Quartile Calculator
Find Q1, Q2, Q3 and the interquartile range.
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How it works
Quartiles divide a data set into four equal parts, and this calculator finds all three quartiles along with the interquartile range from a list of numbers. You enter the values, and it sorts them and returns the first quartile, the median, the third quartile, and the interquartile range, or IQR. The first quartile marks the point below which a quarter of the data lie, the median splits the data in half, and the third quartile marks the three-quarter point, so together they carve the data into four equal groups. The IQR, the distance from the first to the third quartile, measures the spread of the central half of the data and is a robust alternative to the range because it ignores extreme values. Quartiles and the IQR are the building blocks of the box plot, one of the most useful ways to visualise a distribution, and they are widely used to detect outliers, summarise skewed data, and compare groups. Because they are based on position rather than arithmetic, they are not distorted by a few unusually large or small values the way the mean and standard deviation can be. Enter your data to compute the quartiles and interquartile range.
Q1 = 25th percentile, Q2 = median, Q3 = 75th percentile, IQR = Q3 − Q1
Quartiles split ordered data into four equal parts. The first quartile is the value at the 25 percent position, the second quartile is the median at 50 percent, and the third quartile is at 75 percent. The interquartile range is the third quartile minus the first, capturing the spread of the middle half of the data. The calculator sorts the values and interpolates to find each quartile.
Source:Descriptive statistics
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Worked example
How to use this calculator
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Q1 (25th percentile) updates instantly as you type — no button to press.
Frequently asked questions
What are quartiles?
Quartiles are three values that divide a sorted data set into four equal parts. The first quartile is the 25th percentile, below which a quarter of the data fall; the second is the median; and the third is the 75th percentile. They summarise how data are distributed and are the foundation of box plots and the interquartile range.
What is the interquartile range?
The interquartile range, or IQR, is the difference between the third and first quartiles. It measures the spread of the middle 50 percent of the data, ignoring the lowest and highest quarters. Because it excludes extreme values, the IQR is a robust measure of variability that is not distorted by outliers, unlike the full range or standard deviation.
How are quartiles used to find outliers?
A common rule flags values as outliers if they fall more than 1.5 times the interquartile range below the first quartile or above the third quartile. These boundaries, called fences, separate typical values from unusually extreme ones. This IQR-based method is widely used because it does not assume the data follow any particular distribution.
Is the second quartile the same as the median?
Yes. The second quartile and the median are the same value, the point that divides the data set into two equal halves, or the 50th percentile. It is listed as Q2 in the quartile framework. So finding the quartiles automatically gives you the median as the middle of the three.
Why are quartiles better than the range for spread?
The full range depends only on the minimum and maximum, so a single extreme outlier can make it huge and misleading. The interquartile range instead measures the spread of the central half of the data, ignoring the extremes, which makes it a far more stable and representative measure of variability for real-world data that often contain outliers.