How do Sneak Attacks affect damage in Fallout 4?

Solution 1:

In FinalDamage, of which the formula is as follows:

FinalDamage = PaperDamage x SneakAttackMulti x DamageCoeff × HeadshotMulti

The SneakAttackMulti is the value you're looking for.
This value directly corresponds to the Ninja skill sneak attack multiplier bonuses (e.g. Rank 1 having 2.5 ranged and 4 melee attack damage multiplier), but is, as mentioned in the comments, influenced by other skills and effects (like the Mister Sandman perk, which grants a(n additional) multiplier of up to 0.5 (under certain circumstances), or the unique Pickman's Blade, which adds 0.6 to SneakAttackMulti).

If requesting this information is also intended for playthroughs, be sure - unless you use the Unofficial Patch - to select the associated skills in the right order, as pointed out here, or you might miss out on the full bonus.