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).

LevelCP Multiplier
10.094
1.50.135137432
20.16639787
2.50.192650919
30.21573247
3.50.236572661
40.25572005
4.50.273530381
50.29024988
5.50.306057377
60.3210876
6.50.335445036
70.34921268
7.50.362457751
80.37523559
8.50.387592406
90.39956728
9.50.411193551
100.42250001
10.50.432926419
110.44310755
11.50.4530599578
120.46279839
12.50.472336083
130.48168495
13.50.4908558
140.49985844
14.50.508701765
150.51739395
15.50.525942511
160.53435433
16.50.542635767
170.55079269
17.50.558830576
180.56675452
18.50.574569153
190.58227891
19.50.589887917
200.59740001
20.50.604818814
210.61215729
21.50.619399365
220.62656713
22.50.633644533
230.64065295
23.50.647576426
240.65443563
24.50.661214806
250.667934
25.50.674577537
260.68116492
26.50.687680648
270.69414365
27.50.700538673
280.70688421
28.50.713164996
290.71939909
29.50.725571552
300.7317
30.50.734741009
310.73776948
31.50.740785574
320.74378943
32.50.746781211
330.74976104
33.50.752729087
340.75568551
34.50.758630378
350.76156384
35.50.764486065
360.76739717
36.50.770297266
370.7731865
37.50.776064962
380.77893275
38.50.781790055
390.78463697
39.50.787473578
400.79030001

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.

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