“Percentile” names two different calculations, and most calculators do only one of them. This one does both — and shows the round trip, because asking for the 90th percentile and then asking that value’s rank back does not reliably return 90.
The value at any percentile of your data
The percentile rank of any value
All nine standard percentile methods
The three tie-handling rules for ranks
The round trip, and why it does not close
Which method your software uses
Both directions Nine methods Matches Excel and R Round trip shown
Defaults to type 7, which is Excel’s PERCENTILE and R’s default.
Updated 7 September 2026 · Works in any browser, no installation
The pth percentile is the value below which p% of the data falls. Going the other way, the percentile rank of a value is the share of the data at or below it. Those sound like the same sentence read backwards. On a finite sample they are not, and the gap is not a rounding error.
At a glance
Formula shown
Forward: type 7 places the pth percentile at position (n − 1)·p + 1 in the sorted list and interpolates between the two neighbouring observations. Reverse: the percentile rank of a value is the count of observations at or below it, divided by n.
Scenario support
Reporting the 90th-percentile response time for a service; finding where a test score sits in a cohort; setting a threshold that captures the top 5%; reading a salary band or a growth chart.
Educational estimate
Planning support from the values you enter — not professional advice.
Two different calculations sharing one word
Before computing anything, it is worth being clear which question you are asking, because the two have different inputs and different outputs.
Value from percentage. “What is the 90th percentile of these response times?” You supply a percentage and get back a value in the units of your data — milliseconds, marks, dollars. This is what Excel’s PERCENTILE does, and it is the direction people mean when they say “p90”.
Percentage from value. “What percentile is a score of 72?” You supply a value and get back a percentage. This is PERCENTRANK, and it is the direction meant when a report card says a child is “at the 63rd percentile”.
The confusion is not helped by the fact that both are called percentile calculators, and that a search for one reliably returns the other. Worse, the answers are in different units: one is a measurement, the other is a proportion. Reporting “the 90th percentile is 85” and “85 is at the 90th percentile” are different claims, and only one of them is usually true.
The toggle at the top of the tool switches direction explicitly, rather than leaving you to infer which one you got.
Why the round trip does not close
Here is the smallest example that shows it. Take the numbers 1 through 10 and ask for the 25th percentile.
Type 7 puts it at position (10 − 1) × 0.25 + 1 = 3.25, which is a quarter of the way from the third value to the fourth. So the answer is3.25.
Now ask the other question: what percentile is 3.25? Three of the ten values (1, 2 and 3) are at or below it, so the rank is 30%. You asked for the 25th percentile, got 3.25, and 3.25 turns out to be the 30th percentile.
Nothing has gone wrong. The forward direction interpolates — it is willing to invent the value 3.25, which appears nowhere in your data, because it is modelling a continuous population behind a discrete sample. The reverse direction counts — and you cannot count a quarter of an observation. One operation works in a continuum and the other in whole numbers, so they cannot be exact inverses.
This is not an edge case. Across three thousand randomly generated combinations of dataset and percentile, the round trip came back to where it started only about one time in five. That figure is measured by the verification suite for this page rather than estimated, and the suite fails if it drifts outside the band the sentence above describes.
The practical consequence: do not use one direction to check the other. If a colleague’s p90 does not match the rank you computed for that same number, that is expected behaviour and not evidence of a mistake. The tool prints the round trip on every forward calculation so the gap is visible rather than discovered later.
Ties, and the three ways to count them
In the reverse direction there is a second decision to make, and it only bites when your value appears in the data more than once.
Take 5, 7, 7, 7, 8, 9, 10, 10, 12, 15 and ask where 7 sits.
Count everything at or below it and four of the ten values qualify, giving40%. This is the usual textbook definition and the tool’s default.
Count only what is strictly below and just one value qualifies, giving10%.
Split the difference — count everything below plus half the ties — and you get 25%. This is the mid-rank rule, and it has a property the other two lack: it puts the median at the 50th percentile even when the median is a repeated value. That is why it is standard in rank-based tests such as the Mann-Whitney U.
A thirty-point spread between defensible answers to the same question, from nothing but a convention. On data with no repeated values all three coincide exactly, which is why the choice can go unnoticed for a long time and then matter suddenly — typically on discrete data like test scores, ratings or counts, where ties are everywhere.
Excel is a fourth thing again: PERCENTRANK interpolates rather than counting, so it will not match any of the three on tied data.
A percentile is not a percentage
They share a word and a symbol and mean different things, and conflating them is the single most common error in reading a percentile.
A percentage is a share of a total. Scoring 90% on a test means you got nine tenths of the marks available. It says nothing about anyone else.
A percentile is a position among others. Being at the 90th percentile means you did better than about 90% of the group. It says nothing about how many marks you got.
