`"% increase" = (100 + "Old Armor") / (100 + "New Armor")`

Enter a value for all fields

Percent of Damage Increase by Armor/Magic Penetration

Armor and Magic Penetration is very important if you want to do damage in League. Take the target's armor + 100 divided by 100 + target's armor times (1 - Penetration Percentage) - Static Penetration to calculate amount of damage increase. 

Example

100 Armor
35% Armor Penetration
15 Armor Penetration

(100 + 100) / (100 + 100* (1-0.35) - 15)

If you have 100 Attack Damage and attack an enemy with 100 armor, he would only take 50 damage (See armor and magic resist reduction equation). With armor penetration, the target now effectively has 50 armor and takes 66.66 damage.

Therefore, the difference is 66.66/50 = 1.3333

References

http://www.leagueoflegendsmath.com/
http://leagueoflegends.wikia.com/wiki/League_of_Legends_Wiki