Percentile Calculator
Calculate percentile instantly with our math tool. Shows detailed work, formulas used, and multiple solution methods. Free to use with no signup required.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
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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
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.
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
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.
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.
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.
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.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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