Box Plot Calculator

Work out box plot instantly with clear inputs, formula shown and shareable results.

About Box Plot Calculator

A box plot shows the five-number summary. The box spans the quartiles, the line inside marks the median, and whiskers reach to the furthest point within 1.5 IQRs of the box — anything beyond is flagged as an outlier.

Formulas

Interquartile range

IQR = Q₃ − Q₁

Outlier fences

Q₁ − 1.5·IQR and Q₃ + 1.5·IQR

Worked example

With the default values below, Box Plot Calculator returns Min | Q₁ | Median | Q₃ | Max of 7 | 15 | 21 | 27 | 45. Change any input above and every figure here is recalculated in your browser.

Inputs used

Data values: 7, 12, 15, 18, 21, 24, 27, 33, 45
Whisker length in IQRsminimum 0.1: 1.5

Results

Min | Q₁ | Median | Q₃ | Max: 7 | 15 | 21 | 27 | 45
Interquartile range: 12.00000000
Lower fence: -3.000000
Outliers beyond the fences: 0

Step by step

1Values used
2Interquartile range
3Outlier fences
4Min | Q₁ | Median | Q₃ | Max= 7 | 15 | 21 | 27 | 45
5Interquartile range= 12.00000000
6Lower fence= -3.000000
7Outliers beyond the fences= 0

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For the sample data?

Q₁ = 15, median = 21 and Q₃ = 27, so the IQR is 12 and the fences sit at −3 and 45.

Why 1.5 IQRs?

Tukey chose it as a practical compromise: for normal data it flags only about 0.7% of observations.