CP Multiplier by Level
CP Multiplier (CPM) is a number which Niantic uses to scale the attributes of a pokemon based on its level. Examples of attributes which depend on CPM are attack, defense, stamina, and capture probability. There is one CPM value for each possible pokemon level (and half level).
| Level | CP Multiplier | stardust cost | sd | xl |
|---|---|---|---|---|
| 50 | 0.84029999 | 0 | 520,000 | 296 |
| 49.5 | 0.83779999 | 15000 | 520,000 | 296 |
| 49 | 0.83529999 | 15000 | 505,000 | 276 |
| 48.5 | 0.83279999 | 14000 | 490,000 | 256 |
| 48 | 0.83029999 | 14000 | 476,000 | 236 |
| 47.5 | 0.82779999 | 14000 | 462,000 | 216 |
| 47 | 0.82529999 | 14000 | 448,000 | 199 |
| 46.5 | 0.82279999 | 13000 | 434,000 | 182 |
| 46 | 0.82029999 | 13000 | 421,000 | 165 |
| 45.5 | 0.81779999 | 13000 | 408,000 | 148 |
| 45 | 0.81529999 | 13000 | 395,000 | 133 |
| 44.5 | 0.812799985 | 12000 | 382,000 | 118 |
| 44 | 0.81029999 | 12000 | 370,000 | 103 |
| 43.5 | 0.8078 | 12000 | 358,000 | 88 |
| 43 | 0.8053 | 12000 | 346,000 | 76 |
| 42.5 | 0.802799995 | 11000 | 334,000 | 64 |
| 42 | 0.8003 | 11000 | 323,000 | 52 |
| 41.5 | 0.797800015 | 11000 | 312,000 | 40 |
| 41 | 0.79530001 | 11000 | 301,000 | 30 |
| 40.5 | 0.792803968 | 10000 | 290,000 | 20 |
| 40 | 0.7903 | 10000 | 280,000 | 10 |
| 39.5 | 0.7874736075 | 10000 | 270,000 | |
| 39 | 0.784637 | 10000 | 260,000 | |
| 38.5 | 0.7817900548 | 9000 | 250,000 | |
| 38 | 0.77893275 | 9000 | 241,000 | |
| 37.5 | 0.7760649616 | 9000 | 232,000 | |
| 37 | 0.7731865 | 9000 | 223,000 | |
| 36.5 | 0.7702972656 | 8000 | 214,000 | |
| 36 | 0.76739717 | 8000 | 206,000 | |
| 35.5 | 0.7644860647 | 8000 | 198,000 | |
| 35 | 0.76156384 | 8000 | 190,000 | |
| 34.5 | 0.7586303683 | 7000 | 182,000 | |
| 34 | 0.7556855 | 7000 | 175,000 | |
| 33.5 | 0.7527290867 | 7000 | 168,000 | |
| 33 | 0.74976104 | 7000 | 161,000 | |
| 32.5 | 0.7467812109 | 6000 | 154,000 | |
| 32 | 0.74378943 | 6000 | 148,000 | |
| 31.5 | 0.7407855938 | 6000 | 142,000 | |
| 31 | 0.7377695 | 6000 | 136,000 | |
| 30.5 | 0.7347410093 | 5000 | 130,000 | |
| 30 | 0.7317 | 5000 | 125,000 | |
| 29.5 | 0.7255756136 | 5000 | 120,000 | |
| 29 | 0.7193991 | 5000 | 115,000 | |
| 28.5 | 0.7131691091 | 4500 | 110,000 | |
| 28 | 0.7068842 | 4500 | 105,500 | |
| 27.5 | 0.70054287 | 4500 | 101,000 | |
| 27 | 0.69414365 | 4500 | 96,500 | |
| 26.5 | 0.6876849038 | 4000 | 92,000 | |
| 26 | 0.6811649 | 4000 | 88,000 | |
| 25.5 | 0.6745818959 | 4000 | 84,000 | |
| 25 | 0.667934 | 4000 | 80,000 | |
| 24.5 | 0.6612192524 | 3500 | 76,000 | |
| 24 | 0.65443563 | 3500 | 72,500 | |