The two come apart completely. On a brutally hard exam, 55% might be the 95th percentile. On an easy one, 90% might be the 40th. A child at the 25th percentile for height is not “25% as tall” as anyone; they are shorter than three quarters of children their age, which is an entirely ordinary place to be.
Percentiles are also not evenly spaced in the units of the data. Moving from the 50th to the 60th percentile usually covers a small distance, because that is where observations are dense. Moving from the 95th to the 99th can cover an enormous one. This is exactly why engineers watch p99 latency rather than the mean: the tail is where the bad experiences live, and an average hides it.
Reading a published percentile
Most percentiles people encounter are not computed from data they hold. They come from a reference population, and that changes what they mean.
Growth charts place a child against a reference sample of thousands, not against their classmates. The percentile only means what it says if the reference population is the right one — which is why WHO and CDC charts differ, and why the choice matters for infants.
Standardised test percentiles are usually against a norming cohort from a specific year, not against everyone who sat the test with you. A percentile from a 2019 norm and one from a 2024 norm are not directly comparable.
Salary bands depend entirely on who was surveyed. A 75th-percentile figure for a role means little without the sample’s geography, company size and seniority mix.
Service latency percentiles have a subtler problem: percentiles do not average. You cannot take the p99 of each of ten servers and average them to get the p99 of the fleet, and you cannot average hourly p99s to get a daily one. The correct figure has to be computed from the combined observations, which is why monitoring systems store distributions rather than summaries.
In every case the question to ask is the same: percentile among whom? A percentile without a stated reference population is not a fact about anything.
What a percentile cannot tell you
Three limits worth holding onto.
It carries no sense of distance. Two people one percentile apart may be separated by a rounding error or by a wide margin, depending on where in the distribution they sit. Percentiles are ranks, and ranks discard magnitude by design.
Extreme percentiles need a lot of data. A p99 computed from 50 observations is determined by the single largest value, which makes it almost meaningless: you need on the order of hundreds of observations before a p99 is stable, and thousands for a p99.9. The tool will happily compute a 99th percentile of ten numbers, and you should not trust it.
It describes the sample you supplied. Nothing here produces a confidence interval around a percentile, and percentiles from small samples move noticeably when a single observation is added. Treating a sample percentile as a population value is a separate inferential step this page does not take.
One further caution: because percentiles are positional, they exist for any data you can rank — including ordinal data where the intervals between categories are not equal. That is a genuine strength. But it also means a percentile can be computed on data where the underlying numbers do not support arithmetic, and it will look just as authoritative as one that does.
Method. The forward direction implements all nine Hyndman-Fan types from the single position rule in the paper, defaulting to type 7 so the answer matches Excel, R, NumPy and Sheets. The reverse direction counts rather than interpolates, and exposes all three tie conventions instead of silently choosing one. The claim that the round trip fails roughly four times in five is a measurement, not an impression: the suite runs three thousand generated (dataset, percentile) pairs on every change and fails if the rate leaves the band this page describes. That engine is verified against 0 assertions in total, including every type checked against R’s published output. The count and the per-case breakdown are published on the formula verification page.
Related calculators
Where this goes next:
QuartileQ1, Q2 and Q3 by all eleven conventions in common use — Excel, R, Tukey hinges and the TI-84 rule — with a warning when they disagree.
IQRInterquartile range, the 1.5 × IQR outlier fences, and exactly which values fall outside — with a slider that corrupts one value so you can watch the range move while the IQR does not.
Five Number SummaryMinimum, Q1, median, Q3 and maximum, drawn as a box plot with every one of your observations plotted underneath it — so you can see what the summary threw away.
Standard DeviationSample and population standard deviation, plus variance, mean, median, quartiles, z-scores, outliers, and confidence intervals.
Weighted AverageEach value carries the weight you give it, with every item's share of the total shown as a percentage so you can see what is actually driving the answer.
Average PercentageAveraging 50% and 100% gives 99.02%, not 75%, when the groups are 2 and 100 — the page weights by group size and shows the naive answer beside it.
An educational tool for describing a dataset you supply. Percentiles here are computed from your sample; published percentile bands for growth charts, test scores or benchmarks come from reference populations this tool does not have.
Published a percentile calculator that does both directions — the value at a percentile and the percentile rank of a value — because the word names two different calculations and most tools implement one of them.
Shows the round trip on every forward calculation, because the two directions are not inverses: asking for the 25th percentile of 1 through 10 gives 3.25, and 3.25 ranks back at the 30th. Measured across three thousand generated cases, the round trip closes only about one time in five, and the suite fails if that rate leaves the band the page describes.
Exposes the three tie-handling rules for percentile rank instead of choosing one silently, since on a dataset with repeated values they can differ by thirty points.
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