CP Multiplier

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
1 0.094
1.5 0.1351374318
2 0.16639787
2.5 0.192650919
3 0.21573247
3.5 0.2365726613
4 0.25572005
4.5 0.2735303812
5 0.29024988
5.5 0.3060573775
6 0.3210876
6.5 0.3354450362
7 0.34921268
7.5 0.3624577511
8 0.3752356
8.5 0.387592416
9 0.39956728
9.5 0.4111935514
10 0.4225
10.5 0.4329264091
11 0.44310755
11.5 0.4530599591
12 0.4627984
12.5 0.472336093
13 0.48168495
13.5 0.4908558003
14 0.49985844
14.5 0.508701765
15 0.51739395
15.5 0.5259425113
16 0.5343543
16.5 0.5426357375
17 0.5507927
17.5 0.5588305862
18 0.5667545
18.5 0.5745691333
19 0.5822789
19.5 0.5898879072
20 0.5974
20.5 0.6048236651
21 0.6121573
21.5 0.6194041216
22 0.6265671
22.5 0.6336491432
23 0.64065295
23.5 0.6475809666
24 0.65443563
24.5 0.6612192524
25 0.667934
25.5 0.6745818959
26 0.6811649
26.5 0.6876849038
27 0.69414365
27.5 0.70054287
28 0.7068842
28.5 0.7131691091
29 0.7193991
29.5 0.7255756136
30 0.7317
30.5 0.7347410093
31 0.7377695
31.5 0.7407855938
32 0.74378943
32.5 0.7467812109
33 0.74976104
33.5 0.7527290867
34 0.7556855
34.5 0.7586303683
35 0.76156384
35.5 0.7644860647
36 0.76739717
36.5 0.7702972656
37 0.7731865
37.5 0.7760649616
38 0.77893275
38.5 0.7817900548
39 0.784637
39.5 0.7874736075
40 0.7903

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.