Quick answer
The interquartile range is IQR = Q3 − Q1, the spread of the middle half of the data. For 1 to 8 with the inclusive method, Q1 = 2.75, Q3 = 6.25 and IQR = 3.5.
Enter the data. The calculator returns the IQR and the quartiles.
Related tools: Range Calculator: Range of a data set. Mean Median Mode Range Calculator: Mean, median, mode and range of a data set. Standard Deviation Calculator: Sample or population standard deviation with variance and mean.
How to use the Interquartile Range Calculator
- Type data set, for example 1, 2, 3, 4, 5, 6, 7, 8.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Data set | Text, such as 1, 2, 3, 4, 5, 6, 7, 8 | — |
Formula and method
Formula
rank = p × (n − 1); linear interpolation between neighbouring ranks (inclusive method)
IEEE-754 double precision; shown to at most 6 decimal places.
Excel QUARTILE.INC / NumPy default method. Other textbooks use different quartile conventions that give slightly different values.
Worked examples
This example is verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Data set = 1,2,3,4,5,6,7,8.
| Result | Value |
|---|---|
| IQR | 3.5 |
| Q1 | 2.75 |
| Q3 | 6.25 |
The first line is the headline result (iQR). Below it the interquartile Range Calculator lists q1 and q3, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Why use the IQR
Unlike the range, the IQR ignores the extreme quarter at each end, so one outlier cannot change it. Replacing 8 with 800 in the example leaves Q1 = 2.75 and Q3 = 6.25, so the IQR is still 3.5, while the range jumps from 7 to 799.
Outlier fences
Values below Q1 − 1.5 × IQR (here −2.5) or above Q3 + 1.5 × IQR (here 11.5) are flagged as outliers in a box plot. Quartile definitions vary between software, so state the method used.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Data set: entering "5" shows "Enter at least 2 numbers." beside that field and no result.
Choosing between the Interquartile Range Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Range Calculator](/statistics/range-calculator/) | data set | Range |
| [Mean Median Mode Range Calculator](/statistics/mean-median-mode-range-calculator/) | data set | Mean |
| [Standard Deviation Calculator](/statistics/standard-deviation-calculator/) | data set and data type | Population standard deviation (σ) |
| [Z-Score Calculator](/statistics/z-score-calculator/) | value, mean and standard deviation | Z-score |
| [Median Calculator](/statistics/median-calculator/) | data set | Median |
Background: descriptive statistics
Population statistics divide by n and sample statistics divide by n − 1 (Bessel's correction), because a sample tends to understate variability. Use the population version when your data is every value in the group, and the sample version when it is a subset.
Defaults differ between tools, and so do quartile conventions, which can give slightly different values for small data sets; this page states the method it uses.
Assumptions and limitations
- At least 2 values
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for data set to confirm this.
Frequently asked questions
Is IQR in the same units as the data?
Yes. Q3 and Q1 are data values, so their difference keeps the data's units.
What does a large IQR mean?
The middle half of the data is widely spread.
What is a quartile deviation?
Half of the IQR, here 1.75.
What does the Interquartile Range Calculator calculate?
Interquartile range of a data set. It returns IQR, Q1 and Q3.
What formula does the Interquartile Range Calculator use?
rank = p × (n − 1); linear interpolation between neighbouring ranks (inclusive method). Excel QUARTILE.INC / NumPy default method.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. At least 2 values.
What is an example of a interquartile Range result?
With data set 1,2,3,4,5,6,7,8, the iQR is 3.5.
Related calculators
- Range Calculator — Range of a data set.
- Mean Median Mode Range Calculator — Mean, median, mode and range of a data set.
- Standard Deviation Calculator — Sample or population standard deviation with variance and mean.
- Z-Score Calculator — Standardize a value using a mean and standard deviation.
- Median Calculator — Median of a data set.
- Relative Standard Deviation Calculator — Relative standard deviation (RSD) as a percentage.
- Percentile Calculator — The value at a given percentile of a data set.
- Descriptive Statistics Calculator — Count, mean, median, mode, spread, quartiles and range in one place.
- Mode Calculator — Mode of a data set.
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods (itl.nist.gov/div898/handbook)
- Standard textbook definitions (e.g. Moore, McCabe & Craig, Introduction to the Practice of Statistics)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.