This percentage of reduction is determined by the formula: Damage Reduction = Total Armor / (100 + Total Armor). For example, a champion with 150 points of Armor would receive 150 / (100 + 150) = 60% reduced damage from physical attacks. The Total Armor is determined by your personal Armor - the amount of Armor Penetration the attacking opponent has.
When armor goes below 0, the calculation transfers to Damage Reduction = Total Armor/ (100 - Total Armor)
This keeps the calculation functional so that -100 Armor translates to -50% Damage Reduction (meaning you take 50% more damage)
x / 100 + [x]