About the Quartile Calculator
Quartiles split a sorted list of numbers into four equal parts. The first quartile Q1 marks the point below which a quarter of the data falls, the median Q2 is the middle, and the third quartile Q3 marks the point below which three quarters fall. The distance between Q1 and Q3 is the interquartile range, a measure of spread that ignores extreme values. This calculator gives you the whole five-number summary, the IQR and the outlier fences from Tukey's rule. Because books, calculators and Excel use slightly different methods, you can choose the one that matches yours.
Updated October 2026
How to use the Quartile Calculator
- 1Paste or type your numbers, separated by commas, spaces or new lines.
- 2Pick the quartile method your textbook or software uses.
- 3Read Q1, the median and Q3 in the results.
- 4Use the interquartile range and fences to see whether any values are outliers.
- 5Copy the summary to use in your report or box plot.
The three methods explained
With the method that leaves out the median, an odd-sized list is split around its middle value and that value belongs to neither half. The inclusive method keeps the middle value in both halves. The Excel method uses a position formula and interpolates, so it can give a quartile that is not in your list at all.
For large data sets the three give nearly the same answers. Differences show up mainly in small lists such as exam questions.
Reading a five-number summary
- Minimum and maximum show the full range.
- Q1 and Q3 show where the middle half of the values sit.
- A median closer to Q1 than to Q3 suggests the data is skewed to the high side.
- A long gap between Q3 and the maximum often hints at outliers.
Related maths tools
The Percentile Calculator finds any other cut point, the Variance Calculator measures spread around the mean and the Average Calculator gives the mean, median and mode. For test results the Z-Score Calculator shows how far a value sits from the mean.
Features
- Minimum, Q1, median, Q3 and maximum
- Interquartile range
- Lower and upper outlier fences
- Lists any outliers it finds
- Three methods, including Excel QUARTILE.INC
- Any number of values
Frequently asked questions
How do I find the quartiles of a data set?
Sort the numbers, find the median, then find the median of the lower half for Q1 and the median of the upper half for Q3. For 3, 5, 7, 8, 12, 13, 14, 18, 21 the median is 12, Q1 is 6 and Q3 is 16 with the method that leaves out the middle value.
Why do different tools give different quartiles?
There is no single agreed definition. Some methods include the median in each half when the count is odd, others leave it out, and spreadsheets interpolate between values. All are valid, so choose the one your course or software expects.
What is the interquartile range?
It is Q3 minus Q1, the width of the middle half of the data. Because it ignores the top and bottom quarters, extreme values barely affect it, which makes it a robust measure of spread.
How are outliers decided?
The common rule from John Tukey flags any value more than 1.5 times the IQR below Q1 or above Q3. Those limits are the lower and upper fences. A value outside them is worth checking, but it is not necessarily an error.
Can I use it for a box plot?
Yes. A box plot draws a box from Q1 to Q3 with a line at the median, and whiskers out to the smallest and largest values inside the fences. The minimum, quartiles and maximum shown here are exactly the numbers you need.
Does the order of my numbers matter?
No. The calculator sorts the list itself, so you can paste values in any order. Repeated values count each time they appear.