Quartile Calculator

Background.

The Quanta quartile calculator splits any dataset into four equal-sized quarters and reports the three boundary values — Q1, Q2, and Q3 — that mark those splits, along with the interquartile range (Q3 − Q1) as a bonus spread statistic. Quartiles are simply percentiles at three fixed, well-known positions: Q1 is the 25th percentile, Q2 is the 50th percentile (the median), and Q3 is the 75th percentile. Together they answer 'how is this data distributed across its range' in a single glance, which is exactly the information a box-and-whisker plot is built to display.

The question this calculator answers is different from a plain median lookup or a spread measurement. Asking 'what is my median' only tells you where the centre sits; asking 'what is my quartile' tells you where a quarter and three-quarters of the way through the data sit as well, giving you a sense of how the lower half and upper half of the dataset are each internally distributed. A dataset where Q1 sits close to the minimum and Q3 sits close to the maximum is spread out fairly evenly; a dataset where Q1 and Q3 both huddle close to Q2 is tightly clustered around its centre with the extremes reserved for a small number of unusual values.

A detail worth stating plainly, because it is exactly the kind of thing that causes two 'correct' calculators to disagree: there is more than one accepted mathematical convention for computing quartiles, in exactly the same way there is more than one convention for percentiles in general. This calculator uses linear interpolation between the two closest ranks — the method Hyndman and Fan's definitive 1996 survey labels 'Type 7' — which is the default behaviour of R's quantile() function, NumPy, pandas, and Microsoft Excel's QUARTILE and QUARTILE.INC functions. Older textbooks and some graphing calculators instead use John Tukey's original 'hinges' method, or Excel's alternative QUARTILE.EXC function, both of which can produce a slightly different Q1 or Q3 for the same dataset — most noticeably with small sample sizes, where the exact rounding convention has more room to matter. Neither method is wrong; they are different, well-documented conventions, and this page tells you exactly which one you're getting.

Use this calculator whenever you need the classic Q1/Q2/Q3 split — for building a box plot by hand, checking a homework answer, or getting a fast sense of how a dataset's lower and upper halves are shaped. If you specifically want the single interquartile-range number as a standalone spread statistic (comparable to the range or the standard deviation), the dedicated interquartile-range calculator headlines that number directly. If you want to know exactly which individual data points count as outliers under the 1.5×IQR rule, the outlier calculator applies these same quartiles to flag specific values rather than just reporting the summary statistics.

What is quartile calculator?

A quartile is one of three values that divide a sorted dataset into four equal-sized groups, each containing roughly one quarter of the observations. The first quartile (Q1) is the value at the 25th percentile — one quarter of the data lies at or below it. The second quartile (Q2) is the value at the 50th percentile, which is exactly the median — half of the data lies at or below it. The third quartile (Q3) is the value at the 75th percentile — three quarters of the data lies at or below it. Quartiles are the specific case of the more general concept of a percentile, evaluated at three fixed, standard positions. When the requested percentile position does not land exactly on one of the sorted data points — which is the common case — the value must be interpolated, and different statistical software packages use different, well-documented interpolation conventions. This calculator implements Type 7 (per Hyndman & Fan's 1996 taxonomy of nine competing methods), matching the default behaviour of R, NumPy, pandas, and Excel's QUARTILE/QUARTILE.INC functions.

How to use this calculator.

1. 01Paste your dataset as comma-separated numbers, in any order — the calculator sorts them internally.
2. 02You need at least 4 values for quartiles to be meaningful.
3. 03Read Q1, Q2, and Q3 in the results. Q2 is always the ordinary median of the dataset.
4. 04Use the IQR (Q3 − Q1) shown alongside the quartiles as a quick spread check, or move to the dedicated interquartile-range or outlier calculators for a deeper dive into spread and outlier detection.
5. 05If you compare this result against Excel, a graphing calculator, or a textbook and see a slightly different Q1 or Q3, check which quartile convention that tool uses — see the FAQ below.

The formula.

Sort the n values into ascending order statistics x₍₁₎ ≤ x₍₂₎ ≤ … ≤ x₍ₙ₎. For each quartile proportion p (0.25 for Q1, 0.5 for Q2, 0.75 for Q3), compute the interpolated rank position h = 1 + p·(n − 1). If h lands exactly on an integer, the quartile equals x₍ₕ₎ directly. Otherwise, interpolate linearly between the order statistics just below and just above: quartile = x₍⌊h⌋₎ + (h − ⌊h⌋)·(x₍⌈h⌉₎ − x₍⌊h⌋₎). This is the Type 7 method from Hyndman and Fan's 1996 taxonomy — the default in R, NumPy, pandas, and Excel's QUARTILE/QUARTILE.INC. The IQR is simply Q3 − Q1, per the NIST/SEMATECH e-Handbook's definition of the interquartile range as the 75th percentile minus the 25th percentile.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Hyndman, R.J. & Fan, Y. (1996). 'Sample Quantiles in Statistical Packages.' The American Statistician, 50(4), 361-365 — the peer-reviewed survey of nine competing sample-quantile conventions; this calculator implements Type 7.
2. [2]OpenStax. Introductory Statistics 2e. Rice University, 2023. §2.3, 'Measures of the Location of the Data' — quartile definitions and worked examples.
3. [3]NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.2 — Measures of Scale. Defines the interquartile range as the 75th percentile minus the 25th percentile.
4. [4]Tukey, J.W. (1977). Exploratory Data Analysis. Addison-Wesley — origin of the box-and-whisker plot and the alternative 'hinges' quartile convention referenced in the FAQ.