Casting multiple spells in a single round

If you don't cast a bonus action spell you can cast as many as you have actions and reactions

As long as the bonus action is used for something that isn't a spell you can cast as many spells as you have actions and reactions. Without something else granting extra actions you are realistically limited to 3 spells.

For example: Fighter 2 Wizard 18 uses action surge to cast fireball, gets counterspelled, counterspells the counterspell as a reaction, uses other action to cast cloudkill.

If you cast a bonus action spell you can still cast shield or counterspell as long as it is not on your turn.

Turns and rounds are not the same, the bonus action restriction is only on your turn, not the whole round.

RAW is a bit vague in possible interpretations (particularly given the way English -- US or UK -- can be). As a matter of practice as used by Chris Perkins, Matt Mercer, and as indicated in Sage Advice by Crawford, a spell cast as a reaction is "outside" the usual scope of Action/Bonus Action/Action Surge parameters (hence, why Crawford indicated that a wizard could cast Fireball as his action, have someone else attempt to Counterspell it as their Reaction, but the initial caster then use his own Reaction to support/"protect" the Fireball spell with his own Counterspell. Given the rest of game balance, a character could cast a Bonus Action spell, an Action Cantrip, and have a Reaction-appropriate spell (whether a Shield or Counterspell, as full spells, or where applicable a Cantrip, unless the character has Warcaster which would allow their Reaction to be a "full" spell, as it were, targeting the opportunity-inducing source, which keeps it in-sync with a normal Reaction spell, as it were).

Situational instances like Action Surge (which require no "action/bonus action" for a character to use) could rightly be interpreted as allowing another Cantrip -- particularly as Action Surge isn't common among most casters and is of very limited "ammo", as it were -- realistically only usable once per rest unless the character is of considerable high-level multi-classing so as to get more than one Surge... and at that point, it really doesn't matter because the challenges most characters will face at those levels aren't going to be overcome by some random "bonus" Cantrip...

As far as I know you can actually cast 5 (or 4 depending on interpretation of bonus action spell rules) in a round if you have taken 1 level as a wild magic sorcerer and 2 levels as a fighter. The relevant oddities are

• Fighter's action surge

  Starting at 2nd level, you can push yourself beyond your normal limits for a moment. On Your Turn, you can take one additional action on top of your regular action and a possible Bonus Action.

• Roll on the Wild Magic Surge (WMS) table and hit 81-82 (on a d100 roll). There are a couple of conditions that trigger the following:

  the DM can have you roll on the Wild Magic Surge table immediately after you cast a sorcerer spell of 1st level or higher.

• Entry 81-82 on the WMS table reads:

  You can take one additional action immediately.

So your five spells could look like this:

• Cast a cantrip as an action.
• Cast a level 1+ bonus action sorcerer spell spell (can use sorcerer's quicken spell to make an action spell a bonus action spell). Roll on the WMS table and hit 81 or 82.
• Cast a cantrip using this extra action from Wild Magic.
• Cast a cantrip using the action from Action Surge.
• Cast a reaction spell (e.g. shield).

Note: If you interpret the bonus action spell rule

You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.

to mean you can only cast one other spell during the entire turn, then you can only cast 4 (strike the bonus actions spell from the above list and instead hit the WMS on one of the other two action spells).

Although Miniman's answer seems the most straightforward, there seems to be one thing most answers on this page are not taking into account, which is the RAI in this Sage Advice Compendium entry:

Can you also cast a reaction spell on your turn? You sure can! Here’s a common way for it to happen: Cornelius the wizard is casting fireball on his turn, and his foe casts counterspell on him. Cornelius has counterspell prepared, so he uses his reaction to cast it and break his foe’s counterspell before it can stop fireball.

The casting time for Counterspell is "1 reaction, which you take when you see a creature within 60 feet of you casting a spell," and it is a "3rd level abjuration."

This example has a wizard casting a spell as an action, and as a reaction, and neither are cantrips with a casting time of 1 action.

