Percentile Calculator

Percentile rank · quartiles · box plot

Find percentile rank, value at percentile, or full summary
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Find percentile rank, value at percentile, or full quartile summary.

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What Are Percentiles?

A percentile indicates the value below which a given percentage of observations fall. If you score in the 85th percentile on a test, you performed better than 85% of test-takers. Percentiles are essential for comparing individual values to a larger distribution.

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Percentile Rank

Given a specific value, percentile rank tells you what percentage of the dataset falls at or below it.

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Value at Percentile

Given a target percentile (e.g., 75th), find the data value that separates the lower p% from the upper.

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Quartiles & Box Plot

Q1, Q2 (median), and Q3 divide data into four equal parts. The box plot visualizes this five-number summary.

Percentile Formulas

Percentile Rank (midpoint formula):  PR = ((B + 0.5E) / n) × 100

Where B = values below, E = values equal, n = total count

Value at Percentile (linear interpolation):  L = (n + 1) × p / 100

If L is fractional, interpolate between x⌊L⌋ and x⌈L⌉

Worked Example

Data (sorted): [12, 15, 18, 22, 25, 28, 30, 35, 40, 45] (n=10)
Find: 75th percentile
Step 1: L = (10+1) × 75/100 = 8.25
Step 2: x8 = 35, x9 = 40
Step 3: Interpolate: 35 + 0.25 × (40 − 35) = 36.25
Result: The 75th percentile is 36.25

Quartiles, IQR & Outlier Detection

Min Q1 Median Q3 Max Outlier IQR = Q3 − Q1
IQR:  IQR = Q3 − Q1
Outlier Fences:  Lower = Q1 − 1.5×IQR  |  Upper = Q3 + 1.5×IQR

Five-Number Summary

MeasurePercentileDescription
Minimum0thSmallest value in the dataset
Q125th25% of data falls below this value
Median (Q2)50thThe middle value that splits data in half
Q375th75% of data falls below this value
Maximum100thLargest value in the dataset

Common Applications of Percentiles

Standardized Testing

SAT, GRE, and IQ tests report percentile ranks so students can compare performance to the population of test-takers.

Salary & Income

Income percentiles help compare your salary to industry or national benchmarks. The 50th percentile is the median salary.

Growth Charts

Pediatricians use percentile charts to track children’s height and weight relative to age-matched populations.

Performance SLAs

Network engineers use P95 or P99 response times to set service-level agreements that account for tail latency.

Frequently Asked Questions

A percentile is a value below which a certain percentage of observations fall. For example, the 90th percentile is the value below which 90% of data lies. Percentile rank is the reverse: given a specific value, it tells you what percentage of the dataset falls below that value.
Data are sorted in ascending order. The position is calculated as L = (n+1) × p/100. If L is a whole number, use that position’s value. If L is fractional, interpolate linearly between the two adjacent values. Different software may use slightly different interpolation methods.
Quartiles divide sorted data into four equal parts. Q1 is the 25th percentile (25% of data falls below it). Q2 is the 50th percentile (the median). Q3 is the 75th percentile. The interquartile range (IQR = Q3 − Q1) measures the spread of the middle 50%.
The IQR method flags values as potential outliers if they fall below Q1 − 1.5×IQR or above Q3 + 1.5×IQR. These boundaries are called fences. Values beyond 3×IQR from the quartiles are considered extreme outliers. Context matters — not all flagged points are errors.
A five-number summary consists of the minimum, Q1, median, Q3, and maximum. It provides a concise description of data distribution and is the basis for box plot visualization. Together these five values show center, spread, and symmetry of the data.
Percentiles are used in standardized testing (SAT, GRE), salary and income comparisons, pediatric growth charts, network performance monitoring (P95/P99 response times), and quality control to establish tolerance limits in manufacturing.

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