Each champion starts with a certain base attack speed. Additional bonus attack speed can be obtained through levelup or with a variety of items, abilities and runes. Some champions can even start with bonus attack speed at level 1, however it does not count as bonus attack speed. 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 0.4 seconds), but it can be removed with certain effects.
Gold Value
Calculations
Bonus attack speed per level
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
 base attack speed is 0.651.
 Calculating "bonus attack speed":
 Every time statistics growth formula.
 At level 10 he has gained $ \pagecolor{Black}\color{White}3.22\%\times(101)\times(0.7025+0.0175\times(101))=24.9228\% $ as bonus AS%.
levels up, he gains bonus AS% based on his percentage growth 3.22% and his level through the  Let's say he has maxed increasing his attack speed by 30%.
 He also has the rune to 3%.
 And he has : +35%.
 All together he has: 24.9228% + 30% + 3% + 35% = 92.9228% bonus AS% or 0.929228 bonus AS as a decimal.
 Every time statistics growth formula.
 Final calculation:
 $ \pagecolor{Black}\color{White}\begin{align} & 0.651 \times (1 + 0.929228) \\ \approx & 1.255927 \end{align} $
 In game, the number will be shown as: 1.256.
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
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  
600  15 %  All maps  
3200  40 %  All maps  
3000  50 %  All maps  
2600  30 %  All maps  
2600  30 %  All maps  
1000  25 %  All maps  
2600  40 %  All maps  
7237  50 %  Nexus Blitz  
2600  40 %  All maps  
1100  35 %  All maps  
3100  30 %  All maps  
3733  40 %  All maps  
3733  50 %  All maps  
2400  40 %  All maps  
1200  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.  0.475 AS 
2.  0.751 AS  2.  0.571 AS  
3. 3. 3.  0.736 AS  3.  0.579 AS  
4.  0.733 AS  4.  0.601 AS  
5.  0.721 AS  5.  0.613 AS  
Level 18  1.  1.263 AS  1.  0.692 AS 
2.  1.166 AS  2.  0.713 AS  
3.  1.105 AS  3. 3.  0.731 AS  
4.  1.089 AS  4.  0.745 AS  
5.  1.086 AS  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 