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Spell Sniper says

When you cast a spell that requires you to make an attack roll, the spell’s range is doubled.

Distant Spell says

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.

Would my Fire Bolt go 240 feet, 360 feet or 480 feet if I use both?

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RAW both effects apply, but it's not clear if the range should be 480 or 360. It depends on if you interpret double as "x2" or "+100%". While previous editions of the game made it clear that "doubling a double is a triple," as far as I can tell 5e doesn't tell you what to do either way.

However, this exact question was asked to Jeremy Crawford on Twitter, and he responded that the range should be 480:

ChaosDingus
@ChaosDingus
@JeremyECrawford If you have Spell Sniper and use Distant Spell, is the range quadrupled?
12:06 PM - 27 Sep 2015


Jeremy Crawford
@JeremyECrawford
@ChaosDingus Yep!
10:06 AM - 12 Oct 2015

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480 Feet

Why? Firebolt has a default range of 120ft. If you have the Spell Sniper feat, which is always active, your Firebolt range increases to a permanent 240ft.

Now, each time you cast Firebolt, the range is locked in at 240ft.

Should you choose to use Distant Spell, which doubles the range, it doubles 240ft to 480ft .

Once Spell Sniper applies, 120ft doesnt exist anymore for Firebolt.

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