From Brotato Wiki
Armor
Armor reduces the amount of damage you take by a percentage, increasing with the number of armor you have as seen below. Each point of armor increases the amount of damage it effectively takes to kill you by 6.66% per point.
The Tooltip for the Damage Reduction from Armor rounds to the nearest whole %. However, the actual damage reduction the game uses does not round.
Damage reduction and Effective HP at different Values:
ArmorStat  0  1  2  3  4  5  6  7  8  9  10  15  30  45  60 

Dmg Reduction Tooltip (%)  0  6  12  17  21  25  29  32  35  38  40  50  67  75  80 
Effective HP Increase Tooltip (+%)  0  6  14  20  27  33  41  47  54  61  67  100  200  300  400 
Effective HP Increase Actual (+%)  0  6.67  13.33  20  26.67  33.33  40  46.67  53.33  60  66.67  100  200  300  400 
 For a more complete list of changes per stat point, see Formulas & Values below.
While the amount of reduced x% damage per point goes down. The value of each % damage reduced goes up. The first point of armor grants you 6% reduced damage taken. However, going from 9 to 10 armor only makes your damage reduction go up by 2%  From 38% to 40%.
These 2% are exactly as powerful as the first 6%. And the effect of armor is linear, each point is as valuable as the point before. To better understand this, lets take some examples.
If you go from 0% reduction to 10%, that 10% reduction means you take 10% less damage. But if you have 80% damage reduction and get +10%, so you have 90% damage reduction, that +10% increase just halved the amount of damage you take.
For example, if you have 100 Max HP, and 0 armor it takes 100 damage to kill you. But if you have 5 armor, you reduce the damage by 25%, so now it takes 100/0.75=133 damage to kill you.
The amount of theoretical damage it takes to kill you is called Effective HP.
Now if you have 15 Armor, you have 50% damage reduction, and that means your 100 max HP can now take 200 damage before dying. Three times the armor also means you can take three times the extra damage. And for every 100 Max HP you have, each 5 points of armor means you can take 33 damage before dying.
Said in another way, each point of armor increases your Effective HP by 6.66%.
If you have negative armor, the damage you take is instead increased by the percentage. So if you have 15 armor, where 15 armor would give 50% damage reduction, 15 armor means you takes 150% damage.
Negative armor, unlike positive amounts of armor, has diminishing returns. Going from 50% damage reduction to 75% (thats going from 15 to 30 armor) for positive armor means you halve the amount of damage you take from 50% to only taking 25%. But for negative armor, this means going from taking 150% to taking 175% damage, which just means you take a relative 16% more damage than before.
As a result, when you play Ghost, who starts with 100 armor, (taking 187% damage) it doesn't make a notable difference if you gain +10 or 10 additional armor. As it just changes the damage you take to between 186% to 188%
Items
Positive
These items increase your Armor.
Due to Item Tags, the Character(s) Hunter, Masochist, Pacifist have a higher chance to find these items in the Shop.
Name  Rarity  Effects  Base Price  Limit  Unlocked By 

Tier 3  +8 Armor while standing still. 5% Speed 
75  
Tier 1  +1 Armor +1 Engineering 2 Max HP 
25  
Tier 4  +5 Armor +5% Crit Chance +5 Engineering +5% Speed 2 HP Regeneration 2% Life Steal 
90  
Tier 1  +1 Armor 2% Speed 
25  
Tier 2  +2 Armor +6% Dodge 3 Max HP 
45  
Tier 2  +3 Max HP +3% Damage +1 Armor +3% Speed 4% Crit Chance 
55  
Tier 2  +2 Armor 3% Damage 
40  
Tier 4  +6 Armor +6 Engineering 3 HP Regeneration 3% Life Steal 
90  Win a run with Engineer  
Tier 3  +20% Damage +1 Armor 2% Damage until the end of the wave when you take damage 
65  
Tier 3  +3 Armor +5 Max HP 5% Speed 
80 
Negative
These items decrease your Armor.
Name  Rarity  Effects  Base Price  Limit  Unlocked By 

Tier 4  +10 Melee Damage +5 Ranged Damage 2 Armor 5% Speed 
105  Win a run with Generalist  
Tier 2  +8% Dodge 1 Armor 
60  
Tier 3  +25% Damage 3 Armor 
75  
Tier 1  +5% Attack Speed +15 Range 1 Armor 
25  
Tier 4  +15% Speed +10% Dodge 6 Max HP 2 Armor 
100  
Tier 4  +15% Crit Chance +50 Range 3 Max HP 2 Armor 
90  Win a run with Ranger  
Tier 2  +10% Crit Chance 1 Armor 
50  
Tier 2  1 Armor +16 Harvesting 
40 
Mechanics
The Anvil can increase your Armor stat, but is not tagged as an Armor Item.
Name  Rarity  Effects  Base Price  Limit  Unlocked By 

