Attack speed (AS or ASPD) is a stat that is the frequency of a unit's basic attacks. They are measured and displayed as attacks per second.
Each champion starts with a certain base attack speed, and some bonus attack speed is gained at each levelup.
Additional bonus attack speed can be obtained with a variety of items, abilities and runes. Bonus attack speed stacks additively, and each bonus point acquired directly affects its statistic. Bonus attack speed is a percentage of the base attack speed. Therefore, champions with higher base attack speed benefit more from bonus attack speed.
Attack speed cannot be increased beyond 2.5 attacks per second (or 1 attack every two fifths of a second, or 0.4 seconds).
Calculations
Base attack speed
Every champion's base attack speed (AS_{base}) is calculated using a hidden variable called attack delay,^{[1]} which ranges from −0.10 to 0.3. As AS_{base} is the value that is modified by bonus attack speed, and the amount shown at level 1 for most champions (excepting those with bonus attack speed at level 1), it is the value shown on the League of Legends Wiki.
$ \pagecolor{Black}\color{White}{\it AS}_{\rm base} = {0.625 \over 1 + {\it attack\ delay}} $
Bonus attack speed sources
 Champions gain an attack speed percentage every time they level up, which ranges from roughly 0  6% (the exact number depending on the specific champion) and can be calculated through the statistics growth formula.
Bonus AS% stacks additively.
 Example: grants +35% attack speed and also grants +50% attack speed, so the champion gains +85% in total.
Notes:
 Final attack speed cannot go above the cap of 2.5 attacks per second.
 Many ingame tooltip percentages (such as runes) have been rounded, so results may be slightly different unless the precise numbers are known.
Example
 Calculating base attack speed:
 attack delay is −0.04.
 $ \pagecolor{Black}\color{White}{0.625 \over (1  0.04)} = {0.625 \over 0.96} = 0.651041 \overline{6} $. This is base attack speed, seen at level 1 (without runes, etc.).
 The number seen in game is rounded to 3 decimal places: 0.651.
 Calculating "bonus attack speed":
 Every time statistics growth formula.
 At level 18 he has gained $ \pagecolor{Black}\color{White}3.22\% \times\left({7 \over 400}\times(18^21)+{267\over400}\times(181)\right)=54.74\% $ as bonus AS%.
levels up, he gains bonus AS% based on percentage growth 3.22% and his level through the  At 18 he has maxed increasing his attack speed by 30%.
 Let's say he has the rune to 3%.
 Let's also say he has : +35%.
 All together he has: 54.74% + 30% + 3% + 35% = 122.74% bonus AS% or 1.2274 bonus AS as a decimal.
 Every time statistics growth formula.
 Final calculation:
 $ \pagecolor{Black}\color{White}\begin{align} & {0.625 \over 0.96} + \left({{0.625 \over 0.96} \times 122.74\%}\right) \\ =& 0.651041\overline6 + ({0.651041 \times 122.74\%}) \\ \approx & 1.450128 \end{align} $
 In game, the number will be shown as: 1.450.
Attack speed as scaling
The major part of champion abilities that use attack speed will scale with base attack speed. But some abilities scale with the total or bonus attack speed the champion has.
Champions
Increasing attack speed
Items
Item  Cost  Amount  Availability 

Champion abilities
Allytargeted
User only
 and
 and
 and
 and
 and
Runes
Decreasing attack speed
Attack speed reductions stack multiplicatively and take percentages off the final attack speed value after all bonus attack speed has been factored in. Attack speed reductions are affected by Tenacity, but not by Slow resist.
Items
Champion abilities
 and
Capped attack speed
The majority of champions are capped at 2.5 attacks per second. But some champion abilities make it impossible to reach that cap:
Notes
 All percentages listed in a champion's attack speed statistic are approximations.
 Many abilities can scale indirectly with attack speed (for example, through the flat cooldown reduction per attack with ).
List of champions' attack speed
Champion Level  Top 5 champions  Bottom 5 champions  

Level 1  1.  0.8 AS  1.  0.481 AS 
2.  0.749 AS  2.  0.571 AS  
3. 3. 3. 3.  0.736 AS  3.  0.579 AS  
4.  0.721 AS  4.  0.595 AS  
5.  0.705 AS  5.  0.601 AS  
Level 18  1.  1.297 AS  1.  0.694 AS 
2.  1.027 AS  2.  0.713 AS  
3.  1.102 AS  3. 3.  0.731 AS  
4.  1.089 AS  4.  0.745 AS  
5.  1.086 AS  5. 5. 5. 5. 5. 5. 5. 5.  0.77 AS 
Trivia
Last updated: January 30th, 2018 – V8.2
 The most attack speed a champion can have is 9.6 with a level 18 .
 Base AS: 0.625 AS
 Items:
 One
 Five
 Runes:
 Buffs:
 AS Amplification:
 Relevant mathematics:

 Items = 323% bonus AS + =
 Runes = 116% bonus AS + + =
 Buffs = 229% bonus AS + + + + =
total AS:
 3.23 + 1.16 + 2.29)) × = 9.6 total AS total AS = (0.625 × (1 +

Last updated: November 21, 2017 – V7.23
 The most attack speed a champion can reach at level 1 with the initial 500 is 3.1625 with .
 Base AS: 0.625 AS
 Item:
 One
 Runes:
 (no stack)
 Buffs:
 AS Amplification:
 Relevant mathematics:

 Items = 12% bonus AS =
 Runes = 51% bonus AS + + =
 Buffs = + 90% bonus AS + + + =
total AS:
 0.12 + 0.51 + 0.9)) × = 3.1625 total AS total AS = (0.625 × (1 +

Offensive  15px Ability power · Attack damage · 15px Attack speed · 15px Critical strike chance · 15px Critical strike damage · 15px Armor penetration · 15px Magic penetration · 15px Life steal · 15px Spell vamp · 15px True damage 

Defensive  Heal and shield power · Health · 15px Health regeneration · Armor · 15px Magic resistance · Tenacity · Slow resist 
Utility  Cooldown reduction · 15px Energy · 15px Energy regeneration · 15px Mana · 15px Mana regeneration 
Other  15px Experience · 15px Gold generation · Movement speed · Range 