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A critical hit allows you to roll all damage dice twice.

Critical Hits

When you score a critical hit, you get to roll extra dice for the attack's damage against the target. Roll all of the attack's damage dice twice and add them together. Then add any relevant modifiers as normal. To speed up play, you can roll all the damage dice at once.

For example, if you score a critical hit with a dagger, roll 2d4 for the damage, rather than 1d4, and then add your relevant ability modifier. If the attack involves other damage dice, such as from the rogue's Sneak Attack feature, you roll those dice twice as well.

(PHB, page 196.)

However, the unarmed strike deals 1 damage (unless you're a monk or have the Tavern Brawler feat). On a critical hit, does an unarmed strike do 1 damage before ability modifiers, or 2 damage before ability modifiers? Or to put it differently, does an unarmed strike deal 1d1, or just 1?

(This would apply to any other attacks that always deal 1 damage, such as the Bat's Bite attack, but unarmed strike seemed like the most obvious example.)

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RAW

No damage dice => No dice to double

Sucks, but them's the rules. So a critical hit with an unarmed strike does nothing more than 1 damage, excluding modifiers. (I'll be excluding those for the rest of the answer) The tables in the player's handbook doesn't list a "1d1", just 1 damage. "1" is not a dice roll, it's a number.

Of course, the designers do seem intent on making unarmed strikes do 1 damage. I doubt it's a typo, especially considering the basic rules have been updated (it's on v0.2). They even supplied a feat (tavern brawler in PHB) and a class (monk) which increases the unarmed strike damage from 1+mod to some actual dice (like a 1d4). If they never intended the damage of unarmed strikes to be so lame, why would they provide that feat and that class?

Possible RAI and RAF; The Spirit of Critical Hits

Critical hits seem to be meant to do more damage than a normal hit. This is reflected in the doubling of an attacks damage dice. It makes you generally do more damage than normal, although there is a slim chance that you don't do as much on that strike. You can see the odds for some weapon dice values here.

If you're looking to extend this logic to critical hits, I suggest instantiating a house rule for upping it to a 1d4 or supply 2 damage on a critical hit. This could be a fun rule, and it may alleviate the disappointment your players feel while getting that critical hit while hitting something with their... fists? ("Unarmed Strike" is really vague!)

However, it does seem that the designers really did want unarmed strikes to not hit hard unless you've had some experience. Once again, this is because of the Tavern Brawler feat in PHB and the monk class. Is this because they want people to use weapons unless they're a monk or a tavern brawler? Were they afraid of things like the grapplemancer builds coming into 5e? Hard to say. You could ask wizards of the coast by emailing sageadvice@wizards.com.

A Note

5e greatly acknowledges the importance of house rules in D&D culture, so I would not stick with the RAW reading of this. In that article linked above, written by Jeremy Crawford, one of the two lead designers for 5e, says:

We expect DMs to depart from the rules when running a particular campaign or when seeking the greatest happiness for a certain group of players.

The RAW just is not fun and takes the joy out of a critical hit. Come up with a rule that seems right (doubling to 2 damage, or going to 1d4 damage, or something else) for your group. In the words of Jeremy Crawford:

Fifth edition now belongs to the thousands of groups playing it.

Modify 5e to have fun in your group!

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    \$\begingroup\$ It should be noted that an Unarmed Strike is 1 + STR Modifier in damage. \$\endgroup\$ – DaveFY Aug 7 '15 at 19:25
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Its seems reasonable to double it, treating it as if it's a die that always rolls the same result. After all, it's hardly a critical hit if it doesn't do anything.

The alternative, taking the "Critical Hits" passage literally, would not just impact unarmed strikes and creatures that do a flat 1 hp of damage. It would also mean that a DM choosing to take the listed average for a monster's attack would not double the result either, because there are no dice to roll twice.

There is plenty of room for someone to declare that by RAW, 1 hp damage attacks and taking-the-average monster attacks cannot benefit from critical hits. Though it's a fair literal interpretation, it's one that gives weird side-effects contrary to expectations of how both game and world should work. It's also RAW to use one's judgement where the rules seem to miss a corner case, and I think this is a clear case of one such corner.

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    \$\begingroup\$ For what it’s worth, when I roll a critical hit, I use the listed (average) damage plus an actual die roll for the critical portion. I think I’ve even seen instructions to do it that way in one of the rulebooks or supplementary bits. \$\endgroup\$ – Bradd Szonye Feb 21 '15 at 1:32
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    \$\begingroup\$ @Bradd If you come across the cite again, that might be very enlightening. \$\endgroup\$ – SevenSidedDie Feb 21 '15 at 1:38
  • \$\begingroup\$ I couldn’t find it in the basic rules. I’ll try to remember to check my DMG when I’m home. \$\endgroup\$ – Bradd Szonye Feb 21 '15 at 1:42
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    \$\begingroup\$ Sadly, Jeremy Crawford supports the literal reading: "An unarmed strike deals 1 + Str. modifier damage, even on a critical hit." \$\endgroup\$ – Michał Politowski Jun 19 '16 at 8:35
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Unarmed strikes do not get damage multiplied on a critical hit

RAW

As other answers have said: critical hits only double damage that you roll.

Roll all of the attack's damage dice twice and add them together.

Unarmed strikes do not have any damage rolled. So, RAW, critical hits do not increase the damage of unarmed strikes. See [this Q&A][2] for further discussion of this.

Official designer clarification

Jeremy Crawford agrees and has clarified:

An unarmed strike deals 1 + Str. modifier damage, even on a critical hit.

Rules as Fun

If this rather literal ruling doesn't jive with you as a DM or with your players, then allow it. It is always a buzzkill when you roll a 20 and don't get anything good from it.

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