Quick answer
Quartiles divide ordered data into four parts. With the inclusive method (rank = p × (n − 1) and linear interpolation), the data 1 to 8 give Q1 = 2.75, median = 4.5, Q3 = 6.25 and IQR = 3.5.
Enter the data. The calculator returns Q1, the median, Q3 and the IQR.
Related tools: Standard Deviation Calculator: Sample or population standard deviation with variance and mean. Z-Score Calculator: Standardize a value using a mean and standard deviation. Mean Median Mode Range Calculator: Mean, median, mode and range of a data set.
How to use the Quartile 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 |
|---|---|
| Q1 | 2.75 |
| Median | 4.5 |
| Q3 | 6.25 |
| IQR | 3.5 |
The first line is the headline result (q1). Below it the quartile Calculator lists median, q3 and iQR, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Worked example
For eight values the Q1 rank is 0.25 × 7 = 1.75, so Q1 lies three-quarters of the way between the 2nd and 3rd values: 2 + 0.75 = 2.75. Q3 has rank 5.25, between 6 and 7, giving 6.25.
Methods differ
Textbooks and software use different quartile rules. The exclusive method (rank = p × (n + 1)) would give Q1 = 2.25 and Q3 = 6.75 for the same data. This page uses the inclusive method, matching Excel's QUARTILE.INC, so compare like with like. At least 2 values are required.
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 Quartile 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 |
|---|---|---|
| [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 |
| [Mean Median Mode Range Calculator](/statistics/mean-median-mode-range-calculator/) | data set | Mean |
| [Median Calculator](/statistics/median-calculator/) | data set | Median |
| [Relative Standard Deviation Calculator](/statistics/relative-standard-deviation-calculator/) | data set and data type | Relative standard deviation |
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
What is Q2?
The median, the middle value of the data.
What are quartiles used for?
Box plots, spread measures and the 1.5 × IQR outlier rule.
Why do calculators disagree?
They use different interpolation rules for quartiles.
What does the Quartile Calculator calculate?
Quartiles of a data set. It returns Q1, Median, Q3 and IQR.
What formula does the Quartile 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 quartile result?
With data set 1,2,3,4,5,6,7,8, the q1 is 2.75.
Related calculators
- Standard Deviation Calculator — Sample or population standard deviation with variance and mean.
- Z-Score Calculator — Standardize a value using a mean and standard deviation.
- Mean Median Mode Range Calculator — Mean, median, mode and range of a data set.
- Median Calculator — Median of a data set.
- Relative Standard Deviation Calculator — Relative standard deviation (RSD) as a percentage.
- Variance Calculator — Sample or population variance.
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.