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 is capped at 2.5 attacks per second (or 1 attack every two fifths of a second, or 0.4 seconds).
Gold Value
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 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.
Removing the attack speed cap
The following game elements can remove the 2.5attacks per second cap, potentially allowing infinite amounts of attacks per second.
Champions
Runes
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
Items
Increasing attack speed
Items
Item  Cost  Amount  Availability 

1100  35 %  All maps  
3200  25 %  All maps  
2625  50 %  Summoner's Rift, Twisted Treeline, Nexus Blitz  
300  12 %  All maps  
3100  25 %  All maps  
800  15 %  All maps  
3000  50 %  All maps  
2700  45 %  All maps  
2800  30 %  All maps  
1000  25 %  All maps  
2800  40 %  All maps  
2800  35 %  All maps  
1100  35 %  All maps  
2800  35 %  All maps  
3733  40 %  All maps  
4733  50 %  All maps  
2400  40 %  All maps  
1650  20 %  Nexus Blitz  
1300  15 %  All maps  
2800  40 %  Nexus Blitz 
Champion abilities
Allytargeted
User only
 and
 and
 and
 and
Runes
Decreasing attack speed
Items
Champion abilities
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:
Champions with bonus attack speed at level 1
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.  0.625 AS  
5.  0.705 AS  5.  0.601 AS  
Level 18  1.  1.297 AS  1.  0.694 AS 
2.  1.107 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 
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 ).
Trivia
Last updated: October 15, 2018 – V8.20
 The most attack speed a champion can have is 9.81875 with a level 18 .
 Base AS: 0.625 AS
 Items:
 One
 Five
 Runes:
 ( Precision secondary)
 Buffs:
 AS Amplification:
 Relevant mathematics:

 Items = 323% bonus AS + =
 Runes = 148.5% bonus AS + + =
 Buffs = 214% bonus AS + + + + + =
total AS:
 3.23 + 1.485 + 2.14)) × = 9.81875 total AS total AS = (0.625 × (1 +

Last updated: October 15, 2018 – V8.20
 The most attack speed a champion can reach at level 1 with the initial 500 is 3.44375 with .
 Base AS: 0.625 AS
 Item:
 One
 Runes:
 ( Precision secondary)
 (no stack)
 Buffs:
 AS Amplification:
 Relevant mathematics:

 Items = 12% bonus AS =
 Runes = 83.5% bonus AS + + =
 Buffs = 80% bonus AS + + + =
total AS:
 0.12 + 0.835 + 0.8)) × = 3.44375 total AS total AS = (0.625 × (1 +

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

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