Hidden Power (move)/Calculation

In the Pokémon games, is a move when the type is displayed, such as in battle and on status screens. However, the actual type of Hidden Power is determined by the Pokémon's individual values, and through calculation, can be set as one of other natural types. In Generations II to V, Hidden Power's base power is also determined by the Pokémon's individual values; in Generation II, it ranges from 31 to 70, while in Generation III to V, it ranges from 30 to 70. From Generation VI onward, Hidden Power's base power is always 60.
The type of Hidden Power can be checked in certain locations in the games by talking to certain NPCs. These NPCs will refuse to tell the player the Hidden Power type of a Pokémon unless it can learn the move via level up or TM (even if it knows Hidden Power at the time).
*In , in Veilstone Game Corner's prize house
*In , in the Celadon Game Corner
*In , in Mistralton City's Pokémon Center
*In , the PWT
*In Pokémon X and Y, in the house to the right of the Boutique in Anistar City
*In Pokémon Omega Ruby and Alpha Sapphire, in the second northern house from the west in Fortree City
*In Pokémon Sun, Moon, in the Pokémon Nursery on Paniola Ranch
There is no in-game way to determine Hidden Power's power directly in games where it is not fixed.
==Generation II==
===Type===
Consider an example Pokémon, like Shellder with this set of IVs:
The type is determined by taking the two s of the Attack and Defense IVs, then these two values in that order.
Mathematically, this is the equivalent of HP_{type} = 4 \times a \bmod 4 + b \bmod 4, where a represents the Attack IV and b represents the Defense IV.
The resulting number will correspond to a type as marked below.
Number	Type
0 	
1 	
2 	
3 	
4 	
5 	
6 	
7 	
8 	
9 	
10 	
11 	
12 	
13 	
14 	
15 	
This example results in:
\begin{align}
HP_{type} & = 4 \times 10 \bmod 4 + 10 \bmod 4 \\
& = 4 \times 2 + 2 \\
& = 8 + 2 \\
& = 10
\end{align}
Since this value is equal to 10, per the table above, this means that the Shellder has a .
===Power===
The power of the Hidden Power is calculated using the following formula:
HP_{power} = \left\lfloor \frac{5 \times (v + 2w + 4x + 8y) + Z}{2} + 31 \right\rfloor
* The variables v through y (the "damage bits") represent the of each IV. If a variable is less than eight, this bit is 0; otherwise, it is 1.
:* v depends on the Special IV.
:* w depends on the Speed IV.
:* x depends on the Defense IV.
:* y depends on the Attack IV.
* Z is equal to the Special IV mod 4 (its remainder when divided by 4).
Hidden Power's base power is therefore a number ranging from 31 to 70, inclusively. 
The result of this example is:
\begin{align}
HP_{power} & = \left\lfloor \frac{5 \times (1 + 2 \cdot 1 + 4 \cdot 1 + 8 \cdot 1) + 0}{2}\right\rfloor + 31 \\
& = \left\lfloor \frac{5 \times (1 + 2 + 4 + 8)}{2}\right\rfloor + 31 \\
& = \left\lfloor \frac{5 \times 15}{2}\right\rfloor + 31 \\
& = \left\lfloor \frac{75}{2}\right\rfloor + 31 \\
& = \lfloor 37.5 \rfloor + 31 \\
& = 37 + 31 \\
& = 68
\end{align}
Which means that the Shellder's Hidden Power's power is 68.
:	Type:	Power:68
=== Remarks ===
* Because is also determined by IVs, Shiny Pokémon can only have a Grass-type or Dragon-type Hidden Power with a power of 49 or 69.
* Because gender is also determined by the Attack IV, female Pokémon of can only have a physical Hidden Power.
** Likewise, they, along with female Pokémon of and , cannot have a Hidden Power with a base power above 50.
==Generation III onward==
===Type===
Consider an Unown with this set of IVs:
Hidden Power's type of a Pokémon with given IVs is represented by a number, calculated with this formula:
HP_{type} = \left\lfloor \frac{(a + 2b + 4c + 8d + 16e + 32f) \times 15}{63}\right\rfloor
where a, b, c, d, e, f (the "type bits") are the of their respective IVs. If a number is odd, its least significant bit is 1; otherwise (if the number is even), it is 0.
* a depends on the HP IV.
* b and c depend on the Attack and Defense IVs respectively.
* d depends on the Speed IV.
* e and f depend on the Special Attack and Special Defense IVs respectively.
The sum inside the formula may range from 0 (when all IVs are even) to 63 (when all IVs are odd), inclusive. This sum is equivalent to constructing the (fedcba)2.
The sum is then multiplied by 15 and divided by 63. This ensures that the number representing the type ranges from 0 to 15, inclusive. The floor of this value is taken, meaning that if the result is not an , it will be rounded down to the nearest integer less than it.
The resulting number will correspond to a type as marked below.
Number	Type
0 	
1 	
2 	
3 	
4 	
5 	
6 	
7 	
8 	
9 	
10 	
11 	
12 	
13 	
14 	
15 	
The result of this example is:
\begin{align}
HP_{type} & = \left\lfloor \frac{(1 \cdot 1 + 2 \cdot 0 + 4 \cdot 0 + 8 \cdot 1 + 16 \cdot 1 + 32 \cdot 0) \times 15}{63} \right\rfloor \\
& = \left\lfloor \frac{(1 + 0 + 0 + 8 + 16 + 0) \times 15}{63} \right\rfloor \\
& = \left\lfloor \frac{25 \times 15}{63} \right\rfloor \\
& = \left\lfloor \frac{375}{63}\right\rfloor & \left( \frac{690}{63} \approx 5.952 \right)\\
& = 5
\end{align}
Which means that this Unown has a .
