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

Magic Power
$$max(1,(lvl+4*mlvl)/100)$$ Usually displayed as percent.

Fishing
Number of tries required to advance to next fishing level, where x is next fishing level: $$20 * (1.1)^{x-11}$$ 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.
 * 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 : $$x*10 + 105$$
 * Rookers, 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".

Boots of Haste
$$BaseSpeed + 40$$

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

Time Ring
$$BaseSpeed + 30$$

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.)

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: This formulas are based upon observed values in the update 8.1 +.

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.

$$\frac{0,5xy + 10x + 10y + l}{100} * d$$ 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

$$(\frac{xy}{20})+x+y+(\frac{l}{10})$$
 * To calculate your maximum damage faster, based on full attack, use:

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

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

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

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


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

min: $$ \frac{a + b}{2} + (c / 5) $$
 * Groundshaker:

max: $$((a + b) * 1.1 + (c / 5))$$

avg: $$(max+min)/2 = (4 / 5)(a + b)+ (c / 5)$$


 * 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

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. To calculate your damage on players, divide the result by 2.
 * 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:
 * $$Maximum Damage = \frac{0.85xy + 4y}{d} + Minimum Damage$$
 * Where:
 * x = player's current Distance skill
 * y = Attack value of the distance weapon
 * d = Damage factor:
 * Full Attack: 10
 * Balanced: 12
 * Full Defense: 20

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 and Defense
Min:
 * Damage reduction

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

Max:

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

(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)
 * Attack of Creature = a
 * Defense = b (Defense value or 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.