To find z score for percentile, we check the percentile value in the center part of the normal distribution table. For example, find the z score of the 45^{th} percentile.

The Z score for the 45^{th} percentile is -0.13

Example two, find the z score of the 33^{rd} percentile.

The Z score for the 33^{rd} percentile is -0.44

**Percentile to z score formula**

The formula of percentile to z score formula assumes that the underlying distribution is normal. The formula to calculate percentile to z score is given by;

Where T is the percentile

Notably, we can find the value of the z score of a percentile in excel using the excel function **=Norm.Inv (T,0,1)**

Where T is the percentile

0 is the standard mean

1 is the standard deviation

For example, consider the 40^{th} Percentile, and find the z score in excel.

Thus, the value will be;

The Z-score for the 40^{th} percentile is -0.25335

**Examples to find z score for percentile**

**What z score represents the 95**^{th} percentile

^{th}percentile

The z-score that represents the 95^{th} Percentile is 1.645

**What z score represents the 90**^{th} percentile

^{th}percentile

The z-score that represents the 90^{th} Percentile is 1.282

**What z score represents the 80**^{th} percentile

^{th}percentile

The z-score that represents the 80^{th} Percentile is 0.842

**What z score represents the 75**^{th} percentile

^{th}percentile

The z-score that represents the 75^{th} Percentile is 0.674

**What z score represents the 85**^{th} percentile

^{th}percentile

The z-score that represents the 85^{th} Percentile is 1.036

**What z score represents the 20**^{th} percentile/2^{nd} decile

^{th}percentile/2

^{nd}decile

The z-score that represents the 20^{th} Percentile is -0.842

**Z score percentile table/chart**

Percentile | Z-Score | Percentile | Z score |

1 | -2.326 | 51 | 0.025 |

2 | -2.054 | 52 | 0.05 |

3 | -1.881 | 53 | 0.075 |

4 | -1.751 | 54 | 0.1 |

5 | -1.645 | 55 | 0.126 |

6 | -1.555 | 56 | 0.151 |

7 | -1.476 | 57 | 0.176 |

8 | -1.405 | 58 | 0.202 |

9 | -1.341 | 59 | 0.228 |

10 | -1.282 | 60 | 0.253 |

11 | -1.227 | 61 | 0.279 |

12 | -1.175 | 62 | 0.305 |

13 | -1.126 | 63 | 0.332 |

14 | -1.08 | 64 | 0.358 |

15 | -1.036 | 65 | 0.385 |

16 | -0.994 | 66 | 0.412 |

17 | -0.954 | 67 | 0.44 |

18 | -0.915 | 68 | 0.468 |

19 | -0.878 | 69 | 0.496 |

20 | -0.842 | 70 | 0.524 |

21 | -0.806 | 71 | 0.553 |

22 | -0.772 | 72 | 0.583 |

23 | -0.739 | 73 | 0.613 |

24 | -0.706 | 74 | 0.643 |

25 | -0.674 | 75 | 0.674 |

26 | -0.643 | 76 | 0.706 |

27 | -0.613 | 77 | 0.739 |

28 | -0.583 | 78 | 0.772 |

29 | -0.553 | 79 | 0.806 |

30 | -0.524 | 80 | 0.842 |

31 | -0.496 | 81 | 0.878 |

32 | -0.468 | 82 | 0.915 |

33 | -0.44 | 83 | 0.954 |

34 | -0.412 | 84 | 0.994 |

35 | -0.385 | 85 | 1.036 |

36 | -0.358 | 86 | 1.08 |

37 | -0.332 | 87 | 1.126 |

38 | -0.305 | 88 | 1.175 |

39 | -0.279 | 89 | 1.227 |

40 | -0.253 | 90 | 1.282 |

41 | -0.228 | 91 | 1.341 |

42 | -0.202 | 92 | 1.405 |

43 | -0.176 | 93 | 1.476 |

44 | -0.151 | 94 | 1.555 |

45 | -0.126 | 95 | 1.645 |

46 | -0.1 | 96 | 1.751 |

47 | -0.075 | 97 | 1.881 |

48 | -0.05 | 98 | 2.054 |

49 | -0.025 | 99 | 2.326 |

50 | 0 |

**What is a percentage rank?**

Percentile rank (PR) of a given score in statistics refers to the proportion of scores lower than a given score in a frequency distribution.

To make the meaning of test results more understandable, percentile ranks are frequently used.

According to the test theory, the percentile rank of a raw score is understood to be the proportion of test-takers in the norm group who received a score lower than the score of interest.

Statistics professionals frequently use percentile rank to determine how an individual assessment score or outcome relates to others in a set.

Additionally, knowing the percentile rank can help one gain perspective on how well they did on a particular test.