| 23.5 | 0.6475809666 | 3500 | 69,000 | |
| 23 | 0.64065295 | 3500 | 65,500 | |
| 22.5 | 0.6336491432 | 3000 | 62,000 | |
| 22 | 0.6265671 | 3000 | 59,000 | |
| 21.5 | 0.6194041216 | 3000 | 56,000 | |
| 21 | 0.6121573 | 3000 | 53,000 | |
| 20.5 | 0.6048236651 | 2500 | 50,000 | |
| 20 | 0.5974 | 2500 | 47,500 | |
| 19.5 | 0.5898879072 | 2500 | 45,000 | |
| 19 | 0.5822789 | 2500 | 42,500 | |
| 18.5 | 0.5745691333 | 2200 | 40,000 | |
| 18 | 0.5667545 | 2200 | 37,800 | |
| 17.5 | 0.5588305862 | 2200 | 35,600 | |
| 17 | 0.5507927 | 2200 | 33,400 | |
| 16.5 | 0.5426357375 | 1900 | 31,200 | |
| 16 | 0.5343543 | 1900 | 29,300 | |
| 15.5 | 0.5259425113 | 1900 | 27,400 | |
| 15 | 0.51739395 | 1900 | 25,500 | |
| 14.5 | 0.508701765 | 1600 | 23,600 | |
| 14 | 0.49985844 | 1600 | 22,000 | |
| 13.5 | 0.4908558003 | 1600 | 20,400 | |
| 13 | 0.48168495 | 1600 | 18,800 | |
| 12.5 | 0.472336093 | 1300 | 17,200 | |
| 12 | 0.4627984 | 1300 | 15,900 | |
| 11.5 | 0.4530599591 | 1300 | 14,600 | |
| 11 | 0.44310755 | 1300 | 13,300 | |
| 10.5 | 0.4329264091 | 1000 | 12,000 | |
| 10 | 0.4225 | 1000 | 11,000 | |
| 9.5 | 0.4111935514 | 1000 | 10,000 | |
| 9 | 0.39956728 | 1000 | 9,000 | |
| 8.5 | 0.387592416 | 800 | 8,000 | |
| 8 | 0.3752356 | 800 | 7,200 | |
| 7.5 | 0.3624577511 | 800 | 6,400 | |
| 7 | 0.34921268 | 800 | 5,600 | |
| 6.5 | 0.3354450362 | 600 | 4,800 | |
| 6 | 0.3210876 | 600 | 4,200 | |
| 5.5 | 0.3060573775 | 600 | 3,600 | |
| 5 | 0.29024988 | 600 | 3,000 | |
| 4.5 | 0.2735303812 | 400 | 2,400 | |
| 4 | 0.25572005 | 400 | 2,000 | |
| 3.5 | 0.2365726613 | 400 | 1,600 | |
| 3 | 0.21573247 | 400 | 1,200 | |
| 2.5 | 0.192650919 | 200 | 800 | |
| 2 | 0.16639787 | 200 | 600 | |
| 1.5 | 0.1351374318 | 200 | 400 | |
| 1 | 0.094 | 200 | 200 | |
| 51 | 0.84529999 | |||
| 50.5 | 0.84279999 |
Half Step Formula
Half levels are calculated on the fly as a quadratic mean of the intervening levels:
$$CPM_{level+.5} = \sqrt{ \frac{CPM_{level}^2 + CPM_{level+1}^2}{2}}$$This formula formula can be rearranged as follows:
$$CPM_{level+.5} = \sqrt{ CPM_{level}^2 - \frac{CPM_{level}^2}{2} + \frac{CPM_{level+1}^2}{2} }$$We can define a new variable CPMStep as:
$$CPMStep = \frac{CPM_{level+1}^2 - CPM_{level}^2}{2}$$Then the CPM formula can be simplified as:
$$CPM_{level+.5} = \sqrt{ CPM_{level}^2 + CPMStep }$$CPMStep has the property of holding constant every ten levels:
| Levels | CPMStep |
|---|---|
| 1-9.5 | 0.009426125469 |
| 10-19.5 | 0.008919025675 |
| 20-29.5 | 0.008924905903 |
| 30-39.5 | 0.00445946079 |
CPMStep is halved by level 30. This is the reason CP gain for Pokemon after level 30 to be halved.
