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Review mixed spreadsheet text carefully because every numeric-looking token becomes an observation.
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Use 50 for the median, 75 for Q3, or a tail cutoff such as 90, 95, or 99.
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Choose the definition required by the report or system you need to reproduce.
Choose 0 through 8 decimal places without changing the underlying percentile.
Leave blank to omit the reverse-rank row from the percentile snapshot.
Midrank splits tied observations; the alternatives count all ties or none.
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A percentile gives a sorted data set a position-based cutoff. P50 is the median, P75 marks a value around three quarters of the way through the ordered observations, and P95 is often used to examine a slow or unusually large tail. This is different from an average: a few extreme observations can pull the mean sharply while leaving the middle rank nearly unchanged.

Percentiles appear wherever relative position matters more than a total. Schools use them to compare scores, service teams use them for response times, laboratories summarize measurement distributions, and compensation reports use them to describe pay ranges. The result always belongs to the data that was collected. A precise P90 cannot correct a biased sample, mixed units, missing observations, or numbers copied from unrelated spreadsheet columns.

Observation
One numeric value in the sample.
Order statistic
An observation identified by its position after the sample is sorted.
Quantile
A cutoff on a probability scale from 0 to 1. A percentile expresses the same position from 0 to 100.
Interpolation
A weighted value between two neighboring observations when the requested rank is fractional.

There is no single percentile convention for every report. Inclusive interpolation anchors the minimum at P0 and the maximum at P100. Nearest rank selects an actual observed value. Exclusive interpolation places observations at interior positions and cannot return some extreme percentiles from small samples. Two systems can therefore produce different, defensible cutoffs from the same values.

Ties create another distinction when the question is reversed. To find the percentile rank of a value, one rule may count values strictly below it, another may count values at or below it, and a midrank rule assigns half of the tied observations to each side. The rule should match the spreadsheet, statistical package, policy, or report being reproduced.

Sample size limits interpretation. P99 from thousands of measurements can describe a useful tail pattern; P99 from ten values is driven almost entirely by the maximum. Compare the method, inspect the sorted observations, and keep collection conditions consistent before comparing percentiles across groups or time periods.

How to Use This Tool:

Begin with the numeric sample, then choose the definition used by the result you need to reproduce.

  1. Paste the observations into Data set, or load a CSV or TXT file smaller than 1 MB. Review mixed spreadsheet text carefully because every numeric-looking token is treated as an observation.
  2. Enter a Percentile from 0 through 100 and choose Inclusive interpolation, Nearest rank, or Exclusive interpolation.
  3. Set Display precision only for the shown result. It does not change the underlying calculation.
  4. Optionally enter a Rank value and choose how ties are counted to answer the reverse question of where that value sits in the sample.
  5. Check the selected cutoff and rank, then compare the three methods and scan the sorted values before using the number in another report.
    If exclusive interpolation reports that the percentile is outside the usable range, choose a percentile between the displayed bounds or use the definition required by your source system.

Interpreting Results:

The selected percentile value is a cutoff under one named method, not a universal property of the sample. A fractional rank means two neighboring observations were interpolated. Nearest rank always points to one observed position.

  • Use the method comparison to detect a material definition difference before matching another spreadsheet or report.
  • Use the sample count and sorted values to catch stray IDs, dates, mixed units, or a sample too small for the requested tail.
  • Read the optional percentile rank with its tie rule. Midrank, at-or-below, and below-only answers differ whenever the lookup value is repeated.
  • Compare groups only when the measured quantity, unit, collection window, filtering, and percentile method are the same.

Technical Details:

Let x1 through xn be the observations in ascending order, and let p be the requested percentile divided by 100. Each method maps p to a rank and then either selects an order statistic or interpolates between two adjacent order statistics.

Formula Core:

Inclusive interpolation uses the same position rule as R type 7 and Excel PERCENTILE.INC. The zero-based index is i.

i=(n-1)p , Q=x⌊i⌋+1 +(i-⌊i⌋) (x⌈i⌉+1-x⌊i⌋+1)

Nearest rank uses a one-based rank, clamps it to the sample, and returns an observed value.

r=min(n,max(1,⌈np⌉)) ,Q=xr

Exclusive interpolation uses rank r = (n + 1)p. It is valid only when that rank lies from 1 through n, inclusive.

r=(n+1)p , 1n+1 ≤p≤ nn+1
MethodRank behaviorPossible result
InclusiveInterpolates over positions 1 through n, with P0 and P100 at the endpoints.Observed or interpolated value
Nearest rankUses the ceiling of np, clamped from 1 through n.Observed value only
ExclusiveInterpolates using (n + 1)p; extreme requests can fall outside the sample.Observed, interpolated, or unavailable

The reverse-rank calculation counts observations below the lookup value and then handles equal values according to the selected rule. If b values are below, e are equal, and n is the sample size, the midrank percentage is:

R=b+e2n×100

At-or-below replaces the numerator with b + e; below-only uses b. The five-number summary and interquartile range always use inclusive interpolation, even when another method is selected for the headline percentile.

Input text is scanned for signed decimal or scientific-notation numbers. At most 5,000 detected values are calculated; later tokens are reported as ignored. Sorting and arithmetic retain full numeric precision, while the selected display setting rounds only the presented values from 0 through 8 decimal places.

Worked Examples:

One sample, three P75 answers

The values 84, 92, 75, 88, 91, 79, 85, 90, 94, and 87 sort to 75, 79, 84, 85, 87, 88, 90, 91, 92, and 94. Inclusive P75 is 90.75, nearest-rank P75 is the eighth observation at 91, and exclusive P75 is 91.25. The difference comes from rank definition, not from a change in the data.

A tied reverse rank

For 10, 20, 20, and 40, the value 20 has one observation below and two equal observations. Its midrank is 50%, at-or-below rank is 75%, and below-only rank is 25%. Reporting the percentage without the tie rule would be ambiguous.

References: