Percentile Calculator
Find the value at any percentile of your data set, or flip it around and find the percentile rank of a given value. Enter your numbers separated by commas, choose a mode, and get the result along with a complete five-number summary, descriptive statistics, and a full percentile table.
Formula
Worked example
For 4, 8, 15, 16, 23, 42 (n = 6) at k = 90: R = 0.90 x (6 - 1) = 4.5. The value lies halfway between index 4 (= 23) and index 5 (= 42), so P90 = 23 + 0.5 x 19 = 32.5. Reverse: the rank of 15 is (2 + 0.5 x 1) / 6 x 100 = 41.7th percentile.
What a percentile tells you
A percentile marks the value below which a given share of a distribution falls. The 90th percentile is the point at or below which roughly 90% of the data sits, leaving only the top 10% above it. Percentiles are used everywhere: growth charts describe a child's height at the 50th or 75th percentile, exam boards report where a score ranks, engineers set reliability targets such as "P95 latency under 200 ms", and salary surveys give the 10th and 90th percentile income figures. Because percentiles are rank-based rather than arithmetic, they are robust to extreme outliers in a way that means and standard deviations are not.
Forward mode: finding the value at a percentile
Enter your data, select "Value at a given percentile", and type k (0 to 100). The calculator sorts your values from smallest to largest, then computes the fractional rank R = (k / 100) x (n - 1). If R is a whole number, the answer is simply the value at that position. When R falls between two positions, the result is linearly interpolated: lower value plus the fractional part of R times the gap to the next value. This is identical to the method used by NumPy's default, Excel's PERCENTILE.INC, and Google Sheets, so results match those tools exactly.
Reverse mode: finding the percentile rank of a value
Switch to "Percentile rank of a given value" and type any number, even one that does not appear in your data. The calculator counts how many data points fall strictly below your value, adds half the count of values equal to it, then divides by the total count and multiplies by 100. This "midpoint" convention avoids over-penalising tied values and is standard in social science and education. The result tells you what share of the distribution lies at or below your target, which is the definition of a percentile rank.
Five-number summary and descriptive statistics
Alongside the requested percentile, this calculator always shows the five-number summary: minimum, Q1 (25th), median (50th), Q3 (75th), and maximum. These five numbers describe a distribution completely enough to sketch a box-and-whisker plot. The interquartile range (IQR = Q3 - Q1) captures the spread of the middle half of the data and is a common measure of dispersion that is immune to outliers. The mean and population standard deviation are also shown so you can compare the typical value and its spread side by side.
Full percentile table
Toggle "Show full percentile table" to generate a complete breakdown at every 5th percentile from the 1st through the 99th, including all quartile and decile marks. This is useful when you need a quick overview of the whole distribution, for example to see where the bulk of the data clusters, identify gaps or clusters, or extract multiple thresholds for reporting without re-entering the data each time.
Percentiles, quartiles, deciles and the median
These are all the same idea at different granularities. The median is the 50th percentile and splits the data in two. Quartiles (Q1, Q2, Q3) split it into four equal parts; the distance between Q1 and Q3 is the IQR. Deciles split it into tenths: D1 is the 10th percentile, D9 is the 90th. Quintiles split it into fifths. All of these can be read directly from the percentile table or computed individually using the k field. For SAT scores or standardised test results, the College Board often reports at Q1, Q3 and the 25th/75th percentile range, which you can reproduce here by entering class data and reading those rows from the table.
Common percentile benchmarks
| Percentile | Common name | Meaning |
|---|---|---|
| 0th | Minimum | The smallest value in the data set |
| 25th | Q1, first quartile | Bottom quarter of the distribution |
| 50th | Median, Q2 | Middle value; half the data is above and below |
| 75th | Q3, third quartile | Top quarter begins here |
| 90th | P90 | Common performance / salary benchmark |
| 95th | P95 | Latency SLA target; top 5% threshold |
| 99th | P99 | Extreme outlier threshold in engineering |
| 100th | Maximum | The largest value in the data set |
Widely used cut-points and their plain-English meaning.
Frequently asked questions
Why is the percentile value not one of the numbers I entered?
This calculator uses linear interpolation (the NIST and Excel PERCENTILE.INC method). When the requested percentile falls between two sorted data points, it returns a value blended proportionally between them rather than rounding to the nearer point. That produces a smoother, more precise estimate than nearest-rank methods, which is why the answer can be a number that does not appear in your original list.
What is the difference between a percentile and a percentage?
A percentage is a fraction of a whole: scoring 80% means you answered 80 of every 100 questions correctly. A percentile is a rank within a group: being in the 80th percentile means your score exceeds roughly 80% of the people being compared. You can score 80% on a test yet be in the 95th percentile if most other test-takers scored lower.
What is the difference between a percentile and a percentile rank?
A percentile is a value on the measurement scale (for example, the 90th percentile of test scores is 720 points). A percentile rank is the percentage of data at or below a given value (for example, a score of 720 has a percentile rank of 90). The forward mode of this calculator finds the value; the reverse (rank) mode finds the rank.
Does the order of the numbers matter?
No. The calculator sorts your values before computing, so you can paste them in any order. You can separate them with commas, spaces, or a mix of both; any non-numeric entries are silently skipped.
How do I find multiple percentiles at once?
Enable the "Show full percentile table" toggle. It generates values at every 5th percentile (1st, 5th, 10th, 15th, ..., 95th, 99th, 100th) plus all quartile and decile markers, all computed from your data in one pass.
What is the interquartile range (IQR) and why does it matter?
The IQR is Q3 minus Q1, the width of the box in a box plot. It represents the spread of the middle 50% of your data and is robust to outliers: a single extreme value cannot change Q1 or Q3 the way it shifts the mean or standard deviation. The IQR is used to define outliers in Tukey's method: any value more than 1.5 times the IQR below Q1 or above Q3 is considered a mild outlier.
How is this different from Excel's PERCENTILE.EXC function?
Excel offers two functions. PERCENTILE.INC (which this calculator matches) assigns percentiles over the closed interval [0, 100] using the rank R = (k/100) x (n - 1). PERCENTILE.EXC uses R = (k/100) x (n + 1) - 1, an open-interval formula that cannot return the exact minimum or maximum and requires k to be between 1/(n+1) and n/(n+1). For most data sets the difference is small, but PERCENTILE.INC is the more common default and is the standard recommended by NIST.