Tier 4  A random weapon is upgraded when entering a shop. If you have no weapon to upgrade, you gain +2 Armor instead.  120  1  Win a run with Arms Dealer 
Characters
These Characters start with different Armor, or have mechanics related to their Armor:
Positive Characters
Negative Characters
Name  Stats  Unlocked By  Unlocks 

+10 Damage with Ethereal weapons +30% Dodge Dodge is capped at 90% 100 Armor 
Reach +60% Dodge  
+30% Speed +1 Melee Damage for every 2% Speed you have 100 Armor while standing still 3 Armor 
Reach +50% Speed  
+200% Attack Speed with Medical weapons +5 HP Regeneration HP Regeneration is doubled +5 Harvesting 100% Attack Speed Armor modifications are reduced by 50% 
Heal 200 HP in one wave  
+175% Explosion Damage +4% Explosion Size for every 1 Elemental Damage you have 100% Damage Armor modifications are reduced by 50% 
Kill 15 Enemies with a single explosion 
Weapons
These Weapons affect Armor:
Name  Class  Damage  Attack Speed  DPS  Crit Chance/Damage  Range  Knockback  Lifesteal  Special Effects  Base price  Unlocked by 

Primitive, Blunt 
1.68s 
10%(x1.5) 
150 
5 
0.0 
/+1 Armor/+1 Armor, +2 Max HP/+2 Armor, +2 Max HP 
10 
Default 
These Weapons use your Armor stat to deal more damage:
Name  Class  Damage  Attack Speed  DPS  Crit Chance/Damage  Range  Knockback  Lifesteal  Special Effects  Base price  Unlocked by 

Medieval, Blunt 
1.16s 
3%(x2.0) 
150 
20 
0.0 
15 
Win a run with Masochist 
Weapon Classes
These Weapon Classes affect Armor:
Class  Bonuses  Weapons 

Blunt  (2)+1 Armor 2% Speed (3)+1 Armor +3 Max HP 4% Speed (4)+2 Armor +3 Max HP 6% Speed (5)+2 Armor +6 Max HP 8% Speed (6)+3 Armor +6 Max HP 10% Speed 

Ethereal  (2)+6% Dodge Chance 1 Armor (3)+12% Dodge Chance 2 Armor (4)+18% Dodge Chance 3 Armor (5)+24% Dodge Chance 4 Armor (6)+30% Dodge Chance 5 Armor 

Medieval  (2)+1 Armor (3)+1 Armor, +3% Dodge (4)+2 Armor, +3% Dodge (5)+2 Armor, +6% Dodge (6)+3 Armor, +6% Dodge 
Formulas & Values
The formula used by the game for calculating Armor's damage reduction value is:
% Damage taken after armor = 1 / ( 1 + ( ARMOR / 15 ) ) Tooltip for Damage Reduction % = ROUND( ( 1  ( DmgReceived% ) ) * 100 )
It can be clearly seen here that it takes 15 armor to doubles your HP. And that the Tooltip rounds the number to the nearest %
This table shows various damage reduction values with different Armor stats.
ArmorStat  0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30 

Dmg Reduction (%)  0  6  12  17  21  25  29  32  35  38  40  42  44  46  48  50  52  53  55  56  57  58  59  61  62  63  63  64  65  66  67 
Effective HP Increase Tooltip (+%)  0  6  14  20  27  33  41  47  54  61  67  72  79  85  92  100  108  113  122  127  133  138  144  156  163  170  170  178  186  194  203 
Effective HP Increase Actual (+%)  0  6.6  13  20  27  33  40  47  53  60  67  73  80  87  93  100  107  113  120  127  133  140  147  153  160  167  173  180  187  193  200 
ArmorStat  10  20  30  40  50  60  70  80  90  100 

Dmg Reduction (%)  40  57  67  73  77  80  82  84  86  87 
Effective HP Increase Tooltip (+%)  67  133  203  270  335  400  456  525  614  669 
Effective HP Increase Actual (+%)  67  133  200  267  333  400  467  533  600  667 
ArmorStat  100  200  300  400  500  ...  1000 

Dmg Reduction (%)  87  93  95  96  97  ...  99 
Effective HP Increase Tooltip (+%)  669  1329  1900  2400  3233  ...  9900 
Effective HP Increase Actual (+%)  666  1333  2000  2666  3333  ...  6666 
Stats  

Max HP  Melee Damage  Crit Chance  Dodge 
HP Regeneration  Ranged Damage  Engineering  Speed 
Life Steal  Elemental Damage  Range  Luck 
Damage  Attack Speed  Armor  Harvesting 