical useage.

      You are correct that mail was worn under plate, but that’s precisely it: mail was always worn under plate, and so when you wore plate there was never any need to include “mail” in the description of your armour.

      Just like nobody ever said “chain mail”, because they were the same thing.

      1. Small note: “Plate Mail” or rather “Plated Mail” or “Plate and Mail Armour” is actually a thing although it is more of a description of a type of armour rather than the armour’s formal name…and it is most definitely misused.

        It refers to a subset of mail which has the plates built into the structure of the mail rather than being a combination of plate armour worn over the top of mail. Karuta tatami armour and Karuta tatami armour are examples of this style and I believe the style is used in other regions as well but I am less familiar with the non-Japanese styles.

  1. And that’s the first rule of 5e that I threw right out the window. A Leathery scaled lizardman and squishy Human who are both barbarians or monks with the same stats should NOT have the same AC, and allowing separate calculations for NPCs vs PCs is lazy game design and not consistent with creating rules that apply to the world as a whole.

    1. Thanks for commenting!

      If you allow a lizardfolk barbarian with Dexterity 14 and Constitution 18 to stack bonuses and have an AC of 19 at level 1, that’s completely up to you. When your players also multiclass into Draconic Bloodline sorcerer for a second layer of scales, and also into monk for a sixth sense to warn them against danger, and thereby walk around with a flat, say, 24 to AC, then we would love to hear how it impacts your game.

      We prefer to use AC as a threshold for when a character must act to avoid, turn away, or otherwise prevent an attack from doing them mortal harm (i.e. lose hit points). Certainly, a barbarian will be better able to withstand physical injury as a result of a supernaturally-thick hide (whether or not it actually corresponds to a physiological change), but a fire-based ranged attack will still burn them, a shocking grasp spell will still electrocute them, et cetera.

      AC has been kept deliberately low in 5th edition compared to other editions in order to ensure players do not forget their own mortality. We find that messing with that leads to complications. If you are able to avoid it, then we wish you the best.

      One final note we would make about the idea of lizardfolk vs. barbarian toughness that you seem to be hung up on. Try to imagine the meaning behind the numbers. Lizardfolk may have scales, certainly, but a barbarian’s AC bonus is derived from their Constitution modifier, which translates to stamina just as much as it does to hardiness. The lizardfolk barbarian with a Constitution of 16 who uses their natural armour bonus to get an AC of 15 could get exhausted sooner than the human barbarian who has a Constitution of 18 and who uses that to get an AC of 16. With less stamina, the lizardfolk becomes an easier target as the fight goes on, regardless of the superior protection against physical harm offered by his scales.

      At least, that’s how we would play it.

      1. When you have to work that hard to explain why something that makes complete sense DOESN’T work that way, then maybe your just messing with numbers arbitrarily in order to enforce a videogame style game balance that makes DMing easier so that you can sell more product. Doesn’t mean the system isn’t functional enough to work with the few changes I would make. A lizard man barbarian, monk SHOULD be able to use his innate toughness, reflexes , barb Stamina training (if that’s the way you choose to explain it) and monk “sixth sense” to be harder to hit than someone without any one of those particular features.. as for stacking a “second layer” of Scales ie. natural AC, well those of use who have played for more than a few years now that same types don’t stack and that’s just fine.

        1. Thank you for commenting!

          Once again, when your players decide to multiclass for unarmed AC of 20+ and still benefit from the various abilities that require them to be unarmoured (spellcasting, increased movement, etc.), then we’d be interested to hear how it impacts your game.

          Also, Dungeon Master’s Workshop is not affiliated with Wizards of the Coast. We aren’t trying to sell products, we’re simply explaining how the rules work because they’ve been designed a certain way in order that classes are largely on a level playing field.

  2. I thought the Natural Armor replaced the base 10AC for these races, I guess I was wrong. I mean it just seemed like 10 was the Natural Armor for Humanoid base characters based on the wizard, monk and Barbarian AC calculations. Still thank you for the clarification.

    1. Thanks for commenting!

      That’s pretty close to what happens. Your base AC goes from being 10 + Dex modifier to, say, 13 + Dex modifier. If it helps, you can treat regular AC as have a natural armour of 10 + Dex modifier; since you don’t count as being armoured while wearing natural armour, there’s functionally no consequence to thinking about it this way.

      Just remember that even though you don’t count as wearing armour while benefiting from natural armour, it is a separate method to calculate your AC than the monk or barbarian’s Unarmoured Defence feature and so it they can’t be active at the same time. You can’t be a lizardfolk barbarian who adds their Constitution modifier to their regular AC with natural armour.

      Best!
      – the Archmage

  3. Hey very nice read thank you. Question: Does the size of the race/creature affect AC at all? I read somewhere that ‘size small’ creatures for example would have 1 higher AC than ‘size medium’ creatures, and that a ‘size large’ creature would have 1 lower AC.

    1. Thank you for your question!

      You may have been speaking to someone who is accustomed to earlier editions of D&D. For example, in 3rd edition (the closest mechanically to 5th edition), Small characters had a number of perks: +1 to Armour Class, +1 on attack rolls, and a +4 bonus on Hide checks.

      In 5th edition, all racial abilities and perks are presented in chapter 2, “Races”, of the Player’s Handbook. If it’s not there, they don’t have it; that includes bonuses to Armour Class.

      To answer your question specifically: No, the size of a creature does not inherently alter their AC in 5th Edition. Making a halfling does not confer an automatic +1 Size bonus to AC, as it did in 3rd, just like making a Large creature (if you were to be permitted to do so) wouldn’t confer an automatic -1.

  4. This ruling official or not does not seem well thought out
    “Formulas for calculating AC do not stack” this would make sense if the formulas were complete. They only how the bonus is applied to your AC , implying they are complete would mean the sundry items as you call them don’t add to your AC. Said formulas only show how that one bonus is applied.
    Identical bonuses don’t stack , no kidding . A player trying to get the unarmored bonus from a monk and barbarian ether didn’t read the rules right or is trying to pull one over on his GM. Mage armor and Draconic Resilience are not identical , but lets face it , no mater how many different ways you can increase your base AC to 13 it will still only be 13, so they don’t stack. If a GM doesn’t want a sorcerer/monk player he/she should just say so not make excuses
    Now lets look at the numbers, is a sorcerer/monk unbalanced , dex 18 wis 18… wait that’s not right a balanced character is one made with the point system the max stat bonus you can have before level 4 is +3 , wow your right a character with unbalanced does result in a character with unbalanced stats. now lets look at what the real numbers would be
    AC13 +3(dex) +3(wis) = level 2 AC 19 (band by this ruling) , wow looks big don’t it , you sure about that?
    Cleric level 1 AC 16 (chain mail) +2(shield) +/- 0(dex of 8 doesn’t matter with heavy armor) =18 , or not, +2(shield for faith) level 1 AC 20 (still legal) Even if you ignore the spell its still only a one point difference at least 3 classes can start with those stats and you pay for it. First , its very restrictive on how you place your stats. on top of that you are multi-classing , that means even if you only take one level other then your main class , your advancement will always be behind and you will never get your level 20 ability

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