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The Animate Dead spell allows you to raise and control zombies or skeletons. The number changes with spell level, and a character's spell slots change as they level up too.

How can do I calculate the maximum number of undead controllable indefinitely with Animate Dead?

Not including items, feats, tricks, just the number/CR of undead per level that a character can control.

user-781943
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Animate Dead lets you raise 1 undead, and requires you to use the spell to reassert control over it every 24 hours. When cast with a spell slot of 4th level or higher, you can raise/reassert control over 2 additional undead for each slot level above 3rd.

  • 3rd Level Slot: 1 undead at a time
  • 4th Level Slot: 3 undead at a time
  • 5th Level Slot: 5 undead at a time
  • 6th Level Slot: 7 undead at a time
  • 7th Level Slot: 9 undead at a time
  • 8th Level Slot: 11 undead at a time
  • 9th Level Slot: 13 undead at a time

Animate Dead is available to Wizards, Clerics, Circle of Spores Druids, and Oathbreaker Paladins. The first 3 all have the full number of spell slots, while Oathbreakers have less.

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If we assume that CR is perfectly balanced, a full caster can multiply their power by using Animate Dead. A level 20 caster can create CR20 worth of zombies, incredible! However zombies have only 8AC, 22HP, +3 hit, 4 damage, 20ft speed, while skeletons have 13AC, 13HP, +4 hit, 5 damage, 30ft speed. Spending all your spell slots to maintain a shambling horde may not be an effective use of your abilities.

user-781943
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    This might be more than the question requires but it is worth noting that a level 20 Wizard can regain two 5th level slots per day allowing an additional 10 minions/2.5 CR –  Jul 01 '20 at 01:37
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    @Odo Definitely a good thing to be aware of. Cheers – user-781943 Jul 01 '20 at 01:56