Quartile Calculator
Calculate Q1, median, Q3, IQR and the full five-number summary of any data set instantly, with Tukey fences for outlier checks.
About the Quartile Calculator
This quartile calculator produces the five-number summary of any numeric data set: minimum, first quartile (Q1), median, third quartile (Q3) and maximum, plus the interquartile range (IQR) and total range. These five numbers are the backbone of a box plot and describe a distribution without assuming it is normal.
Quartiles split sorted data into four equal parts: 25% of values fall at or below Q1, 50% at or below the median, 75% at or below Q3. This tool computes them with linear interpolation (the QUARTILE.INC method used by Excel and Google Sheets), so results match your spreadsheet. It also reports the Tukey fences — Q1 − 1.5×IQR and Q3 + 1.5×IQR — the standard cutoffs for flagging outliers.
Because quartiles rank data rather than average it, they are robust: one wild value barely moves them, unlike the mean and standard deviation. Everything is computed locally in your browser.
How to Use the Quartile Calculator
- 1Paste at least four numeric values, separated by commas, spaces or new lines.
- 2Read Q1, median and Q3, plus min, max, IQR and range.
- 3Use the Tukey fences shown below the results to spot potential outliers.
- 4Copy the summary for your report or homework with one click.
Frequently Asked Questions
How are quartiles calculated? A worked example
For 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49 (n = 11), Q1's position is (11 − 1) × 0.25 = 2.5, halfway between the 3rd value (15) and 4th (36), giving 25.5. The median is the 6th value, 40. Q3's position is 7.5, halfway between 41 and 42 → 41.5. IQR = 41.5 − 25.5 = 16.
What is the interquartile range used for?
The IQR measures the spread of the middle 50% of the data, immune to extreme values. It drives the standard outlier rule: anything below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is a potential outlier. It is also the height of the box in a box plot.
Why do different calculators give different quartiles?
There are several legitimate quartile conventions — inclusive vs exclusive of the median, interpolated vs nearest value. This tool uses the inclusive interpolation method (Excel's QUARTILE.INC / R type 7). On larger data sets the methods converge; on tiny sets they can differ noticeably.
What is a five-number summary?
Minimum, Q1, median, Q3 and maximum — the five values that sketch a distribution's location, spread and skew at a glance, and exactly what a box-and-whisker plot draws. This calculator outputs all five plus IQR and range.
Do I need to sort my data first?
No — the calculator sorts internally. Paste values in any order, separated by commas, spaces, semicolons or new lines, and duplicates are handled correctly.