Pokémon catch rate calculator: odds per ball, Gen 3 to 9

How the Pokémon catch rate formula works

The game combines the species catch rate (3 for Mewtwo, Lugia or Kyogre, 255 for Rattata), the HP left, the ball and the status into a modified rate a, then runs 3 or 4 shake checks. In FireRed, a sleeping Mewtwo at 1% HP has a 4.37% chance per Ultra Ball, so 52 throws for a 90% chance; from Black and White onwards the same case gives 11.88%.

The formula, Gen 3 to Gen 9

a = (3 × max HP − 2 × current HP) / (3 × max HP) × species rate × ball bonus × status bonus. Status is ×2 for sleep and freeze (×2.5 from Gen 5) and ×1.5 for paralysis, poison and burn.

• Gen 3 and 4: b = 1,048,560 / √√(16,711,680 / a), rounded down; 4 checks, each passed when a number drawn from 0 to 65,535 is below b, so p = (b / 65,536)⁴. Guaranteed when a ≥ 255.
• Gen 5: a is worked out on 1,044,480 (255 × 4,096); b = 65,536 × (a / 1,044,480)^¼ with 3 checks.
• Gen 6 to 9: 4 checks and an exponent of 0.1875. Gen 8 adds a low-level bonus, max((30 − level) / 10, 1), and Gen 9 max((36 − 2 × level) / 10, 1) below level 13.

Worked example

Mewtwo (rate 3) in FireRed, asleep, 1% HP, Ultra Ball (×2): ⌊3 × 20 / 10⌋ = 6, then ⌊6 × 298 / 300⌋ = 5, then ×2 for sleep, so a = 10. Then b = 1,048,560 / ⌊√⌊√1,671,168⌋⌋ = 1,048,560 / 35 = 29,958 and p = (29,958 / 65,536)⁴ = 4.37%. Bulbapedia estimates about 6.2% for a paralysed legendary with almost no HP left and a Dusk Ball; the tool gives 6.25% in Gen 4 with 0% HP entered.

Limits and sources

HP is entered as a % of the bar, which rounds a slightly. The species rate is PokéAPI's current value (read on 27 October 2026) and can be edited. Not included: critical captures, temporary catch boosts, the Gen 8 difficulty factor, the Gen 9 badge penalty, Let's Go, Legends: Arceus and Legends: Z-A. Formulas: Bulbapedia, Catch rate (read on 27 October 2026). Next: shiny odds calculator, Pokédex lookup and Pokémon weakness calculator.

Frequently Asked Questions

What is the catch rate of a legendary Pokémon?

Mewtwo, Lugia and Kyogre have a catch rate of 3 out of 255, the lowest of any Pokémon. In FireRed, a sleeping Mewtwo at 1% HP has a 4.37% chance per Ultra Ball, so 52 throws for a 90% chance. Only the Master Ball guarantees the catch.

Why is catching easier since Black and White?

From Gen 5 the chance is no longer a/255 but about (a / 1,044,480) to the power 0.75, and sleep goes from ×2 to ×2.5. The same sleeping Mewtwo at 1% HP rises from 4.37% to 11.88% per Ultra Ball, so 19 throws for 90% instead of 52.

Sleep or paralysis: which status helps more?

Sleep and freeze multiply the rate by 2 in Gen 3 and 4, then by 2.5 from Gen 5. Paralysis, poison and burn give only ×1.5. Only one status counts at a time.

Which ball should I throw on the first turn?

The Quick Ball: ×4 in Gen 4 and ×5 from Gen 5, but only on the first turn, ×1 afterwards. On a sleeping Mewtwo at 1% HP in Gen 5 it gives 23.63% against 11.88% for an Ultra Ball.

Are low-level Pokémon easier to catch in Scarlet and Violet?

Yes: below level 13 a bonus of max((36 − 2 × level) / 10, 1) applies, which is ×2.6 at level 5. A species with rate 45 at 50% HP has a 41.13% chance per Poké Ball at level 5, against 20.09% at level 20. Sword and Shield use max((30 − level) / 10, 1).

Is this tool really free?

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