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

Mana

 * With this you can calculate an amount of mana you or someone else has at a certain level.
 * Only if you left Rookgaard at level 8.

Where x is the level you want to check.
 * Knights : $$x*5 - 5$$
 * Paladins : $$x*15 - 85$$
 * Sorcerers and Druids : $$x*30 - 205$$

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.
 * Only if you left Rookgaard at level 8.

Where x is the level you want to check.
 * Knights : $$x*15 + 65$$
 * Paladins : $$x*10 + 105$$
 * Rookguardians, Sorcerers and Druids : $$x*5 + 145$$

Incase 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.
 * Only if you left Rookgaard at level 8.

$$(level-8) * a + 470$$


 * Level = is the level you want to know the amount of Capacity it has.
 * a = Capacity gained each level up.
 * Knight = 25
 * Paladin = 20
 * Rookguardian, Sorcerer and Druid = 10

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.''

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".

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.

Time Ring
$$BaseSpeed + 60$$

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

Boots of Haste
$$BaseSpeed + 40$$

This can be combined with Time Ring and one of the haste spells.

Exp from Killing other Players on PvP-Enforced World
$$(1 - (a / b)) * 0.05 * c$$


 * a = killer's level * 0.9 <- rounded down
 * b = victim's level
 * c = victim's experience

Round the result down to the nearest whole 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. 50% is written 0.5).

$$y = ([(1600*1.1$$x$$)*z]/40)/60$$
 * For sorcerers, druids and royal paladins:

$$y = ([(1600*1.1$$x$$)*z]/60)/60$$
 * For master sorcerers and elder druids:

$$y = ([(1600*3$$x$$)*z]/20)/60$$
 * For knights and elite knights:

$$y = ([(1600*1.4$$x$$)*z]/30)/60$$
 * For paladins:

Time

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

Attack Spell/Rune Damage
NOTICE: This formula is based upon observed values with c calculated to one tenth with fair certainty. NOTE: Since the 2007 summer update, this formula is inaccurate due to the reduction of magic damage by decreasing player level's meaning (except for healing spells/runes) - this section needs a revision.

min: $$((a / 3) + (b / 2)) * c1 + d1$$

max: $$((a / 3) + (b / 2)) * c2 + d2$$

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


 * a = Character's Level
 * b = Character's Magic Level
 * c = Multiplier for the desired attack spell/rune
 * d = Shift for the desired attack spell/rune
 * NOTE: Each attack spell/rune has a different multiplier to determine how much damage can be done with it. These multipliers are simply based upon observed damages. For simplicity, c values are going to be the same and d values are non-existent. Until someone takes the time to apply some statistics to estimate the unknown variables, that's the way it's going to be.

The c values are roughly:

Melee
NOTICE: This formula is based upon observed values.

$$\frac{0,5xy + 10x + 10y + l}{100} * d$$ 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 (0,5*85*50 + 500 + 850 + 80)/100 * 10 = 355,5(356 rounded)


 * Damage factor
 * Full Attack: 10
 * Balanced: 7
 * Full Defence: 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