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

Percentile to Z-Score Calculator

Jeff Sauro • December 4, 2007

Enter the area under the normal curve (a proportion between 0 & 1) and get the Z-critical value, one-sided or two-sided. To convert a Z-Score into a percentage use the Z-Score to Percentile Calculator. See also the interactive Graph of the Standard Normal Curve.

Proportion of AreaZ-Score
  

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


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 35 Comments

June 28, 2014 | ice wrote:

how it work. please tell me how it work. from area to z score.
What formular are you use ?
Help me please ! 


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October 16, 2013 | George Gillson wrote:

Why don't you put both calculators (Z to percentile and percentile to Z) on the same page? 


August 26, 2013 | Sw wrote:

Sorry - some typo error - Resend with corrections:


I want to get some benchmark numbers or to define some targets for my internal surveys/KPIs.
I have a report which comprise of data gathered through similiar surveys, carried out over 98 schools, sample size of ~34,000 students.
If I plot histograms of responses (total agree/satisfied) and do some statistical analysis for each survey question (mode, median, mean, percentiles - 25th, 75th and 90th), is it right to take the 90th percentile reading as the "top 10% satisfaction level" and use it as our target KPI?
 


August 26, 2013 | Sw wrote:

I want to get some benchmark numbers or at least use data of some form similar industry to define some targets for my internal surveys/KPIs.
I have a report which comprise of data gathered through similiar surveys carried out over 98 schools, same size of ~34,000 students.
If I plot histograms of responses (total agree/satisfied) for each survey question, with statistical data (mode, median, mean, percentiles - 25th, 75th and 90th), is it right to take the 90th percentile reading as the "top 10% satisfaction level" and use it as our target KPI? 


April 30, 2013 | Umesh W wrote:

Gud Calculator,made my job easy 


March 27, 2013 | anonymous wrote:

Very nice:-) 


November 26, 2012 | anonymous wrote:

I have been pulling out hair by the roots! Finally, thanks so much for making my Year! 


September 25, 2012 | mhay wrote:

. A company pays its employees an average wage of $3.25 an hour with a standard
deviation of 60 cents. If the wages are approximately normally distributed,
Determine:
a) the proportion of workers getting wages between $2.75 and $3.69 an hour
b) The minimum wage of the highest 5%.
 


August 13, 2012 | Clyde Killian wrote:

Nice programs for those that want the concepts but are not into the math. I will use this link in my course. 


July 30, 2012 | LaVerne wrote:

This is a great site that made everything easy to understand. I will recommend this to my friends 


February 21, 2012 | Brian Twomey wrote:

Jeff is not only a decent individual but he knows his Z scores, standard deviations, probabilities and his overall mathematics well. I highly recommend Jeff and his services for any mathematical needs. Brian Twomey 


November 11, 2011 | Becky wrote:

Thanks for the Z score calculator...after being stuck on Stats homework for 20 minutes because I couldn't understand how to find a z score with a % (because the instructor didn't provide that instruction) your site helped me zip right through z scores and the rest of the problem on my homework! 


November 1, 2011 | Ebby Mubanga wrote:

It's really GREAT to come across such a UNIQUE website. Please keep it up! Can you please share some more practical examples on calcuation of z scores, correlations, and other related stuff. Thanks. 


October 13, 2011 | anonymous wrote:

i want to know what is the percentile rank if you have t score of 62? 


October 10, 2011 | Valeria Regecova wrote:

useful 


July 16, 2011 | anonymous wrote:

Love having something right on the internet - I don't have to lug around statistical tables just to calculate a z-score from a percentile! 


June 5, 2011 | anonymous wrote:

this site does not know how to turn percentiles into zscores...  


September 13, 2010 | anonymous wrote:

i want to get z score for 10th percentile. what is the big deal?? 


March 18, 2010 | Dan wrote:

Only professional statisticians know how to calculate this. The rest of you damn trolls can use a graphing calculator function:
invNorm(*percent in decimal form*) 


March 3, 2010 | alexandria wrote:

Drew...get a life its not that cool.... 


March 3, 2010 | Drew fickleson (Go math!) wrote:

I LOVE MATH!!! THIS IS THEEEE GREATEST WEBSITE EVAAAA!!! LIKE OMG!!!! I LOVE IT!!!!!!!
BLESS YOU FOLKS WHO PUT THIS DANDY SITE TOGETHER!! BLESS YOU!!! 


March 3, 2010 | alexandria wrote:

i would like to see the problem solved step by step 


February 1, 2010 | JOE M. wrote:

If A's are given to students who scored 90% above the mean, what would be the minimum Z score of someone receiving an A? 


January 22, 2010 | anonymous wrote:

need instructions or I wouldn\'t be looking for how to figure this out 


January 22, 2010 | anonymous wrote:

need instructions or I wouldn\'t be looking for how to figure this out 


January 19, 2010 | lordly nunki wrote:

Thanks, it's very helpful for my theses 


October 27, 2009 | Aaron wrote:

If n=6 than what would the 6 Z values be and what formula do you use?

Thanks 


August 7, 2009 | Betsy wrote:

How can I find the z score with 26.9 as the mean and 8 as the standard deviation? 


July 23, 2009 | anonymous wrote:

Would like to see the formula 


July 7, 2009 | Phyllis Irvine wrote:

What is the Standard Score for a T Score of 45? Do you have a conversion chart (Standard scores with T scores equivalent)? 


September 23, 2008 | EA wrote:

awesome, saved us a bunch of work at uni :D 


September 8, 2008 | Sinead wrote:

Is it legitimate to transform data in z-scores, using standardised norms, and use this as the DV in a subsequent analysis (e.g. ANOVA) 


February 21, 2008 | anonymous wrote:

Hi - it would be reassuring if you could also generate a pictorial representation. Otherwise, very handy tool; thanks 


February 20, 2008 | jim gillett wrote:

How can I find the mean and standard deviation if all I know is the percent under the curve and two of the actual data points 


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Jeff's Books

Quantifying the User Experience: Practical Statistics for User ResearchQuantifying the User Experience: Practical Statistics for User Research

The most comprehensive statistical resource for UX Professionals

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Excel & R Companion to Quantifying the User ExperienceExcel & R Companion to Quantifying the User Experience

Detailed Steps to Solve over 100 Examples and Exercises in the Excel Calculator and R

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A Practical Guide to the System Usability ScaleA Practical Guide to the System Usability Scale

Background, Benchmarks & Best Practices for the most popular usability questionnaire

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A Practical Guide to Measuring UsabilityA Practical Guide to Measuring Usability

72 Answers to the Most Common Questions about Quantifying the Usability of Websites and Software

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