The amount of levels the character will have to gain in order to gain a perk. (lower is better)”— Fallout Tactics in-game description
Perk rate is a derived statistic. It affects how often the character is allowed to pick a perk. A character's perk rate depends on his race and on certain traits such as Skilled (which increases the rate) or Fear the Reaper (which decreases it). Some perks, like Divine Favor, may decrease the perk rate as well.
Fallout, Fallout 2
In Fallout and Fallout 2 and Fallout Tactics, the perk rate is 3, which means that it is possible to pick a new perk every 3 levels. You are not able to save up perks to use at future perk acquiring levels. Any unselected perk will be lost forever at the next perk level if you do not select one before this time. E.g. level 3 > perk not chosen, level 6 > perk not chosen (level 3 perk point lost), level 9 > better criticals chosen (level 6 perk point lost).
In Fallout 3, the perk rate is always 1 - that is, you can pick a new perk every level.
Fallout: New Vegas
In Fallout: New Vegas, the perk rate is 2 - You can pick a new perk every 2nd level.
In Fallout 4, the perk rate is 1 again like in Fallout 3. Perks in-general have been changed in Fallout 4 and are directly related to the progression of the player's character.
In Fallout 76, the perk rate is 1 like in both Fallout 3 and Fallout 4. Similar to Fallout 4, perks are directly related to the progression of the player's character. At level 50 and on, the player is given a choice between picking a new perk or reallocating a SPECIAL point.
In Fallout Tactics, the racial perk rate for humans is 3, which means that they can pick a new perk every 3 levels. The rate is 4 for ghouls, super mutants and deathclaws, and 2 for dogs. Robots cannot pick Perks at all, i.e. their perk rate is infinity. You are able to save up perks to use at a later time. There is one Trait for Ghouls (Fear the Reaper) and one Perk (Divine Favor) which can improve the Perk Rate of characters. It is, therefore, possible to have Human and Ghoul characters with a Perk Rate of 2.
Fallout: Brotherhood of Steel
In Lionheart (a non-Fallout game using the SPECIAL system), the first perk is taken at Level 2, not 3, but the subsequent perks are taken every 3 Levels.