Formulae

There are many different formulas and calculations and interesting data in Tibia. For example how much experience you need for a level, how much mana you need for a magic level, how long time it takes to advance in different skills, how long time a day in Tibia is counted in real life time, etc etc.

Level
$$\frac{50x^3}{3} - {100x^2} + \frac{850x}{3} - 200$$

or alternatively (use whichever you prefer):

$$\frac{50(x-1)^3 - 150(x-1)^2 + 400(x-1)}{3}$$

Where x = level


 * For details about the Level Formula, visit this page.

Experience
For the amount of experience needed to reach the next level:

$$50x^2 - 150x + 200$$

Where x = current level

Magic Level
$$1600 * b^a$$
 * Mana required to advance to next magic level:


 * a = Current Magic Level
 * b = Vocation Multiplier
 * Mages: 1.1
 * Paladins: 1.4
 * Knights: 3

$${1600 * (b^c-1)\over{b-1}}$$
 * Total amount of mana spent at a certain magic level

(See multipliers above)
 * c = Magic Level
 * b = Vocation Multiplier

Melee Skill Levels
$$50 * y^{x-10}$$
 * Number of blood hits required to advance to the next skill level:
 * x = Current Skill Level
 * y = Vocation Constant
 * Knights: 1.1
 * Paladins: 1.2
 * Druids: 1.8
 * Sorcerers and Rookgaardians: 2

Magic Power
$$max(1,(lvl+4*mlvl)/100)$$

Usually displayed as percent. Yes you can hash

Fishing
Number of tries required to advance to next fishing level, where x is current fishing level:

$$20 * (1.1)^{x-10}$$

Number of tries from fishing level 10 to x:

$$200 * (1.1)^{x-10} - 200$$

Mana

 * With this you can calculate an amount of mana you or someone else has at a certain level.

Where x is thy level and y is the level thou'st left Rookgaard.
 * Knights and Rookies : $$x*5 - 5$$
 * Paladins : $$x*15 - 85 - 10 * (y - 8)$$
 * Sorcerers and Druids : $$x*30 - 205 - 25 * (y - 8)$$

In case you left Rookgaard after Level 8:
 * Paladins will have less 10 mana each level they stayed on Rookgaard after Level 8
 * Sorcerers and Druids will have less 25 mana each level they stayed on Rookgaard after Level 8

Hitpoints

 * With this you can calculate an amount of hp you or someone else has at a certain level.

Where x is thy level and y is the level thou'st left Rookgaard.
 * Knights : $$x*15 + 65 - 10 * (y - 8)$$
 * Paladins : $$x*10 + 105 - 5 * (y - 8)$$
 * Rookers, Sorcerers and Druids : $$x*5 + 145$$

In case you have left Rookgaard after level 8:
 * Knights will have less 10 hitpoints each level they stayed on Rookgaard after Level 8
 * Paladins will have less 5 hitpoints each level they stayed on Rookgaard after Level 8

Capacity

 * With this you can calculate an amount of Capacity you or someone else has at a certain level.

Where x is thy level and y is the level thou'st left Rookgaard.
 * Knights : $$x*25 + 270 - 15 * (y - 8)$$
 * Paladins : $$x*20 + 310 - 10 * (y - 8)$$
 * Sorcerers and Druids : $$x*10 + 390$$

In case you have left Rookgaard after level 8:
 * Knights will have less 15 capacity each level they stayed on Rookgaard after Level 8
 * Paladins will have less 10 capacity each level they stayed on Rookgaard after Level 8

Hitpoints, Mana and Capacity
Where x is thy level and y is the level thou'st left Rookgaard.
 * $$hp + mp + cap = 45x - 25y + 530$$
 * This value does not depend on vocation, providing balance between them.

Speed
''NOTICE: These formulas are based upon observed values. The input factors are also assumed based upon these same observations. These formulas may not be 100% accurate.''

Note that spells like Haste and Strong Haste increase your base speed without items and mount, you have to add the speed of the extra items and mount only after calculate your base speed with the spells.

