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From page 164 of the PHB (here is the equivalent section of the Basic Rules):

Spell Slots. You determine your available spell slots by adding together all your levels in the bard, cleric, druid, sorcerer, and wizard classes, half your levels (rounded down) in the paladin and ranger classes, and a third of your fighter or rogue levels (rounded down) if you have the Eldritch Knight or the Arcane Trickster feature. Use this total to determine your spell slots by consulting the Multiclass Spellcaster table.

If I have a level 3 ranger and multiclass into paladin, how are my available spell slots calculated?

  • (ranger/2, rounded down) plus (paladin/2, rounded down)
  • (ranger + paladin)/2, rounded down

Which one is it?

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Your second way.

"... by adding together all your levels" would mean that your second example (ranger + paladin)/2 rounded down is how you'd work it. The rule doesn't have you segregate the levels before dividing if they are the same category. The example given in the book is a case of two different categories being combined, otherwise it would not have arrived at 5th level.

In your example, the result is 2 on the table, giving you 3 first level spells total for both this level and the next level you attain (be it 3/2 or 4/1).

The categories boil down to four the way the rules are presented:

*Note: (Thanks @Nick) As a practical matter, for both Ranger and Paladin, some DM's will rule that you would use the multiclassing spell rules once you are level 2 since both of those classes have their spellcasting feature come on line at 2d level. (See the tables and class description for each class). Ruling that once spellcasting is 'turned on' by one class it is always on will not break the game.

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Your first way is correct

According to Jeremy Crawford's tweet here:

Multiclass spell slots: when dividing the levels of multiple classes, you divide, round down, and then add the results together.

Also remember Paladin and Ranger don't have the spell casting feature until 2nd level so you can't add them until you have at least 2 levels in either class. Which is another indicator that you round down before adding.

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    \$\begingroup\$ Since Crawford's tweets are no longer considered official rulings, you may want to expand your answer to support it by citing the rules (or perhaps by pointing out that the rules are ambiguous and so this is the best indication of designer intent, if that is instead the case). \$\endgroup\$ – V2Blast Aug 2 '19 at 4:24
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As much as I am loathe to say it in any answer...

Consult your DM

The rules on what order to add levels together, when to divide, and when to round are unclear. The normal rules of mathematical operations can't help us because it's not actually presented as an equation. The language used is imprecise - it doesn't use any words that indicate order of operations or grouping (such as "then" or "combined").

Unfortunately, the guy who's supposed to provide clarity refused to do so:

Q: RAI, it seems multiclassing shouldn't be terrible. RAW, due to rounding, an EK5/AT5 doesn't have 2nd lvl spells. Thoughts?

A: Multiclassing—this optional rule is designed to make class combinations possible, not necessarily ideal. Work with your DM to fine tune.

Jeremy Crawford, via Twitter

When told the question was being asked from an AL standpoint, where "DM discretion" can't be consistently applied, he declined to provide any further response.

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  • \$\begingroup\$ I just realized the one who'd made the tweet he was responding to there was you... :) \$\endgroup\$ – V2Blast Apr 1 at 4:22
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    \$\begingroup\$ @V2Blast Yup... at the time, he was the source. His response was disappointing. \$\endgroup\$ – T.J.L. Apr 1 at 12:30
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The first way is correct, as further evidenced by the introduction of the Artificer in Eberron: Rising from the Last War.

The optional artificer multiclassing rule for spell slots says:

Add half your levels (rounded up) in the artificer class to the appropriate levels from other classes to determine your available spell slots.

First, this confirms that at the very least, when one of your half-caster classes is Artificer, you divide your levels in Artificer, then round them up, before adding them to anything else. If you are a multiclass Artificer/Paladin, the second way listed in the OP (add first, then divide and round) is simply incompatible with the rules for artificer. The rules listed here for artificer demonstrate that the intent is that the dividing and rounding occurs before adding the results together.

To be clear, this is my argument: the Artificer's multiclassing rules are improving the Artificer's implementation of an existing mechanic not introducing a new mechanic entirely. If the correct ruling was "add first, then divide and round", then the Artificer's rules represent a completely new method that we have to add on top of the existing one. If the correct ruling is "divide and round first, then add", the Artificer's rules just changes the direction of the rounding in the already established mechanics for mutliclassing half casters.

I argue that change to an existing mechanic is more likely to be the correct ruling than a new mechanic that must be considered in addition to the original. And you may disagree. But I am adding to the body of evidence for a particular ruling that in this answer was only given JC tweet evidence.

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    \$\begingroup\$ I would disagree with this. All the artificer does is add on artificer/2(round up) to the end of the things you add up. So it's fullcasters + (Paladins+Rangers)/2 round down + Artificer/2 round up + (EK+AT)/3 round down. The artificer is rounded separately, and doesn't inform the paladin+ranger issue at all. \$\endgroup\$ – Nick Jul 6 at 14:29
  • \$\begingroup\$ Perhaps worth noting is that the OP's Ranger 3 would actually change nothing when immediately multi-classing into Paladin. In other words, a Ranger 3 and a Ranger 3 + Paladin 1 would have the exact same spell slots regardless of the rounding method used \$\endgroup\$ – Medix2 Jul 6 at 14:55
  • \$\begingroup\$ I'm gonna have to go with @Nick on this one - this is a specific rule that applies only to the Artificer. It doesn't provide any insight to the equally specific rules in the PHB. This does not change the PHB, only errata can do that. Of course, by the Twitter exchange in my answer, it's all working as intended and you're supposed to "work with your DM to fine tune". \$\endgroup\$ – T.J.L. Jul 6 at 18:47
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    \$\begingroup\$ Im not saying the artificer rule applies in any way to any class besides artificer. Im just arguing that it makes more sense that the artificer rule be a special case of the rule for other half casters. \$\endgroup\$ – Thomas Markov Jul 6 at 18:49

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