A Wizard knows between 9 and 290 spells in 5e, depending on their level and access to spellbooks. A 1st-level Wizard knows six 1st-level spells and three cantrips. Each time a character gains a Wizard level, they learn two additional Wizard spells for which they have spell slots.

On this basis alone, a Wizard will know the following number of Wizard spells at each level:

Additionally, a Wizard can copy any Wizard spell of 1st-level or higher from a spell scroll or spellbook into their own spellbook. This costs 50 gp and requires 2 hours per spell level (e.g., a 5th-level spell costs 250 gp and takes 10 hours to learn).

Making a copy of this spell book requires 10 gp and 1 hour per spell level. This is important because if a Wizard loses their spellbook, they also lose all the spells they don’t have prepared at the time of the spellbook’s loss.

Because of this system, a Wizard can technically know every 1st-level spell or higher on the Wizard class spell list, totaling 285 spells (counting only those in the Player’s Handbook, Xanathar’s Guide to Everything, and Tasha’s Cauldron of Everything). A Wizard can learn a maximum of 5 cantrips starting at 10th level. Together, this means the maximum spells a Wizard can know is 290.

A Wizard can technically achieve this feat at 17th level. However, most campaign settings don’t feature enough spell scrolls and/or spell tomes to allow for a Wizard to actually learn every spell on their spell list by 20th level.

Note that multiclassing, especially to a class with access to more cantrips and primal/divine spells, can net a character an even greater number of spells.

Player’s Handbook, page 113-4

Matt Zane

Author, DnD Lounge

Matt Zane started DnD Lounge in 2021. Matt began playing DnD 5e in 2015, and has been DMing since 2017. He loves optimization, but also enjoys looking for creative ways to use spells and abilities that follow the spirit and letter of the rules. He also eschews pure optimization in favor of a more balanced approach, where building a character is primarily about serving an interesting story arc and party dynamics rather than maxing out DPR.