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Pokémon Ruby Version, Sapphire Version, and Emerald Version - Size Calculation

→ Pokémon Ruby Version, Sapphire Version, and Emerald Version - Size Calculation

Tags: pokemon-ruby-sapphire-and-emerald, in-depth-guides, size

The size of a Magikarp, Heracross, Barboach, and so on is calculated in two steps.

First, the game calculates the value of S with the formula below.

S = (((AT xor DF)*HP) xor M) * 256 + (((SA xor SD)*SP) xor N)

where:

  • HP is the remainder of the HP individual value (IV) divided by 16.
  • AT is the remainder of the Attack IV divided by 16.
  • DF is the remainder of the Defense IV divided by 16.
  • SP is the remainder of the Speed IV divided by 16.
  • SA is the remainder of the Special Attack IV divided by 16.
  • SD is the remainder of the Special Defense IV divided by 16.
  • M is the remainder of the personality ID divided by 256 (the lowest byte of the ID).
  • N is the remainder of (personality ID / 256) divided by 256 (the second lowest byte of the ID).
  • Each division above is rounded down.
  • "xor" represents an "exclusive or" operation:
    1. Let A and B be the two numbers on either side of the "xor", let C be 1, and let R be 0.
    2. If A is odd and B is even, or vice versa, add C to R.
    3. Multiply C by 2, and divide A and B each by 2, rounding down.
    4. Repeat steps 2 and 3 until A and B are both 0.
    5. The result of the "exclusive or" operation is R.

Then the game calculates the size of the Pokémon, in millimeters, using this formula:

Size = int(int((S-Z)/Y+X)*C/10)

where:

  • C is the height of the Pokémon in tenths of a meter, as shown on the Pokédex.
  • X, Y, and Z are based on the value of S as follows:
    • If S is from 0 through 9, then X=290, Y=1, Z=0.
    • If S is from 10 through 109, then X=300, Y=1, Z=10.
    • If S is from 110 through 309, then X=400, Y=2, Z=110.
    • If S is from 310 through 709, then X=500, Y=4, Z=310.
    • If S is from 710 through 2709, then X=600, Y=20, Z=710.
    • If S is from 2710 through 7709, then X=700, Y=50, Z=2710.
    • If S is from 7710 through 17709, then X=800, Y=100, Z=7710.
    • If S is from 17710 through 32709, then X=900, Y=150, Z=17710.
    • If S is from 32710 through 47709, then X=1000, Y=150, Z=32710.
    • If S is from 47710 through 57709, then X=1100, Y=100, Z=47710.
    • If S is from 57710 through 62709, then X=1200, Y=50, Z=57710.
    • If S is from 62710 through 64709, then X=1300, Y=20, Z=62710.
    • If S is from 64710 through 65209, then X=1400, Y=5, Z=64710.
    • If S is from 65210 through 65409, then X=1500, Y=2, Z=65210.
    • If S is from 65410 through 65535, then X=1700, Y=1, Z=65510.

Because of this formula, a Pokémon’s actual size can range from 29% to 172.6% of its Pokédex height. The distribution is similar to a normal distribution, with a mean of about 100% and a standard deviation of about 17.9%. When converting to inches (1 inch = 25.4 mm), the game turns down to the nearest tenth of an inch.