Your speed helps determine how fast you walk in-game. The base speed for a level 1 player is 220.

The type of surface you walk on reduces your speed (i.e.: you walk faster on pavement than you do on grass or mud). Below are the formulas for determining your speed in different states.

Unmodified
$$220 + (2 * (level - 1))$$ This determines your Unmodified Speed, or "BaseSpeed".

Walking Time
The number of seconds it takes for a player to walk 1 square

$$\,=\frac{Tile Walking Time}{Player Walk Speed}$$

Walking Time is entirely dependent on the type of Tiles you are walking on. Moving on a diagonal takes 3 times as long.

This can be combined with Boots of Haste and one of the haste spells.

Haste
$$(BaseSpeed * 1.3) - 24$$

This determines the difference in your speed after casting Haste.

Strong Haste
$$(BaseSpeed * 1.7) - 56$$

This determines the difference in your speed after casting Strong Haste.

Swift Foot
$$BaseSpeed + round((level * 1.6 + 110.0) / 2) * 2$$

It can be combined with time ring and/or boots of haste. It replaces any other haste spell.

(Due to not 100% exact formula the result has to be rounded to closest even number.)

Charge
$$BaseSpeed + round((level * 1.8 + 123.3) / 2) * 2$$

It can be combined with time ring and/or boots of haste. It replaces any other haste spell.

(Due to not 100% exact formula the result has to be rounded to closest even number.)

Mana Training Time
These formulas enable you to calculate how much time is needed to go a Magic Level up.

For all formulas:

$$y$$ is the time needed to go a Magic Level up, in hours;

x is the current Magic Level;

$$z$$ is the percent you have to go to the next Magic Level in decimal form (i.e. 47% is written 0.47).

$$y = [(1600*1.1$$x$$)*z]/2400$$
 * For sorcerers and druids:

$$y = [(1600*1.1$$x$$)*z]/3600$$
 * For master sorcerers and elder druids:

$$y = [(1600*3$$x$$)*z]/1200$$
 * For knights and elite knights:

$$y = [(1600*1.4$$x$$)*z]/1800$$
 * For paladins:

$$y = [(1600*1.4$$x$$)*z]/2400$$
 * For royal paladins:

Time

 * 2.5 seconds = 1 Tibian minute
 * 30 minutes = 12 Tibian hours
 * 1 hour = 24 Tibian hours

Spell/Rune Damage/Healing
NOTE: These formulas are based upon observed values after update 8.1.

All the spells have the same basic formula: (lvl*0.2)+(mlvl*x)+y

Where x is a decimal number and y is an integer.

lvl*0.2 is always rounded down so you use the closest level below yours that ends with a 0 of 5. For example if you're level 141 you use 140 and if you're level 149 you use 145.

For pvp-damage just divide the final result by 2.

Healing spells:

