Find the percentile rank of any value in a data set — with the sorted data and every count shown. Free, exact, and mobile-friendly.
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A percentile tells you where a value stands relative to everyone else. If your test score is at the 82nd percentile, you outscored 82 percent of test-takers — a far more informative statement than the raw score alone. Our free Percentile Calculator takes any data set and any value, then computes the percentile rank with the standard textbook formula, showing the sorted data and every count so the result is fully transparent.
Percentiles are the language of standardized testing (SAT, GRE, MCAT), pediatric growth charts, income statistics, and athletic combine results. They compress an entire distribution into a single intuitive number: what fraction of the group did I beat? Unlike the mean, which a few extreme outliers can distort, a percentile rank describes position directly — no distributional assumptions required.
This page goes beyond the button: you will learn the two common percentile definitions (percentile rank vs. the value at a percentile), see the formula worked by hand on real data, explore practical uses from exam scores to marathon times, and learn the mistakes that make percentile claims misleading — like confusing the 90th percentile with “90 percent correct.”
There are two related but different ideas sharing the name. The percentile rank of a value x answers: “what percentage of the data falls at or below x?” The value at the k-th percentile answers the reverse: “below what value do k percent of the data fall?” This calculator computes the rank: given your score, it tells you your standing. Test-score reports (“82nd percentile”) are ranks; growth charts (“the 50th percentile height for age 10 is 138 cm”) are values.
The standard rank formula used here is: percentile rank = (B + 0.5E) ÷ N × 100, where B is the count of values strictly below x, E is the count equal to x, and N is the total count. Giving half-credit to ties (the 0.5E term) is the fairest convention when duplicates exist — it places a tied value in the middle of its tied group rather than at the top or bottom of it.
Percentiles are intimately related to quartiles: the 25th percentile is the first quartile (Q1), the 50th is the median (Q2), and the 75th is the third quartile (Q3). The interquartile range (Q3 − Q1) then describes the spread of the middle half of the data. So learning percentiles also unlocks box plots, five-number summaries, and outlier detection in one stroke.
Percentile rank of x = (B + 0.5 × E) ÷ N × 100
B = values strictly below x, E = values equal to x, N = total values. Sort the data first; then count.
Data: 65, 70, 72, 75, 78, 80, 82, 85, 88, 90 (N = 10). Find the rank of x = 82. Sorted already. Values below 82: 65, 70, 72, 75, 78, 80 — that is B = 6. Values equal: E = 1. Rank = (6 + 0.5 × 1) ÷ 10 × 100 = 6.5 ÷ 10 × 100 = 65th percentile. A score of 82 beats 65% of this class.
Data: 70, 75, 80, 80, 80, 85, 90 (N = 7). Rank of x = 80: B = 2 (70, 75), E = 3. Rank = (2 + 0.5 × 3) ÷ 7 × 100 = 3.5 ÷ 7 × 100 = 50th percentile — exactly the median, which is the sensible answer for the middle of a tied cluster. Without the half-credit for ties, the answer would swing between 28.6 and 71.4 depending on convention, which shows why the 0.5E term matters.
Same ten scores; rank of x = 90 (the maximum). B = 9, E = 1: rank = (9.5) ÷ 10 × 100 = 95th percentile — not 100th. No value in a finite data set can be at the 100th percentile under this formula, because you cannot outscore 100% of a group that includes yourself. The minimum possible rank is 100 × 0.5 ÷ N (5th percentile for N = 10).
Twelve runners finish a local 10K with times (minutes): 42, 45, 47, 48, 50, 52, 53, 55, 57, 60, 63, 70. You finished in 53 minutes — how did you do? B = 6 (everyone under 53), E = 1, N = 12: rank = 6.5 ÷ 12 × 100 ≈ 54.2nd percentile. Slightly above the middle of this particular field — but note the rank describes this race only, not runners in general.
A college applicant sees “SAT math 720, 94th percentile.” That single number tells her more than the 720 alone: only about 6% of test-takers scored higher. Admissions offices love percentiles precisely because raw scores drift year to year as tests are recalibrated, while the percentile’s meaning — your position in the pack — stays fixed. Whenever you compare performance across different tests or years, convert to percentiles first.
