Usability, Customer Experience & Statistics

Z-Score to Percentile Calculator

Jeff Sauro • December 3, 2007

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. Selecting one side provides the area only above or below the Z-value. See also the interactive Graph of the Standard Normal Curve. To convert a percentage into a Z-Score use the Percentile to Z-Score Calculator.

 Shaded area is % of the area under the curve.Shaded area is % of the area under the curve.
Z-ScorePercent of Area100-Percent

Download this calculator in an excel file or take a Crash course in Z-scores



Watch a Short Demo



About Jeff Sauro

Jeff Sauro is the founding principal of MeasuringU, a company providing statistics and usability consulting to Fortune 1000 companies.
He is the author of over 20 journal articles and 5 books on statistics and the user-experience.
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There are 59 Comments

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May 12, 2016 | Mark wrote:

8hDWi0 http://www.y7YwKx7Pm6OnyJvolbcwrWdoEnRF29pb.com 


March 25, 2016 | Jorge Maldonado wrote:

Thanks for this calculator! There are others online, but this is the first one that does it out to 10 decimal places, which is essential for finding the low (but non zero!) probabilities in the tails. Thanks again! 


March 16, 2016 | Donald Cox wrote:

There appears to be a bug in the calculator. When I put in 0 for the zscore I get an answer of 100 for percent of area, when it should be 50, in my understanding. 


January 17, 2016 | Ilham Abdalla Bashir Fadl wrote:

You make my life easy . Millions of thanks to ease understanding of the Z score areas...  


September 9, 2014 | dam wrote:

what is the formula used to calculate it? 


July 19, 2014 | Sarah wrote:

Thank you for this page, I mean that sincerely. I don't have a mathematical mind and being walked through simplifies this process for me. This page and your expertise is much appreciated! 


July 19, 2014 | Sarah wrote:

Thank you! Your simplified a process I over complicated! 


December 14, 2013 | Ali wrote:

Thanks a lot 


April 17, 2013 | Joan wrote:

Hi, great resource for quick and easy calculations; however, when I pop in a negative Z score (especially small negative scores) the accompanying graph does not represent the values of the percentiles given below. They don't make sense. Perhaps a glitch? 


March 5, 2013 | Jenn wrote:

So helpful!  


September 17, 2012 | Dumb Dave wrote:

Viki - I think it is sad that Mensa would let you join after you "just took and IQ test"...guess their standards are getting lower.  


September 15, 2012 | Stewart wrote:

Wonderful. I'm working on a new game and would like to check my figures.
Example: Successful events pay 8:1, the player wins 8 times the bet, or loses the bet. n = Number of events = 1000, r = Number of successful events = 101,
p = Probability of success on a single trial =0.10,
1-p = Probability of failure = 0.90. What is the Z score?
 


August 17, 2012 | Viki wrote:

I just took and IQ test so that I can join mensa, and passed. I wanted to convert to percentile: 99.62. I think it's sad that so few people (including me) can understand math well enough to understand how the universe works. Apparently there's a whole cohort of people who feel this way and some have tried to redo physics so that it's easy. They seem to have a metaphysical notion that the universe just wouldn't be so complicated, maybe out of universal kindness, I don't know. A book "Physics on the Fringe" by Margaret Wortheim is about these fringe thinkers. 


August 13, 2012 | Clyde Killian wrote:

Really nice calculator of probability associated with Z score. The graphic of the normal curve really enhances understanding of this content. 


August 11, 2012 | harshani nilushika wrote:

if i got 65 for 4 subjects in my exam what will be my z-score 


May 7, 2012 | anonymous wrote:

you spelled "anonymous" wrong 


March 25, 2012 | Vicente Cassepp Borges wrote:

Congratulations. I wish the figure of the normal curves decrible the data with more precision, but your calculator is very nice. 


March 15, 2012 | ABHISHEK wrote:

VERY BAD CALCULATOR
PLEASE TRY TO MAKE IT ACCESS EASY 


March 14, 2012 | Mohammed Umar wrote:

The word excellent cannot describe this site and its contents ! 


March 11, 2012 | Dana Gentles wrote:

I like this calculator, its doing the z score good job  


December 30, 2011 | Brian R. wrote:

Thank you, Jeff, so much for making available this calculator. It is great. I have used it many times over several years. It is very handy for someone like me running a small non-proft research institute without a lot of "resources." 


May 22, 2011 | janet wrote:

makes it easier to understand 


May 1, 2011 | Roger Bachmann wrote:

This sure beats looking up the z-table in a book. Nice explanation as well. 


January 20, 2011 | sean courtney wrote:

excellent resource. just what my students need. 


December 21, 2010 | Jo wrote:

Clear and easy! 