This contradicts and calls into question the the text in the Player's Handbook regarding how many spells can be cast in a turn, or round.

It also contradicts Miniman's statement "So if you cast a bonus action spell and a regular action cantrip, then trigger an AoO in the same turn, you would not be able to use your reaction to cast Shield."

Perhaps the text should read:

You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action, and/or a spell with a casting time of 1 reaction.

Additionally, I agree that the use of "a cantrip" is ambiguous in that it could be read allowing multiple cantrips, and that reading isn't game-breaking. With that reading you have bonus + action + reaction + action surge + action surge = 5. I don't think it would be game-breaking to take it one-step further (which would also simplify things) by saying "You can cast one spell with a casting time of bonus action, one spell with a casting time of 1 action, one spell with a casting time of 1 reaction, and any additional spells which are cantrips with a casting time of 1 action." I say "simplify," because I have seen in play many casters lose track of this anyway, and cast an extra spell they shouldn't have with no one noticing.

I am not sure if any abilities can give you more reactions, but if there were such things, given the above ambiguities, it seems you could cast more spells that way also.

You can cast an unlimited number of spells in a turn provided infinite luck. You can keep casting spells provided each time you cast a spell you get a 1 on the surge roll and you roll 81-82 on the surge table. That effect gives you an additional action which could be another spell. Also you could just surge into a spell that surges into a spell to go beyond your provided spell slots.

I'd argue that you could "effectively" get 6 spells in a turn, and 7 in a round, if you consider twinned spell to be the equivalent of casting two spells (technically it's casting one spell with two targets. But for all intents and purposes, you're doing a spell twice.). The metamagic text states "you can use only one Metamagic option on a spell when you cast it unless otherwise noted" but it does NOT state you can only use it once per turn. Therefore, you can add a metamagic to every spell you cast on a turn. So you could have something like:

• Cast a bonus action spell ("magic initiate" feat, one of 'Compel Duel, Grasping vines, Hex, Hunter's Mark, Sanctuary, or Shield of Faith').
• Twin above to a second target.
• Cast a cantrip as an action
• Twin above cantrip to a second target
• Cast a cantrip using the extra action provided by the Fighter's feature Action Surge feature.
• Twin above Action Surge cantrip to second target
• Cast a cantrip as a reaction

An additional tack; with action surge you're taking a second full action, but none of your spells are being cast as a bonus action, therefore the text under the bonus action section does not apply (I don't remember reading any restrictions or similar text in any other part of the PHB, please correct me if I'm wrong). That would mean you are not limited to the restriction of casting additional spells as cantripts. Add on a reaction spell, and in one round you can do something like this with a sorcerer(13)/fighter(2):

• action- finger of death: 7d8 + 30 necro dmg + humanoid raised as zombie if killed
• twinned (7sp)- same as above
• action (action surge)- disintegrate: 10d6 + 40 force + turns to dust if killed
• twinned (6sp)- same as above
• reaction- hellish rebuke: 2d10 ("magic initiate" feat)

Could be fun... Either way, it's less spells, but far more damage output in a single turn.

Under Cast a Spell it says not limits on casting more than 1 spell a turn:

PhB pg 192. Casting a Spell: Spellcasters such as wizards and clerics, as w ell as many monsters, have access to spells and can use them to great effect in combat. Each spell has a casting time, which specifies whether the caster must use an action, a reaction, minutes, or even hours to cast the spell. Casting a spell is, therefore, not necessarily an action. Most spells do have a casting time o f 1 action, so a spellcaster often uses his or her action in combat to cast such a spell. See chapter 10 for the rules on spellcasting.

From Chapter 10 rules on spellcasting, it has already been stated above what the rules are for Bonus Action + Cantrips. Various people above have tried to use this Entirely out of context, adding in "Action" where the qoute (which they used) states nothing of the sort.

Yes: when you use a spell with a time of Bonus Action, you can only use a Cantrip in the same round.