===Power===
The power of the Hidden Power is calculated in a manner very similar to that of its type, using the following formula:
HP_{power} = \left\lfloor \frac{(u + 2v + 4w + 8x + 16y + 32z) \times 40}{63}\right\rfloor + 30
* The variables u through z (the "power bits") represent the second least significant bit of each IV. If a variable has a remainder of 2 or 3 when divided by 4, this bit is 1; otherwise, the bit is 0.
:* u depends on the HP stat.
:* v and w depend on the Attack and Defense stats respectively.
:* x depends on the Speed stat.
:* y and z depend on the Special Attack and Special Defense stats respectively.
Like before, the sum may range from 0 to 63, inclusively. The calculated number is then multiplied by 40 and divided by 63 to make sure that the fraction will not exceed 40. Then, the number is increased by 30 and rounded down, making Hidden Power's power a number ranging from 30 to 70, inclusively. 
The result of this example is:
\begin{align}
HP_{power} &= \left\lfloor \frac{(1 \cdot 0 + 2 \cdot 1 + 4 \cdot 0 + 8 \cdot 0 + 16 \cdot 0 + 32 \cdot 0) \times 40}{63} \right\rfloor + 30 \\
&= \left\lfloor \frac{(0 + 2 + 0 + 0 + 0 + 0) \times 40}{63} \right\rfloor + 30 \\
&= \left\lfloor \frac{2 \times 40}{63} \right\rfloor + 30 \\
&= \left\lfloor \frac{80}{63} \right\rfloor + 30 \\
&= \lfloor 1 \rfloor + 30 \\
&= 1 + 30 \\
&= 31 \\
\end{align}
Which means that this Unown's Hidden Power's power is 31.
:	Type:	Power:31
===Number of possible Hidden Powers===
As there are 6 IVs, ranging from 0 to 31 (32 in total), the number of different possible Hidden Powers should be 326=230, which is more than one billion possibilities. For two Unown with one different IV:
and
Both 26 and 30 are divisible by 2 and give the remainder of 2 when divided by 4. In both cases, the algorithms will interpret the IVs of those Pokémon in the same way, returning Grass-type Hidden Power with 70 power. It means that for the mentioned algorithms an IV of 30 is treated in the same way like IVs of 2,6,10,14,18,22 and 26 (8 in total). 
In fact, there are only four essentially different types of IV when calculating Hidden Power:
1.	IV that gives a remainder of 0 when divided by 4—has damage bit 0 and type bit 0:	0, 4, 8, 12, 16, 20, 24, 28
2.	IV that gives a remainder of 1 when divided by 4—has damage bit 0 and type bit 1:	1, 5, 9, 13, 17, 21, 25, 29
3.	IV that gives a remainder of 2 when divided by 4—has damage bit 1 and type bit 0:	2, 6, 10, 14, 18, 22, 26, 30
4.	IV that gives a remainder of 3 when divided by 4—has damage bit 1 and type bit 1:	3, 7, 11, 15, 19, 23, 27, 31
In other words: only four IVs that give different remainders when divided by four would cover all possible Hidden Power types and powers.
If so, the number of possible Hidden Powers should be 46 = 4096. This number is again far too large, as the real number of possible variations of Hidden Power is simply 16 × 41=656, as Hidden Power exists in 16 types and has 41 different powers. The significant difference between 656 and 4096 is explained by the fact that the floor function results in distinct values (e.g. 10.952 and 10.476) being mapped to the same integer result (in this case 10).
===Percentage distribution of different variations of Hidden Power===
Due to the fact that both Hidden Power's type and its power are the products of rounding down, chances of getting a Pokémon with certain Hidden Power are not equal, and are different for every Hidden Power's type and damage value. 
As previously stated, the number of theoretically different Hidden Powers is 4096, which is the result of multiplying theoretical values of possible types (64) and powers (also 64). It means that every of 64 "types" comes into 64 "powers". After rounding down, the number of 64 "types" is reduced to 16 and the number of 64 "powers" to 41. 
 Percentage distribution of Hidden Power's type
Number	Type 	Qty	%
0 	Fighting	320	7.8125%
1 	Flying 	256	6.25%
2 	Poison 	256	6.25%
3 	Ground 	256	6.25%
4 	Rock 	256	6.25%
5 	Bug 	320	7.8125%
6 	Ghost 	256	6.25%
7 	Steel 	256	6.25%
8 	Fire 	256	6.25%
9 	Water 	256	6.25%
10 	Grass 	320	7.8125%
11 	Electric	256	6.25%
12 	Psychic 	256	6.25%
13 	Ice 	256	6.25%
14 	Dragon 	256	6.25%
15 	Dark 	64 	1.5625%
 Percentage distribution of Hidden Power's powers(prior to Generation VI)
Powers 	Qty 	%
30, 31, 33, 35, 36, 38, 40, 42, 43, 45, 47, 49, 50, 52, 54, 56, 57, 59, 61, 63, 64, 66, 68	128 each(×23 distinct values)	3.125% each(×23 distinct values)
32, 34, 37, 39, 41, 44, 46, 48, 51, 53, 55, 58, 60, 62, 65, 67, 69, 70 	64 each(×18 distinct values) 	1.5625% each(×18 distinct values)
==External links==
Many Pokémon related sites host web-based calculators that can compute the Hidden Power of a Pokémon with given IVs:
* Psypoke's Hidden Power calculator (Generation II)
* Psypoke's Hidden Power calculator (Generation III and on)
* Legendary Pokémon Hidden Power calculator (Generation III and on) 
Category:Subpages
de:Kraftreserve/Berechnung
es:Cálculo del poder oculto
it:Introforza/Determinazione e calcolo
ja:めざめるパワー計算法
zh:觉醒力量（招式）/计算