You really can't do it with pen and paper. It requires approximating an integral for which there is no anti derivative. Answer from Deleted User on reddit.com
MeasuringU
measuringu.com › calculators › pcalcz
Z-Score to Percentile Calculator – MeasuringU
Enter a z-critical value and get the area under the normal curve (a percentage). Selecting two-sided provides the area above Z and below -Z. Download this calculator in an excel file or take a Crash course in Z-scores
Videos
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StatCrunch Tutorial - Convert z score to percentile and percentile ...
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Finding Normal Percentiles Using a Z Score Table - YouTube
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Z-scores: Calculating Percentiles - YouTube
How to Find z-Score from Percentile | Statistics Exercises - YouTube
Finding z-score for a percentile | AP Statistics | Khan Academy ...
MathBlog
mathblog.com › statistics › definitions › z-score › z-to-percentile-calculator
Z-score to Percentile Calculator
March 7, 2024 - This Z-Score to percentile calculator instantly computes the percentile associated with any given Z-score. Just enter the Z-score value below, and click Calculate. You may also want to check our Percentile to Z-score chart for normal distribution. The table shows the Z-scores corresponding ...
Reddit
reddit.com › r/askstatistics › how is z-score converted to percentile?
r/AskStatistics on Reddit: How is z-score converted to percentile?
November 14, 2017 -
Everything I find says to reference a converter or a chart, but how is it calculated if I have z-score (standard deviations from mean)?
I'm looking to know how the math works.
Top answer 1 of 5
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You really can't do it with pen and paper. It requires approximating an integral for which there is no anti derivative.
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If you're talking about how to calculate the tail area corresponding to a z-score -- there's a reason why people use tables or computer programs; the integral of the normal density doesn't have a "closed form". You can write various series for it, and there are numerous very accurate approximations (which are used by computer programs, but they're not very nice for a human to use). If you have some need to calculate it when you have no tables or computer, just a calculator with the usual mathematical functions (like sqrt, exp and log), and perhaps the recall of a few important values (like 1.28, 1.645 and 1.96) you can compute pretty well using numerical integration (even Simpson's rule works quite well). Another approach would use linear interpolation in the logit. One nice aspect of these approaches is the accuracy is best where you need it the most -- near significance levels you're likely to use. 2. If you literally mean a percentile of some normal distribution with mean μ and standard deviation σ, and you want the percentile corresponding to the z-score (which itself is a percentile of a standard normal) then that's μ+σz
Statology
statology.org › home › percentile to z-score calculator
Percentile to Z-Score Calculator
April 8, 2025 - Simply enter a percentile in the box below and then click the “Calculate” button. ... Z-scores (also called standard scores) allow statisticians to convert values from any normal distribution into a standard normal distribution. A z-score tells you how many standard deviations a value is from the mean.
Calculator Online
calculator-online.net › z-score-to-percentile
Z Score to Percentile Calculator
For the Z Score to percentile conversion, you need to find the corresponding value of the percentile from the z-score table. A z score to percentile value describes how much percentage of the observation falls below a certain value of the dataset.
Pindling
pindling.org › Math › Learning › Statistics › z_scores_table.htm
Appendix - z-score percentile for normal distribution
Appendix - z-score percentile for normal distribution
Khan Academy
khanacademy.org › math › ap-statistics › density-curves-normal-distribution-ap › normal-distributions-calculations › v › finding-z-score-for-a-percentile
Finding z-score for a percentile (video)
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Home and Learn
homeandlearn.co.uk › excel2007 › z-scores.html
z-scores, percentiles and Excel
Cell C101 should have a percentile value of 100%, meaning this student was better than everyone else. A percentile figure of 77% means these students were better than 77% of their classmates: Percentiles and their z-scores are the same, regardless of your data.
Empiricalrulecalculators
empiricalrulecalculators.com › z-score-to-percentile-converter
Z-Score to Percentile Converter: Easy Normal Distribution
July 21, 2025 - Whether you’re a student analyzing test scores, an analyst evaluating data, or a researcher interpreting results, this tool makes it easy to convert z score to percentile instantly. By entering a z-score, you get the percentage of data below that value, based on the normal distribution percentile ...
Z Score Table
z-table.com › z-scores-to-percentiles-chart.html
Z Scores to Percentiles Chart - Z SCORE TABLE
For instance, the 84th percentile corresponds to a Z Score of 1, meaning that 84% of the data points in a dataset fall below the value with a Z Score of approximately 1. The Percentiles to Z Score Chart typically includes two columns: Percentile and Z Score. By using this chart, you can quickly ...
Albert.io
albert.io › home › z-score calculations & percentiles in a normal distribution: ap® statistics
Z-score Calculations & Percentiles in a Normal Distribution
March 1, 2022 - Use this AP® Statistics review to be sure you understand everything you need to beat z-score questions on the exam. We will tell you all of the concepts related to z-scores, show you how to perform z-score calculations using sample questions, and explain percentiles in a normal distribution.
Edutized
edutized.com › tutorial › calculate-percentile-from-z-score
How to calculate percentile from z score – Edutized
To calculate the percentile from z score, we look at the value directly from the standard normal table and multiply the value by 100. For example, consider a z score of -1.67.
CalculatorD
calculatored.com › z-score-to-percentile
Z Score to Percentile Calculator
By keeping in account the x score normality table enumerate the percentile of the z score value for the 1.7.
My Math Tables
mymathtables.com › statistic › z-score-percentile-normal-distribution.html
Z Score Percentile Distribution Table
Z Score Calculator Z Score to Percentile Calculator · H1: parameter < value · Notice the inequality points to the left · Decision Rule: Reject H0 if t.s. < c.v. H1: parameter > value · Notice the inequality points to the right · Decision Rule: Reject H0 if t.s.
EasyCalculation
easycalculation.com › statistics › zscore-to-percentile.php
Z Score to Percentile Calculator
Calculate the left-tailed, right-tailed, two-tailed and confidence level percentage values from the given z-score value using this online Z score to percentile calculator.