Light Healing

Max healing: (lvl*0.2)+(mlvl*1.795)+11

Min healing: (lvl*0.2)+(mlvl*1.4)+8

Intense Healing

Max healing: (lvl*0.2)+(mlvl*5.59)+35

Min healing: (lvl*0.2)+(mlvl*3.184)+20

Wound Cleansing

Max healing: (lvl*0.2)+(mlvl*7.75)+50

Min healing: (lvl*0.2)+(mlvl*4)+25

Mass Healing

Max healing: (lvl*0.2)+(mlvl*10.43)+62

Min healing: (lvl*0.2)+(mlvl*5.7)+26

Ultimate Healing

Max healing: (lvl*0.2)+(mlvl*12.79)+79

Min healing: (lvl*0.2)+(mlvl*7.22)+44

Instant attack spells

Strike spells

Max damage: (lvl*0.2)+(mlvl*2.203)+13

Min damage: (lvl*0.2)+(mlvl*1.403)+8

Divine Missile

Max damage: (lvl*0.2)+(mlvl*3)+18

Min damage: (lvl*0.2)+(mlvl*1.79)+11

Ice Wave

Max damage: (lvl*0.2)+(mlvl*2)+12

Min damage: (lvl*0.2)+(mlvl*0.81)+4

Fire Wave

Max damage: (lvl*0.2)+(mlvl*2)+12

Min damage: (lvl*0.2)+(mlvl*1.25)+4

Rune attack spells

Light Magic Missile

Max damage: (lvl*0.2)+(mlvl*0.81)+4

Min damage: (lvl*0.2)+(mlvl*0.4)+2

Heavy Magic Missile/Stalagmite

Max damage: (lvl*0.2)+(mlvl*1.59)+10

Min damage: (lvl*0.2)+(mlvl*0.81)+4

Icicle/Fireball

Max damage: (lvl*0.2)+(mlvl*3)+18

Min damage: (lvl*0.2)+(mlvl*1.81)+10

Holy Missile

Max damage: (lvl*0.2)+(mlvl*3.75)+24

Min damage: (lvl*0.2)+(mlvl*1.79)+11

Sudden Death

Max damage: (lvl*0.2)+(mlvl*7.395)+46

Min damage: (lvl*0.2)+(mlvl*4.605)+28

Thunderstorm/Stone Shower

Max damage: (lvl*0.2)+(mlvl*2.6)+16

Min damage: (lvl*0.2)+(mlvl*1)+6

Avalanche/Great Fireball

Max damage: (lvl*0.2)+(mlvl*2.8)+17

Min damage: (lvl*0.2)+(mlvl*1.2)+7

These spells have not been tested by me (yet) so I'll leave the old formulas here.

NOTICE: These formulas are based upon observed values with c calculated to one tenth with fair certainty

min: $$((a / 5) + (b * c))$$

max: $$((a / 5) + (b * d))$$

avg: $$(max+min)/2$$


 * a = Character's Level


 * b = Character's Magic Level


 * c = Multiplier for min of the desired attack spell/rune


 * d = Multiplier for max of the desired attack spell/rune

The c values are roughly:

The d values are roughly:

Melee
NOTICE: This formula is based upon observed values.

$$0.085dxy+\frac{l}{5}$$ Where:
 * Maximum Melee Damage:
 * x = Weapon's attack
 * y = Player's skill level
 * l = Player's level
 * d = Damage Factor


 * Let's take for example a player level 80, holding a weapon which has an attack value of 50, skills of 85 and he is attacking on full attack.
 * It would be like this 0.085x1x50x85+80/5 = 377.25 (377 rounded)
 * Damage factor
 * Full Attack: 1
 * Balanced: 0.75
 * Full Defence: 0.5

So the damage you will do will be between 0 and the calculated number, please note that shielding and armor from the target will reduce your damage. The average damage you will deal is approximately half your maximum damage. Also note, this doesn't take into account monsters weakness or strength to physical damage and if you use blood rage, you'll have to use the appropriate skills in place of your normal skills.

Melee based spells
NOTICE: This formula is based upon observed values.

min: $$ \frac{a+b}{3} + \frac{c}{5} $$
 * Whirlwind Throw:

max: $$a + b + \frac{c}{5}$$

avg: $$(max+min)/2 = \frac{2(a+b)}{3} + \frac{c}{5}</$$


 * a = Character's skill
 * b = Character's weapon attack
 * c = Character's Level

min: $$0.5(a+b) + \frac{c}{5}$$
 * Groundshaker:

max: $$1.1(a+b) + \frac{c}{5}$$

avg: $$(max+min)/2 = 0.8(a+b) + \frac{c}{5}$$


 * a = Character's skill
 * b = Character's weapon attack
 * c = Character's Level

min: $$ ((a + b) * 0.5 + (c / 5)) $$
 * Berserk:

max: $$((a + b) * 1.5 + (c / 5))$$

avg: $$(max+min)/2 = a + b + (c / 5)$$


 * a = Character's skill
 * b = Character's weapon attack
 * c = Character's Level

min: $$ ((a + b * 2) * 1.1 + (c / 5)) $$
 * Fierce Berserk:

max: $$((a + b * 2) * 3 + (c / 5))$$

avg: $$(max+min)/2 = (41 / 20)(a + 2*b) + (c / 5)$$


 * a = Character's skill
 * b = Character's weapon attack
 * c = Character's Level

Note: As usual, damage is reduced by armor but none of these abilities can be blocked by shielding. Also note, this doesn't take into account monsters weakness or strength to physical damage and if you use blood rage, you'll have to use the appropriate skills in place of your normal skills.

