Percentile Calculator
Both directions of the percentile question: which value sits p% of the way up your list, and what percentile a given value ranks at — with the interpolation stated and the convention named.
Percentile Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- 2 to 500 values; linear-interpolation convention only
- Rank direction counts strictly-below (ties share a rank)
In short: Percentile questions run both ways and this page does both. Forward: the 30th percentile of 1 through 8 sits at position 1 + 0.30×7 = 3.1, so it interpolates to 3.1 — a tenth of the way from 3 to 4. Backward: the value 5 has 4 of the 8 values below it, so it ranks at the 50th percentile. The two uses are different questions — one places a cutpoint in the data, the other places the data on a scale — and they use different arithmetic, which the page shows rather than blurs.
Formula
position = 1 + (p/100)(n−1)
rank(x) = 100 × #(values < x) / n
the forward direction interpolates between neighbours; the rank counts strictly smaller values — both conventions stated, never mixed.
Worked Example
- Sort. the list, once, for both directions.
- Forward. the p-th value lives at position 1 + (p/100)(n−1); the fractional part interpolates between the neighbours.
- Backward. give x and the page counts the values strictly below it — that share, times 100, is the percentile rank.
1 through 8: p30 sits at position 3.1 → value 3.1. p50 gives 4.5 (the median). The value 5 ranks at the 50th percentile (4 below, 8 total). p25 and p75 reproduce the interpolated quartiles the quartile page shows under Excel-Minitab.
Strengths & Limits Of This Model
Where this engine is strong
- Both directions on one page with the arithmetic shown
- The convention is named, matching the quartile page
Where it stops
- No nearest-rank or exclusive variants
- No weighted percentiles
Practical Use Cases
Growth charts
a child’s measurements against population tables
Test scoring
what 86th percentile means, computed
SRE and latency
p95 and p99 cutpoints on response time lists
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Percentile Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why do the two directions use different arithmetic?
Placing a cutpoint is interpolation: the p-th value may legitimately land between two observations, so the position law 1 + (p/100)(n−1) slides continuously. Ranking a value is counting: x either is or is not below each observation, so the rank is a share of strictly smaller values. The two meet at the quartiles and median but are different questions everywhere else.
Which percentile convention is this?
The linear-interpolation convention — the same one Excel’s PERCENTILE.INC and Minitab use, and the same one the quartile page labels Excel-Minitab. Other definitions (nearest-rank, exclusive) place the cut slightly differently on small lists; this page names its convention instead of hiding it.
Why does the 30th percentile of a whole-number list land on 3.1?
Because the convention interpolates: position 3.1 is a tenth of the way from the 3rd value (3) to the 4th (4). Rounding to 3 would quietly claim the nearest-rank convention — a different, unstated answer.
What does “86th percentile” mean for a test score?
That 86% of the reference group scored strictly below you — the backward direction on the score list. It does NOT mean 86% correct: percentiles compare you to the group, not to the syllabus. The two meanings get swapped constantly and the swap is always expensive.
Can p be 0 or 100?
Yes — p0 is the minimum and p100 the maximum, the interpolation law’s natural endpoints. The page refuses values outside 0–100 rather than extrapolating past the data.
How does this relate to the quartile page?
The quartiles are the p25, p50 and p75 cutpoints, and the Excel-Minitab convention there IS this page’s interpolation law. That page compares three conventions on the same list; this one goes deep on the one convention and adds the rank direction.
What about the median?
p50 IS the median under this convention — for the default list it returns 4.5, exactly what the median page prints for an even count. One more agreement you can check rather than trust.
Are ties handled?
In the forward direction ties are just neighbouring equal values and interpolation does nothing unusual. In the rank direction the convention counts STRICTLY smaller values, so tied values share the same percentile rank — the page says when ties are present rather than letting the number imply a precision the ordering does not have.