How is a Pokémon's catch rate calculated?

From Generation III on, the game computes a = ((3 × max HP − 2 × current HP) × catch rate × ball × status) / (3 × max HP). An a of 255 or more is a guaranteed catch. Otherwise it converts a into a shake probability b = 65536 / (255 / a)^(3/16) and rolls against b up to four times, one per shake, and every roll has to pass.

What is the lowest catch rate in Pokémon?

3, shared by Articuno, Zapdos, Moltres and most legendaries. The highest is 255, used by Terapagos and many common species.

Does the calculator include Scarlet and Violet's modifiers?

Yes. It applies sandwich Capture Power levels 1 to 3, the back-strike bonus, the missing-badge penalty on high-level targets and the Catching Charm, on top of the ball, status and HP inputs.

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Catch rate.

a = (3M−2H)·rate·ball·status ÷ 3M
P = crit·b + (1−crit)·(b/65536)⁴ · Gen III–IX

bulbasaurgrasspoison

base rate 45/255 · 6.9 kg · Spe 45 · #001

Catch probability · per throw

33.8%

bulbasaur · Ultra Ball · 50% HP · None · Gen IX

Expected balls≈3.0

50% caught by2 balls

95% caught by8 balls

Ball modifier2×

Status modifier1×

Crit capture0.0%

Catch value a60.0 / 255

Target

rate 45

Generation

Status

HP50%

Dex caught · crit0

Conditionsultra ball

Wild level

no bonus at 13+

Capture Power

Back strike

Badges

no penalty at this level

Catching Charm

Ball ↓ · odds at HP →Mod

Scale0% → 100% per throw† uses the condition inputs above · click a row to pick a ball · header to set HP

Caught withincumulative odds

33.8%

1 ball

56.2%

2 balls

71.0%

3 balls

87.3%

5 balls

98.4%

10 balls · hits 95%

99.8%

15 balls

>99.9%

25 balls

>99.9%

50 balls

100%

100 balls

100%

500 balls

Pokémon catch rate calculator and formula guide

Pokémon catch rates range from 3 (Articuno, Zapdos, Moltres, and most legendaries) to 255 (Terapagos and many common species). This calculator uses the exact Gen III-IX formula to compute your real probability of catching any Pokémon under any conditions.

The standard catch formula

From Generation III onward, the game calculates a modified catch value: a = ((3*maxHP - 2*currentHP) * catchRate * ballMod * statusMod) / (3*maxHP). If a reaches 255 the catch is guaranteed. Gen 1 and Gen 2 used different formulas that this calculator does not cover.

From catch value to catch chance: the shake checks

The catch value is not your catch chance. The game converts it into a shake probability b = 65536 / (255/a)^(3/16), then rolls a random number against b four times, once per shake of the ball. The Pokémon is caught only if all four rolls pass, so your real chance per throw is (b/65536)^4. Worked example: Bulbasaur (catch rate 45) in an Ultra Ball at 50% HP gives a = 60, b = 49963, and a real catch chance of about 33.8% per throw, not the 47% that a/128 would naively suggest.

Critical captures (Gen V+) replace the four shake checks with a single one. The chance of a critical capture occurring is floor(min(255, a) * multiplier / 6) / 256, where the multiplier grows with your Pokédex: 0.5x from 31 caught, 1x from 151, 1.5x from 301, 2x from 451, and 2.5x above 600. In the Bulbasaur example with a completed dex, that is a 9.8% chance of a critical capture, lifting the overall odds per throw to about 37.9%.

Key modifiers

Status conditions: Sleep and Freeze give a 2.5x bonus from Gen 5 onward (2x in Gen 3-4). Paralysis, Burn, and Poison give 1.5x in every generation. Always inflict a status before throwing.
Ball types: This calculator models 20 ball types with their conditional bonuses - Net Ball (3.5x for Water/Bug types), Dusk Ball (3x at night or in caves), Timer Ball (scaling with turn count), and more.
Critical capture (Gen V+): A special single-shake-check throw whose chance scales with your Pokédex completion. More registered Pokémon means more frequent critical captures.
HP percentage: Lower HP dramatically improves catch odds. The odds matrix shows every ball at every HP threshold at once.
Scarlet and Violet: a sandwich with Capture Power multiplies the catch value by 1.1, 1.25 or 2 by level, a back strike (the "caught it off guard" opener) doubles it, and a wild Pokémon above the level your badges can command loses 20% per missing badge (obedience runs to level 25 with no badges, plus 5 per badge). The Catching Charm doubles the critical capture multiplier in Let's Go, Sword and Shield, and Scarlet and Violet. The low-level bonus is (36 minus 2 × level) / 10 below level 13, steeper than Sword and Shield's (30 minus level) / 10 below 20.

The odds matrix ranks every ball by effectiveness for your current target, and the cumulative strip shows how many balls you need to be 95% sure - so you know whether to stock up at the Poke Mart before heading into a legendary encounter.