Percentile and Standard Score Calculator

About this tool

A child brings home an 85. What parents usually want to know is where that sits in the class and how many classmates it beats. An 85 means something different when most of the class scored 90 than when most scored 70. Paste the whole set and the rank, percentile and standard scores all follow.

For the twelve scores 62, 70, 75, 78, 80, 82, 85, 88, 90, 93, 95 and 98 with a lookup of 85, six scores fall below it, giving a percentile rank of 54.17%, a mean near 83, a Z score near 0.19 and a T score near 51.9. Rank low-to-high puts it 7th; switching to high-to-low shows 6th while Z and the percentile stay unchanged.

What it does

• TiesTies count as half Every number shown here maps to a field on the form, so changing one value recomputes the rest. The units are printed next to each input, which saves most of the usual mistakes.
• Standard scoresZ and T together The main figures sit at the top of the result panel and the breakdown sits below it, so you can read the conclusion first and audit the steps afterwards. Nothing you type leaves the browser.
• DirectionAscending or descending All arithmetic runs locally in the page. There is no request to a server, no account, and no saved history once the tab is closed. Use the example button if you want a set of values that is known to work.
• SortingSorted list included Intermediate quantities are kept in the detail table. When a total looks wrong, tracing back through those rows is much quicker than staring at the headline number alone.
• BasisPopulation standard deviation The formula is written out in the notes rather than hidden behind a label, so you can check it against a spreadsheet or a textbook. Values are rounded only for display.
• AssumptionsNo assumed maximum mark Inputs are validated before any calculation starts. Empty or impossible values produce a short explanation instead of a zero, a NaN, or a made-up answer.

How to use it

1. Start by filling inenter the score to look up The main figures sit at the top of the result panel and the breakdown sits below it, so you can read the conclusion first and audit the steps afterwards. Nothing you type leaves the browser.
2. Next, setpaste every score on its own line All arithmetic runs locally in the page. There is no request to a server, no account, and no saved history once the tab is closed. Use the example button if you want a set of values that is known to work.
3. Then presspick the ranking direction Intermediate quantities are kept in the detail table. When a total looks wrong, tracing back through those rows is much quicker than staring at the headline number alone.
4. Read thepress Calculate The formula is written out in the notes rather than hidden behind a label, so you can check it against a spreadsheet or a textbook. Values are rounded only for display.
5. Finally, useread the percentile before the rank Inputs are validated before any calculation starts. Empty or impossible values produce a short explanation instead of a zero, a NaN, or a made-up answer.

Things to keep in mind

• Countat least two scores All arithmetic runs locally in the page. There is no request to a server, no account, and no saved history once the tab is closed. Use the example button if you want a set of values that is known to work.
• Constantidentical scores make Z undefined Intermediate quantities are kept in the detail table. When a total looks wrong, tracing back through those rows is much quicker than staring at the headline number alone.
• Comparabilitydo not mix different exams The formula is written out in the notes rather than hidden behind a label, so you can check it against a spreadsheet or a textbook. Values are rounded only for display.
• Stabilitydirection does not change Z Inputs are validated before any calculation starts. Empty or impossible values produce a short explanation instead of a zero, a NaN, or a made-up answer.
• Display capthe sorted list shows 12 rows Every number shown here maps to a field on the form, so changing one value recomputes the rest. The units are printed next to each input, which saves most of the usual mistakes.