# How are numerical bonuses combined?

Are there explicit rules for combining numerical bonuses in 5th edition, or is it just left implicitly to "common sense"? There are special cases (e.g. damage resistance and vulnerability, choice of base AC formulae, identical spell/item effects) which are well-defined, but I can't find a general rule.

# Additive and multiplicative bonuses

Example: Longstrider and Haste for a creature with 30' base walking speed.

Longstrider: You touch a creature. The target’s speed increases by 10 feet until the spell ends.

Haste: Choose a willing creature that you can see within range. Until the spell ends, the target’s speed is doubled [...]

Possible interpretations:

• Always multiply first: (30' × 2) + 10' = 70'
• Always add first: (30' + 10') × 2 = 80'
• Do it in the order the spells were cast
• Player chooses
• GM chooses

# Multiplicative bonuses with one another

Example: Haste and Boots of Speed for a creature with 30' base walking speed.

Boots of Speed: While you wear these boots, you can use a bonus action and click the boots' heels together. If you do, the boots double your walking speed [...]

Possible interpretations:

• Doubling the second time just idempotently repeats the fact that it's been doubled: max(30' × 2, 30' × 2) = 60'
• Doubling the second time means your speed is quadrupled: 30' × 2 × 2 = 120'
• Doubling the second time adds another 100% of your base movement, resulting in an overall tripling: 30' × (100% + 100% + 100%) = 90'. This was the rule in 3rd edition.
• Do you see any examples in the rules about numbers other than movement? Currently the actual question is exclusively about movement, so it should have its tags and title edited to match. If there are other examples where the distinction matters (money math perhaps), then that would be different. Commented Jul 6, 2016 at 19:55
• Commented Jul 6, 2016 at 22:07
• @7SD I chose examples from movement, but the question would also apply to other bonuses to numerical values, e.g. ranges, durations. Sorcerer metamagic springs to mind. Commented Jul 7, 2016 at 0:17

## The order in which the spells were cast matters

Dnd-5e has no ordering system for combining effects. In many video games, there is a set order, usually on a per-effect basis, which means that Spell A + Spell B == Spell B + Spell A. The system checks for these modifiers in the same order every update.

In Dnd-5e, there is no set ordering system. Because there is no explicit ordering system, we cannot assume one exists. If we say that Haste and Longstrider always combine the same way, we are assuming there is a rule that is not actually in play. It may be easier and indeed smarter to say that you always multiply and THEN add, or add and THEN multiply, but such a rule does not exist.

Thus, we must conclude that the order in which the spells are cast matters.

## How do the spells stack and unstack?

PHB pg. 205 (emphasis added)

Combining Magical Effects

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.

This means only that the effects stack. Whether or not the effect is multiplication or addition is irrelevant. It does not hold any bearing on which order the math is done in. It uses added not as a calculation word, but as a word that is directly opposed to replaced. Without this clause, we might think that Haste replaces Longstrider, or vice versa. The math is not being referenced here, only the generic effect. The effects are combined, whatever they are, in the order that they are cast.

It also means that you're only adding the effects while the durations overlap. So if, for instance, Haste ends before Longstrider, you aren't dividing your speed by two, you're simply ONLY adding 10 to your base speed. So, when a spell ends, you should recalculate all spell effects on the speed. No matter the order that the spells began, when one ends you recalculate the new speed. If Longstrider ends early, you recalculate your speed with Haste, which would be 60 (30 × 2). If Haste ends early, you recalculate your speed with Longstrider, which would be 40 (30 + 10). Without a specified order of operations for spells, this is the simplest way to ensure that your speed doesn't get permanently modified due to awkward subtractions of spell effects.

Additionally, if you look at the spell descriptions for Haste and Longstrider, there is no reference to a "base" speed, or "original" speed. Thus, we must conclude that speed is your "current speed".

If you cast Haste first and then Longstrider

• Speed = 30
• Haste Speed = 30 × 2 = 60.

Until the spell ends, the target’s speed is doubled.

• Longstrider Speed = 60 + 10 = 70

The target’s speed increases by 10 feet until the spell ends.

If you cast Longstrider first and then Haste

• Speed = 30
• Longstrider Speed = 30 + 10 = 40
• Haste Speed = 40 × 2 = 80

So, while this may seem silly, it is the way things are. There is no explicit ordering system, so you must use the order in which the spells were cast. Obviously, a DM could rule differently, but this is how the rules are written.

Obviously, to ensure maximum speed, you want to cast Longstrider, then have someone give you Haste, then the Boots of Speed.

• Longstrider speed = 30 + 10 = 40
• Haste speed = 40 × 2 = 80
• Boots of Speed speed = 80 × 2 = 160 feet

Wow, that's really fast! But, it's not the fastest

• Comments are not for extended discussion; this conversation has been moved to chat. Commented Jul 7, 2016 at 1:54

Source: PHB pg.206 under Casting a Spell - Combining Magical Effects, emphasis mine.

Combining Magical Effects

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.

So in your case of Haste and Longstrider, the total cumulative speed bonus on a base movement 30' creature would be 70'.

Broken down as follows:

• Your movement speed = 30
• Longstrider = +10
• Haste = +Your movement speed (+30)

Therefore, 30 + 10 + 30 = 70.

In the case of the boots and haste, it's still referenced off of YOUR movement speed. Which means:

• Your movement speed = 30
• Boots of Speed = +Your movement speed (+30)
• Haste = +Your movement speed (+30)

This would bring the total to 90.

• Comments are not for extended discussion; this conversation has been moved to chat. Commented Jul 7, 2016 at 1:54

# There are no general rules that explain how adding/multiplying bonus work in general

As you say there are a variety of specific cases of how to add or multiply certain things together in the game, but there is no general rule covering when and how to add multiply that applies to every feature in the game. As such each case is up to the DM to adjudicate. As you say, the best we can do is apply common sense judgements at our table and try to remain consistent.

Obviously a negative is impossible to prove, but I have searched every published book, Unearthed Arcana, and Sage Advice (Tweets and compendium), and there is no general rule to be found in any of them.