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The Distant Spell Metamagic option gives you the ability to double the Range of a spell, or give a spell with range of Touch a range of 30ft.

If I would apply this to, let's say, burning hands, which states as Range Self (15ft cone), would this increase the cone size to 30ft or would this cast the spell up to 30ft in front of you, with a 15ft cone still?

Other example, aganazzar's scorcher has a Range of 30ft, and the description states:

A line of roaring flame 30 feet long and 5 feet wide emanates from you in a direction you choose.

Now to me, this implies the same thing as burning hands, but the Range does not contain Self.

RAW I would allow the second case to increase the AoE effect if it is cast with Distant Spell, but not the first, since it is of Range self. But obviously this does not make any sense, so which one is the correct interpretation?

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    \$\begingroup\$ I have removed the code formatting from your question because that formatting is only supposed to be used when actual code is being referenced. This is important to people with text readers for example. \$\endgroup\$ – Rubiksmoose May 11 '18 at 17:47
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Distant spell says:

Whenever you cast a spell that has a range of 5 feet or greater, you can...double the range of the spell.

Distant spell cannot be applied to burning hands

Burning hands has a range of Self. Self is not a number that is 5 feet or greater, therefore you cannot apply Distant Spell to it.

Note that Touch and Self are not the same range. Touch can be applied to any creature upon contact but self only affects the caster.

Jeremy Crawford supports this exact case with a ruling on Twitter:

Distant Spell works only on spells that have a range of 5 feet or greater or a range of touch. That doesn't include spells with a range of self.

Aganazzar's scorcher has its range doubled but not its area

Aganazzar's scorcher has a range of 30 feet. When distant spell is applied to it it will double to 60 feet.

However, it seems that the range does not have any applicability to the spell's effects. Since the line of fire emanates from the caster it seems there is nothing for the range to actually refer to. As written, the spell operates identically to a "Self (30ft line)" spell and perhaps was intended to be written as such.

Regardless, as written, the range would double to 60 feet, but it would have no effect on the length of the line because there is no indication that the two are linked in any way.

Jeremy Crawford seems to support this opinion indirectly via Twitter:

Q: Metamagic Dista[nt] Spell = Sunbeam range increases from 60 ft line to 120 ft line for duration of concentration?

A: Distant Spell can change the range of a spell, not the size of an area of effect created by the spell.

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    \$\begingroup\$ Could you clarify or expand upon the following: "Burning hands has a range of Self. Self is not a number that is 5 feet or greater" in particular, burning hands does not have a range of Self, it has a range of "Self (15 foot cone)" which does include a number that is 5 feet or greater. Could you explain why the parenthetical can be ignored? \$\endgroup\$ – Medix2 Nov 11 '20 at 14:31
  • \$\begingroup\$ @Medix2 You're conflating Range and Area of Effect. Per the PHB, Range is expressed as a simple distance or as "Self." 15ft Cone is a description of the Area of Effect, because Range cannot be a cone--that's an AoE shape, not a Range measurement. This is especially clear if you look at the presentation format used by D&D Beyond--there, the format is always "Range (AoE)." For example, Fireball is listed as 150 ft (20 ft [sphere]), and Lightning Bolt is Self (100ft [line]). Range and AoE are discrete attributes of a spell...Distant Spell only modifies Range, i.e. the point of origination. \$\endgroup\$ – guildsbounty Nov 11 '20 at 15:51
  • \$\begingroup\$ Put more simply... Range is how far away from you the magical effect can Originate, while Area of Effect is how large of an area it impacts. Distant spell lets you relocate the point of origination (boosts Range), not increase the AoE. \$\endgroup\$ – guildsbounty Nov 11 '20 at 15:56
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Distant Spell

When you Cast a Spell that has a range of 5 feet or greater, you can spend 1 sorcery point to double the range of the spell.

When you Cast a Spell that has a range of touch, you can spend 1 sorcery point to make the range of the spell 30 feet.

As you said it makes no mention of self only double distance or if it is touch it becomes 30 ft. So RAW no self spells can't be influenced by this however as always DMs decision is all that matters really.

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