Once per turn when you hit a creature with your pact weapon, you can expend a Pact Magic spell slot to deal an extra 1d8 Force damage to the target, plus another 1d8 per level of the spell slot...
What spell slot? I am not sure what the rule is talking about so I don't know how to calculate it.
It refers to the spell slot you're expending to use this ability, as mentioned earlier in the sentence:
Once per turn when you hit a creature with your pact weapon, you can expend a Pact Magic spell slot to deal an extra 1d8 Force damage to the target, plus another 1d8 per level of the spell slot.
What you're doing with this ability is spending a Warlock spell slot to deal extra damage on an attack with your Pact of the Blade weapon. The damage scales up with the level of the spell slot you use.
As Wagnarokkr says, it's the level of the Pact Magic spell slot you expended. You can confirm the level of your Pact Magic Spell Slot via the Warlock Feature Table. A 5th level Warlock would have 3rd level pact magic slots, giving 1d8+3d8 for 4d8. A 9th level Warlock would have a 5th level pact magic slot for 1d8+5d8 for a total of 6d8. As pact magic doesn't go above the 5th level, this would be the effective cap.
Notably critical hits will double the number of damage dice rolled for an Eldritch Smite.
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The 2024 PHB description is
Once per turn when you hit a creature with your pact weapon, you can expend a Pact Magic spell slot to deal an extra 1d8 Force damage to the target, plus another 1d8 per level of the spell slot...
What spell slot? I am not sure what the rule is talking about so I don't know how to calculate it.
It refers to the spell slot you're expending to use this ability, as mentioned earlier in the sentence:
Once per turn when you hit a creature with your pact weapon, you can expend a Pact Magic spell slot to deal an extra 1d8 Force damage to the target, plus another 1d8 per level of the spell slot.
What you're doing with this ability is spending a Warlock spell slot to deal extra damage on an attack with your Pact of the Blade weapon. The damage scales up with the level of the spell slot you use.
pronouns: he/she/they
As Wagnarokkr says, it's the level of the Pact Magic spell slot you expended. You can confirm the level of your Pact Magic Spell Slot via the Warlock Feature Table. A 5th level Warlock would have 3rd level pact magic slots, giving 1d8+3d8 for 4d8. A 9th level Warlock would have a 5th level pact magic slot for 1d8+5d8 for a total of 6d8. As pact magic doesn't go above the 5th level, this would be the effective cap.
Notably critical hits will double the number of damage dice rolled for an Eldritch Smite.