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CP Multiplier

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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:

LevelsCPMStep
1-9.50.009426125469
10-19.50.008919025675
20-29.50.008924905903
30-39.50.00445946079

CPMStep is halved by level 30. This is the reason CP gain for Pokemon after level 30 to be halved.