Percentiles generalize into a family of quantiles. Quartiles split data into fourths (25th, 50th, 75th percentiles); deciles into tenths; the median is simply the 50th percentile. The five-number summary — minimum, Q1, median, Q3, maximum — compresses a distribution into five intuitive landmarks, and the box plot draws them: a box from Q1 to Q3 with a line at the median, whiskers to the extremes.
The interquartile range (IQR = Q3 − Q1) measures the spread of the middle 50% and powers the standard outlier rule: values more than 1.5 × IQR below Q1 or above Q3 are flagged as outliers. Because quartiles are percentiles, they inherit percentile robustness — a billionaire moving into town changes the mean income dramatically but barely moves the median or quartiles.
Different software computes percentile values (the inverse problem) with slightly different interpolation methods — Excel’s PERCENTILE.INC vs. PERCENTILE.EXC, NumPy’s linear vs. midpoint methods — and they can disagree by a rank or two on small data sets. The rank formula used by this calculator is far more standardized, which is one reason ranks are the safer reporting choice when methods must agree.
Data: 10, 20, 30 (N = 3). Rank of x = 5: B = 0, E = 0, rank = 0 ÷ 3 × 100 = 0th percentile. A value below every data point ranks at the 0th percentile — the floor of the scale.
A pediatric chart says the 75th percentile weight for a 6-month-old is 8.2 kg. That is a percentile value: 75% of healthy 6-month-olds weigh 8.2 kg or less. If your baby weighs 8.2 kg, her percentile rank is 75 — the two statements are mirror images of each other.
Data: 4, 8, 15, 16, 23, 42. What is the percentile rank of 16? (B = 3, E = 1, N = 6 → 3.5 ÷ 6 × 100 ≈ 58.3rd percentile.)
In a class of 200, you rank 10th from the top with no ties. What is your percentile rank? (B = 190, E = 1 → 190.5 ÷ 200 × 100 = 95.25th percentile.)
Why can two students with the same score have different percentile ranks on different tests? (Because rank depends on the whole distribution — the same score beats a different fraction of each group.)
A test-prep company advertises “our students average the 99th percentile.” A skeptical parent asks: 99th percentile of whom? If the comparison group is the company’s own self-selected high achievers rather than all test-takers, the claim is technically true and practically meaningless. Percentiles without a stated reference group are marketing, not measurement — always ask “percentile of what population?”
Contrast a hospital reporting surgical outcomes as risk-adjusted percentile ranks against national benchmarks, with the population, time window, and tie-handling all documented. Same statistic, opposite credibility. The difference is transparency about the denominator — the group you are being compared against determines everything the number means.
The Percentile Calculator computes the percentile rank of a value x in a data set using (B + 0.5E) ÷ N × 100, where B counts values below x, E counts ties, and N is the total. It shows the sorted data and all counts. Key facts: the 90th percentile means outscoring 90% of the group (not 90% correct); quartiles are the 25th/50th/75th percentiles; no finite sample reaches the 100th percentile.
The percentile rank of a value is the percentage of a data set that falls at or below it. A score at the 82nd percentile beat 82% of the group. It measures relative standing, not absolute performance.
Sort the data, count values below x (B) and equal to x (E), then compute (B + 0.5E) ÷ N × 100, where N is the total count. This calculator shows every step.
A percentage is a fraction of a whole (80% correct). A percentile is a rank within a group (80th percentile = beat 80% of peers). The 90th percentile does not mean 90% correct.
The three quartiles are the 25th (Q1), 50th (median, Q2), and 75th (Q3) percentiles. They split sorted data into four equal quarters and form the box of a box plot.
Not under the standard formula for a finite data set — the top value reaches 100 × (N − 0.5) ÷ N (e.g., 95th for N = 10). Claims of “100th percentile” use a looser convention.
Tied values each get half-credit via the 0.5E term, placing them mid-cluster. Without it, results swing wildly depending on whether ties count as “below” or “above.”
The median — half the data falls at or below it. For odd-sized data sets it is the middle value; the percentile formula handles even sizes and ties smoothly.
Raw scores drift as tests change difficulty, but a percentile’s meaning — your position among peers — stays fixed. That is why colleges and growth charts report percentiles.
Cite this page as: Percentile Calculator. Sigma Calculator. Retrieved October 11, 2026, from https://sigmacalculator.net/math-calculators/percentile-calculator/
Last updated: October 11, 2026