YET: when you are an Eldritch Knight, you can a.) Cast True Strike and b.) Action Surge c.) Cast Firebolt with the Truestrike effect on the attack roll. This is exactly what Action Surge is intended to do, and it has a cost for those wanting to dip 2 lvls into Fighter to gain it: lack of 20th lvl caster ability (which in the case of most pure casters is painful).

House-ruling the opposite of this makes Eldritch Knight need further house-ruling to come back into usefullness, or Blade Ward/Truestrike need house ruling. Just keep it simple and don't worry about that extra spell IF it happens. I'm involved in 3 different Adventure League campaigns, 4 home campaigns, and have yet to see anyone bother to even think about taking 2lvls of Fighter to add to their caster.

The maximum spells you can cast in a round is 3. Generally it's going to actually be only 2 on your turn, since reactions are usually outside of your turn.

On page 159 of PHB:

You can only take one bonus action on your turn, so you must choose which bonus action to use when you have more than one available.

Quicken Spell, Action Surge, or a spell that has a normal casting time of 1 Bonus Action all require your bonus action for the turn, so you can only choose one of them each turn.

On your turn you can:

• Move up to your max movement, reduced by various factors and broken up between actions

• Perform 1 Action

• Perform 1 Bonus Action if you have an ability that allows you to use it

• Perform as many Free Actions as your GM allows.

You also have 1 Reaction per round, which is generally outside of your turn, but doesnt have to be.

The book makes this very clear with no room for misinterpretation.

The maximum number of spells a character can cast in a round is 5

You can do the following:

• Cast a cantrip as an action
• Cast a bonus action spell (either one with a casting time of a bonus action, or as a Sorcerer, quicken a regular spell with the casting time of an action).
• Cast a cantrip as a reaction before your turn (e.g. if you have PAM and war caster feat, enemy approach within your melee range triggering AO casting)
• Cast a cantrip as a reaction after your have reaction reset at the start of your turn. (e.g. Dissonant Whisper to drive the target away for triggering AO casting)
• Cast a cantrip using the extra action provided by the Fighter's feature Action Surge feature.

This provides you with the maximum possible spells in a turn. In practice the maximum is 2. One as a bonus action, and then a cantrip as an action, and even more generally, you'll only be casting one spell on your turn, and then perhaps a cantrip as a reaction if you have the War Caster feat.

As Miniman points out, the distinction between turn and round is quite important here. A turn refers to a creature's actual turn whereas a round is comprised of all of the turns before your turn begins again. So you gain a new reaction on each of your turns, but you don't have to use it on your turn (And in fact, it's quite hard to do so). Usually you use your reaction on someone else's turn and thus you would be able to cast a spell as a reaction (such as Shield, or via War Caster).

The maximum number of spells a character can cast in a round is 3. You can only take 1 reaction per round, although some monsters have an ability that allows them to ignore this restriction.

You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.

This means that you can cast a bonus action spell and a regular action cantrip on your turn, and a reaction spell at some point in the round that is not your turn.

A round consists of every creature in the combat taking a turn. This means that you are free to use your reaction in the same round, as long as it's not on your turn.

It's very difficult to trigger a reaction on your own turn anyway, since most of the triggers for reactions are your character's reaction to something else. The only exception I can think of is moving such that you trigger an attack of opportunity, since being attacked is a trigger for a number of reactions.

So if you cast a bonus action spell and a regular action cantrip, then trigger an AoO in the same turn, you would not be able to use your reaction to cast Shield. But if you were attacked after your turn had ended, you would then be able to cast Shield.

Largely unnecessary caveat

There is one point which confuses the issue a bit - the Fighter's Action Surge ability.

You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.

This can be interpreted as meaning either you can cast a single cantrip with a casting time of 1 action in the same turn, or, you can only cast cantrips with a casting time of 1 action in the same turn. If the former, the maximum is 3 as written above. If the latter, you can cast 4 as written in this answer.

Personally, while I'm not sure of the RAW answer here, if a player wanted to waste use their Action Surge on casting a cantrip I would definitely allow it.

Reference: PHB, p. 202.