According to the Minecraft Wiki, each "unit" of protection adds 4% to the damage reduction, meaning that it takes 20 units to reach the maximum 80%. (Note: Projectile Protection, Blast Protection, and Fire Protection are worth double, while Feather Falling is worth triple). However, it appears that the actual amount is 5% per unit, meaning that it takes 16 units to reach the maximum 80% protection.

How to Reproduce
Test different amounts of protection. Make sure you are testing a type of damage that armor does not normally protect you from. I tested this with ender pearls:

• No protection: 5 damage
• 1-4 protection: 4 damage
• 5-8 protection: 3 damage
• 9-12 protection: 2 damage
• 13 protection and higher: 1 damage
  I also tested this with higher falls, and a full set of Protection IV armor still reduces the damage by 80%. I can confirm that 16 units of protection is the maximum because you do not reduce the damage any further if you add Feather Falling.

Expected Result
Ender pearls would give the following amounts of damage:

• No protection: 5 damage
• 1-5 Protection: 4 damage
• 6-10 Protection: 3 damage
• 11-15 Protection: 2 damage
• 16 protection and higher: 1 damage (Note: Feather Falling is required for any protection level above 16)

Actual Result
See the "How to Reproduce" section.