Percentile Calculator

Enter any dataset of numbers to instantly compute the five-number summary, quartiles, IQR, and outlier fences. Look up the percentile rank of any value or find the value at any percentile. A dot plot highlights the IQR band and flags outliers.

Enter Your Data

15 values loaded

Tip: Press Ctrl+Enter to calculate. Separate values with commas or new lines.

Five-Number Summary

Min7
Q11225th pct
Median3850th pct
Q36175th pct
Max89
IQRQ3 - Q1= 49
Fences:[-61.5, 134.5]
n =15

Dot Plot with Quartile Bands

789Q112Median38Q361
Normal valuesOutliers (outside 1.5 x IQR fences)IQR band (Q1 to Q3)

Percentile Lookup

Reference Guide

Percentiles and Quartiles

A percentile tells you what percentage of values in a dataset fall below a given value. If a score is at the 75th percentile, 75% of the values are lower than it.

Quartiles divide a sorted dataset into four equal parts. The three quartile boundaries are Q1 (25th percentile), Q2 (median, 50th percentile), and Q3 (75th percentile).

Q1=median of lower half,Q3=median of upper halfQ_1 = \text{median of lower half},\quad Q_3 = \text{median of upper half}

This tool uses the exclusive-median (Tukey) method: for an odd number of values, the median itself is excluded from both halves when computing Q1 and Q3.

IQR and Outliers

The interquartile range (IQR) measures the spread of the middle 50% of the data. It is resistant to extreme values, making it a better measure of spread than the full range when outliers are present.

IQR=Q3−Q1\text{IQR} = Q_3 - Q_1

Outliers are identified using Tukey fences. Any value outside these bounds is flagged as a potential outlier (shown in red on the dot plot).

Lower=Q1−1.5⋅IQR,Upper=Q3+1.5⋅IQR\text{Lower} = Q_1 - 1.5 \cdot \text{IQR},\quad \text{Upper} = Q_3 + 1.5 \cdot \text{IQR}

Five-Number Summary

The five-number summary is a compact description of a dataset's distribution. It consists of five statistics that together capture both the center and spread.

MinimumSmallest value
Q1 (25th pct)Lower quartile
Median (50th pct)Middle value
Q3 (75th pct)Upper quartile
MaximumLargest value

The five-number summary is the basis for a box-and-whisker plot. The box spans Q1 to Q3, the line inside is the median, and the whiskers extend to the fences.

Computing Percentile Ranks

This tool uses the nearest-rank method. The percentile rank of a value x is the percentage of data values strictly less than x.

PR(x)=#{v∈D∣v<x}n×100\text{PR}(x) = \frac{\#\{v \in D \mid v < x\}}{n} \times 100

To find the value at percentile P (nearest-rank lookup):

index=⌈P100⋅n⌉−1\text{index} = \left\lceil \frac{P}{100} \cdot n \right\rceil - 1

The index is clamped to [0, n-1] so edge cases like P = 0 or P = 100 always return valid data values.