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
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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
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Statistics How To
statisticshowto.com › home › probability and statistics topics index › critical values: find a critical value in any tail › z score to percentile / percentile to z score (calculator)
Z score to Percentile / Percentile to Z Score (Calculator) - Statistics How To
March 6, 2025 - This mini table shows the area ... is .0227. To convert this decimal to a percentile, move the decimal point two places to the right and then add a percentage sign: .0227 becomes 2.27%...
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MedCentral
medcentral.com › calculators › stats-data › z-score-to-percentile-estimation
Z Score to Percentile Calculator
February 13, 2024 - Estimate percentiles from Z scores accurately and efficiently with our professional Z Score to Percentile Estimation tool.
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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.
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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.

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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 ...
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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. Because of this, percentile tables ...
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GeeksforGeeks
geeksforgeeks.org › engineering mathematics › how-to-find-z-score-from-percentile
How to find z score from Percentile - GeeksforGeeks
July 23, 2025 - The calculation of percentiles involves sorting the data set in ascending order and then determining the position of the desired percentile using the formula: ... Step 1: To turn a percentile to a probability simply divide the obtained value by 100.
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Calculator Online
calculator-online.net › z-score-to-percentile
Z Score to Percentile Calculator
Find the Percentile of the z-score value of 1.2. Use the z score normality table of relative values of percentile and z score. Now check the normality table to find the percentile relative to the z score value: Then Z score =1.2 = 0.8849 Z score to percentile formula...
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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.
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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.
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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 determine the Z Score associated with a given percentile and vice versa.
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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.
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MathCracker
mathcracker.com › z-score-percentile-calculator
Z-Score to Percentile Calculator - MathCracker.com
February 23, 2019 - Also, a z-score represents a specific location in the distribution, so that there is a certain area that is to the left of that z-score. And that's exactly how we define the percentile associated to a z-score: it is the area (in percentage terms) that is to the left of that z-score.
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Statology
statology.org › home › how to convert between z-scores and percentiles in excel
How to Convert Between Z-Scores and Percentiles in Excel
March 30, 2020 - We can use the following built-in Excel function to convert a z-score to a percentile: ... cumulative = TRUE returns the cumulative distribution function; FALSE returns the probability distribution function. We will use TRUE to calculate percentiles.
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CalculatorD
calculatored.com › z-score-to-percentile
Z Score to Percentile Calculator
By keeping in account the x score ... < 1.7) = 0.9554 · Calculating Equivalent Percentile Value with the Z score to percentile formula: Percentile = (Z score table value)*100 ·...