What this tool calculates
The calculator sorts a finite numeric list and reports its 25th percentile (Q1), 50th percentile (Q2 or median), and 75th percentile (Q3). Quartiles divide an ordered distribution into four probability-position regions and are useful for describing center and spread.
Several accepted quartile conventions exist. This page documents the exact interpolation used by the implementation so results can be reproduced instead of assuming every statistics package will agree for a small sample.
Inputs
Enter finite numbers separated by commas, spaces, semicolons, or line breaks. Keep repeated observations; removing duplicates changes the empirical distribution. Do not combine values with different units or incomparable definitions.
An empty list is invalid. Before calculation, decide how missing observations, censored values, weights, and data-quality errors should be handled. The tool does not make those choices automatically.
Method and formula
Sort n values from smallest to largest. For percentile proportion p, use the zero-based position:
position = (n − 1) × p
If the position is an integer, select that ordered value. Otherwise linearly interpolate between the values immediately below and above it. Q1 uses p = 0.25, Q2 uses 0.50, and Q3 uses 0.75.
This convention is commonly called an inclusive linear-percentile method. Other software may use hinges, exclusive positions, or no interpolation, particularly with very small n.
Worked example
Enter 1, 2, 3, 4. The list is already ordered and n − 1 = 3.
- Q1 position: 3 × 0.25 = 0.75, so interpolation gives 1.75.
- Q2 position: 3 × 0.50 = 1.5, giving 2.5.
- Q3 position: 3 × 0.75 = 2.25, giving 3.25.
Thus the output is Q1 1.75, median 2.5, and Q3 3.25. A package using a different definition may report different outer quartiles for the same four values.
How to interpret the result
About one quarter of the ordered distribution lies at or below Q1 under the empirical interpolation, and about three quarters lies at or below Q3. The interquartile range is Q3 − Q1; in the example it is 1.5. It describes the middle half's spread and is less sensitive to extremes than the full range.
Report the method whenever values may be compared across tools or publications. Also report the sample size and units; quartiles alone do not reveal multimodality, gaps, or data-collection bias.
Accuracy and limitations
With few observations, interpolation can produce values not present in the data and quartiles are unstable summaries. The tool does not compute confidence intervals, weighted percentiles, outlier fences, box plots, or quantiles for grouped data. Floating-point formatting can round interpolated results.
Quartiles describe the supplied data only. They do not establish a population parameter, causal effect, or acceptable threshold. Sampling design, missingness, measurement quality, and the chosen definition can matter more than displayed precision.
Sources
- NIST/SEMATECH e-Handbook, Quantile-Quantile Plot provides institutional context for quantiles and ordered distribution positions.
- NIST/SEMATECH e-Handbook, Measures of Location situates the median and related summaries within exploratory analysis.
Editorial record
Author: SoupCalc Editorial Team
Last reviewed: August 14, 2026
Review scope: Sorting, (n−1)p interpolation, small-sample method differences, statistical limits, NIST context, and the 1.75/2.5/3.25 example were checked.