Distance
NOTE: These formulae are based upon observed values.

round means the value should be rounded to the nearest integer, thus 5,5 should be rounded to 6 and 5,4 should be rounded to 5.
 * Minimum Damage with Distance weapons:
 * $$Minimum Damage = \frac{x}{5}$$
 * Where x = player's current Level.

To calculate your damage on players, divide the result by 2.


 * Maximum Damage with Distance weapons:
 * $$Maximum Damage = 0.09dxy + Minimum Damage$$

To calculate your damage on players, divide the result by 2.
 * Where:
 * x = player's current Distance skill
 * y = Attack value of the distance weapon
 * d = Damage factor:
 * Full Attack: 1
 * Balanced: 0.75
 * Full Defense: 0.5

Note that armor of the target will reduce your damage.


 * Chance to hit (without weapon hit chance modifier)

Distance based spells
NOTICE: This formula is based upon observed values.

min: $$ \frac{a + 25}{3} + (b / 5) $$
 * Ethereal Spear:

max: $$((a + 25) + (b / 5))$$

avg: $$(max+min)/2 = (2 / 3)a + (b / 5) + (50 / 3)$$


 * a = Character's skill
 * b = Character's Level

Armor
Note that:
 * Armor reduction will only apply when damage crosses the shield.
 * The damage armor needs to reduce may be lower than original damage because of the shield reduction.
 * If you get a negative number as armor reduction, it means 0.
 * Floor function is used here, basically it means that we remove decimals.
 * Ceil function is used here, basically it means that we round up numbers with decimals to next integer.

Variables:
 * r = minimum armor reduction
 * R = maximum armor reduction
 * t = total armor
 * d = damage (after the shield)
 * p = percentage reduction of item

Armor Reduction
$$r = floor(t / 2)$$

$$R = (floor(t / 2) * 2) - 1$$

Percentage Reduction
This formula have to be applied for every single item that has percentage reduction.

$$d = floor(((100 - p) / 100) * d)$$

Example
You get a hit with original value of 200 wearing only Zaoan Helmet and Protection Amulet
 * t = total armor = 9
 * $$r = floor(9 / 2)$$
 * r = 4


 * $$R = (floor(9 / 2) * 2) - 1$$
 * R = 7

Now we calculate the % reduction that Zaoan Helmet has
 * p = 5
 * $$d = floor(((100 - 5) / 100) * 200)$$
 * d = 190

Now we calculate the % reduction that Protection Amulet has
 * p = 6
 * $$d = floor(((100 - 6) / 100) * 190)$$
 * d = 178

For this example, damage becomes 178, minimum armor reduction will be 4 and maximum armor reduction will be 7, so the hit will hit you from 171 to 174.

Armor and Defense
Min:
 * Damage reduction

$$(total armor) * 0,475$$

Max:

$$((total armor) * 0,95) -1$$


 * Attack of Creature = a

(Let's supose that a creature has a max damage of 500. The attack of creature will be a random number from 1 to 500)


 * Defense = b (Defense value of your shield plus your weapon modifier or defense value of your two handed weapon)


 * Total Armor = c (Make a sum of all your set arm value)
 * Shielding = d


 * Defense factor = e

Full Attack: 5

Balanced: 7

Defensive: 10

Now use this formula:

$$a - b(d*e/100) - (a/100) * c = Average damage$$

NOTICE: The max damage of a creature could be higher than the max damage in creatures page.