44 spells
You start with 6 spells, and learn 2 every time you level up. That means that at level 20 you have 44 spells.
How strong is a level 20 DND wizard?
A 20th level wizard is likely to have around 188 hitpoints, so that is likely to kill the wizard.
What level do you get third level spells?
When you reach 20th level, you gain mastery over two powerful spells and can cast them with little effort. Choose two 3rd-level wizard spells in your spellbook as your signature spells.
How many spells does a 3rd level Wizard know?
Each time you gain a wizard level, you can add two wizard spells of your choice to your spellbook. So, assuming you have a 16 Int, a third level Wizard can prepare 6 spells (3 int mod + 3 level), and your spellbook should contain 10 spells, probably 8 1st level and 2 2nd level.
What happens when a wizard reaches level 20?
What happens if a wizard reaches level 20 but has no 3rd-level spells that they can use with the Signature Spells feature? At level 20, a wizard gains the Signature Spells feature.
How many spells does a 3rd level wizard have?
For example, if you’re a 3rd-level Wizard, you have four 1st-level and two 2nd-level Spell Slots. With an Intelligence of 16, your list of prepared Spells can include six Spells of 1st or 2nd Level, in any combination, chosen from your Spellbook.
When do you increase the power of a wizard spell?
Starting at 14th level, you can increase the power of your simpler Spells. When you cast a Wizard spell of 1st through 5th Level that deals damage, you can deal maximum damage with that spell. The first time you do so, you suffer no adverse Effect.
How much damage does a 5th level wizard do?
When you cast a Wizard spell of 1st through 5th Level that deals damage, you can deal maximum damage with that spell. The first time you do so, you suffer no adverse Effect. If you use this feature again before you finish a Long Rest, you take 2d12 necrotic damage for each level of the spell, immediately after you cast it.