Measuring Usability
Quantitative Usability, Statistics & Six Sigma by Jeff Sauro

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 Measuring Usability LLC, a company providing statistics and usability consulting to Fortune 1000 companies.
He is the author of over 20 journal articles and 4 books on statistics and the user-experience.
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Posted Comments

There are 43 Comments

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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