Percentile Calculator
Find any percentile of a data set using linear interpolation on the (P/100)(n-1) rank, matching NumPy's default percentile method.
Percentile Calculator
Calculator
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Formula: Rank = (P/100) × (n−1) (0-based linear interpolation, equivalent to NumPy default) | If rank is not integer, interpolate between adjacent va…
Worked example — P75 = 87.5
Formula
Rank = (P/100) × (n−1) (0-based linear interpolation, equivalent to NumPy default) | If rank is not integer, interpolate between adjacent values
The Pth percentile is the value below which P% of the data falls. Uses linear interpolation between data points.
Worked Examples
Example 1: Test scores
Problem:Scores: 65,70,75,80,85,90,95. Find P75
Solution:Rank=0.75×(7−1)=0.75×6=4.5 → interpolate between nums[4]=85 and nums[5]=90: 85+0.5×(90−85)=87.5
Result:P75 = 87.5
Frequently Asked Questions
What does the 90th percentile mean?
The 90th percentile means 90% of values fall below this number. If your test score is at the 90th percentile, you scored higher than 90% of test takers.
What is the difference between a percentile and a percentage?
A percentage expresses a ratio out of 100 (e.g., you answered 90% of questions correctly). A percentile ranks your score relative to a group (e.g., your score is at the 90th percentile, meaning you scored higher than 90% of other people). You can score 70% on a test and still be at the 95th percentile if the test was hard and most people scored lower.
What are quartiles and how do they relate to percentiles?
Quartiles divide data into four equal parts. Q1 (first quartile) = 25th percentile, Q2 (second quartile/median) = 50th percentile, Q3 (third quartile) = 75th percentile. The interquartile range (IQR = Q3 - Q1) measures the spread of the middle 50% of data and is commonly used to identify outliers, which are defined as values more than 1.5 × IQR below Q1 or above Q3.
Why are percentiles used in medical growth charts?
Growth charts express a child's height or weight as a percentile relative to peers of the same age and sex. A child at the 70th percentile for height is taller than 70% of same-age peers. Pediatricians use these to track developmental trends over time — a child consistently at the 30th percentile is normal, but one dropping from the 70th to the 10th percentile over several visits warrants investigation.
How does linear interpolation work when the rank falls between two data points?
The rank is computed as (P/100) × (n − 1) on a zero-based index, so it is usually fractional. The percentile is then the lower neighbour plus the fractional part times the gap up to the next value. For 10, 20, 30 up to 100 with n = 10, P90 gives a rank of 8.1, which sits between 90 and 100: 90 + 0.1 × 10 = 91.
Why do Excel and other packages report different percentiles for the same data?
There is no single agreed definition. Percentile Calculator uses zero-based linear interpolation with rank = (P/100) × (n − 1), matching Excel PERCENTILE.INC and the NumPy default. PERCENTILE.EXC instead uses (P/100) × (n + 1) on a one-based index and refuses percentiles too near the ends. Nearest-rank methods skip interpolation entirely and always return an actual observation. The gaps shrink as n grows.
What is the difference between a percentile value and a percentile rank?
A percentile value answers which number sits at a given position, so P75 of a score list might be 87.5. A percentile rank runs the other way: given one specific observation, it reports the percentage of the dataset at or below it. Percentile Calculator returns the percentile value. To get a rank instead, count the observations at or below your value and divide by n.
How reliable are extreme percentiles in a small dataset?
Poorly determined at the edges. With only twenty values, the interpolated 99th percentile is pinned almost entirely to the single largest observation, so one unusual reading moves it sharply. A percentile is only stable when several observations sit above it, which means high percentiles need far more data than the median does. Q1, the median and Q3 stay dependable even in small samples.
How do deciles and quintiles relate to percentiles?
They are percentiles at regular spacings. Deciles cut the data into ten parts at the 10th, 20th and so on to the 90th percentile; quintiles cut it into five at the 20th, 40th, 60th and 80th; quartiles use the 25th, 50th and 75th. All are produced by the same interpolation rule, so a decile summary and a percentile summary of the same data never contradict each other.
Why do engineers report p95 and p99 latency rather than the average?
Response-time distributions are strongly right-skewed: a handful of slow requests sit far above a dense cluster of fast ones. The mean is dragged up by those outliers yet still hides how bad the worst cases are. The 95th and 99th percentiles describe the tail directly, so a p99 of 800 ms means one request in a hundred took longer than that, which is exactly what service-level objectives are written against.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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