November 14, 2010 | Michelle Freier Raleigh wrote:

good graphic and verbal presentation 


October 29, 2010 | anonymous wrote:

Be careful using this program. The answers are in percentages. If you want to use the results in equations or compare to probability z-score charts, you have to divide the right side result by 100. 


October 21, 2010 | Robert Glidden Jr. wrote:

Fantastic work! 


April 12, 2010 | saleh wrote:

Hi,
This calculation assumes a normal distibution of scores, right?
Lets say that I got a score of 404 in an exam and the mean is 271 and the SD is 50. The z-score will be 2.66 (z=x-m/sd).
Can I caluculate the percentile corresponding to the score of 404 without assuming a normal distribution of the scores?
Thank you 


April 5, 2010 | Danielle Rice wrote:

I'd like to know what numerical method is used to calculate probabilities. Thanks 


March 25, 2010 | anonymous wrote:

thank you very much helped a lot in my hw 


March 8, 2010 | Aditi M Sengupta wrote:

5. The Maine Education Assessment (MEA), a test completed annually by all students in the state in select grades, has M = 250 and SD = 50. What MEA score separates the upper 30% of the cases from the lower 70%?(EDPS 621, Eastern Michigan University, Winter, 2010) 


March 3, 2010 | Janella annabella Shontella Ivonovich wrote:

math should go die. 


March 3, 2010 | Percepicia wrote:

is there anyway you can show us how to actually do math problems??? and not just tell us the answer???? k. thanks.
percepicia 


January 26, 2010 | Stephanie wrote:

Thank you so much for this incredibly handy tool!It's so appreciated! 


January 9, 2010 | anonymous wrote:

perfect. 


November 12, 2009 | Peter Belamarich wrote:

great 


November 6, 2009 | Kathy wrote:

The pictures are helpful--made me more certain I was using it correctly. I compared the answers to a z-table and both gave the same answer (for 1-sided), so I felt confident I was getting using the info correctly. I don't understand the statistics, just needed to be able to convert a Std Deviation Score to a Percentile for a market potential calculation. 


September 30, 2009 | Sam wrote:

What was the formula that you used to find the area associated with each z-score? 


May 28, 2009 | Tom wrote:

seen a couple people ask the same question, but i'm looking for an actual formula to convert the Z-scores to percentiles. can't find anywhere on the internet that has it. 


April 17, 2009 | troy percival wrote:

i am writing a database and need to make calculations to turn z scores into percentages. I am enquiring if you can help me with the formula that operates the calculator. Many thanks 


March 9, 2009 | Denise wrote:

for a population with a mean of 80 and standard deviation of 12, what is the z-score corresponding to x=71? 


March 3, 2009 | Susan wrote:

6. An aptitude test has a mean of 220 and standard deviation of 10. find the corresponding z score for: a) a test score of 232 b) a test score of 212 


January 26, 2009 | anonymous wrote:

6. An aptitude test has a mean of 220 and standard deviation of 10. find the corresponding z score for: a) a test score of 232 


October 16, 2008 | Verena wrote:

Hi,
I have been using your tool to calculate percentiles from z-score values. Until like a week ago, it worked perfectly fine, but now, when I enter a z-score of 3, one-sided, the value under 100% should be the higher one (in fact, it should be close to 99). Now, however, the higher number is being reported under the % of area section - how can that be? 


September 11, 2008 | Ivy wrote:

Your MS class all took the practice clinical certification exam. The following is a listing of the raw scores that you and your friends received. Compute the z scores for these raw scores where the mean is 55 and the standard deviation is 2.5. What is a “z” score? What does it tell you?

Scores: 60, 72, 48, 53, 56, 51, 50.5, 59.5
x (observation) = 8 mean = 55 standard deviation = 2.5

z = Observation - Mean
Standard Deviation

= 8 – 55 / 2.5 = - 18.8

I don't have a book to find the z score for -18.8. I am not even sure if that is possible to get a z score for -18.8. Thank you for your help. 


June 24, 2008 | Cindy Searcy wrote:

How would I figure a z-score if the mean was 11.9, the std. deviation is .4 and I want to be 95% sure that a bag of chips did not weigh 12 Oz. as specified on bag, and I weighed 30 Bags? 


May 15, 2008 | Alex wrote:

hey, can send me the formula that happens in the BG? 


April 30, 2008 | Steve Kelner wrote:

I can't seem to do a negative z-score. Otherwise outstanding! 


March 19, 2008 | Justin wrote:

I have a normal distribution of Homeruns per week with mean 8.3 and standard deviation of 1.1. My team is projected to hit 10 homeruns in a week while my opponent's team is projected to only hit 8. What is the likelyhood of my team hitting more homeruns during the coming week? I am guessing P(8

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