Histogram maker

Paste a column of numbers, or a whole table and pick the column. The number of bins is a choice rather than a fact, so five standard rules are computed side by side and you choose.

40 values drawn in 14 bins of width 5, from 25 to 95.

What each rule suggests

Rule	Formula	Bins
Sturges	k = ⌈log₂ n⌉ + 1	7
Freedman–Diaconis	h = 2 × IQR / ∛n	17
Scott	h = 3.49 × s / ∛n	7
Square root	k = ⌈√n⌉	7
Rice	k = ⌈2 × ∛n⌉	7

Counts per bin

From (incl.)	To	Count
25	30	8
30	35	16
35	40	9
40	45	5
45	50	1
50	55	0
55	60	0
60	65	0
65	70	0
70	75	0
75	80	0
80	85	0
85	90	0
90	95	1

How to use it

Paste one number per line, or paste a table and choose the column. Blank cells and text are skipped, and numbers written with thousands separators or currency signs are read correctly. The bin-rule menu shows how many bins each rule recommends for your data. Pick one, or set your own count, and the chart and the table of counts update together. Hover over a bar to see its range and count.

The five bin rules

Here n is the number of values, s the sample standard deviation and IQR the interquartile range (third quartile minus first). Rules that give a width are turned into a count by dividing the data range by that width and rounding up.

Sturges (1926): k = ⌈log₂ n⌉ + 1. Derived by assuming the data is roughly normal. It grows very slowly (11 bins for 1,000 values) and under-bins large or skewed datasets.
Freedman–Diaconis (1981): h = 2 × IQR / ∛n. Built on the IQR, which a few extreme values barely move, so it is the most robust of the five. With long tails it can give many bins, most of them empty.
Scott (1979): h = 3.49 × s / ∛n. Optimal for normally distributed data in a mean-squared-error sense. Because it uses the standard deviation, an outlier inflates the width.
Square root: k = ⌈√n⌉. The simplest rule of thumb, and easy to check in your head.
Rice: k = ⌈2 × ∛n⌉. A simple alternative to Sturges that grows faster with n.

Worked example

The sample has 40 delivery times with a median of 33 minutes and one order at 95 minutes. For Sturges, log₂ 40 is 5.32, rounded up to 6, plus one gives 7 bins. For Freedman–Diaconis, the IQR is 37.25 − 30 = 7.25, and ∛40 is 3.42, so the width is 2 × 7.25 / 3.42 = 4.24 minutes. The range is 95 − 26 = 69, so 69 / 4.24 gives 17 bins. Scott uses the standard deviation of 10.88 instead: 3.49 × 10.88 / 3.42 = 11.1 minutes, which gives 7 bins.

The difference matters. At 7 bins, rounded to a width of 10, nearly everything lands in two bars (8 orders from 20 to 30 and 25 from 30 to 40). At the Freedman–Diaconis width, rounded to 5, the peak from 30 to 35 and the tail stretching to 50 both become visible. Scott's rule gives few bins here precisely because the one late order inflates the standard deviation. The IQR does not notice it.

Readable edges

By default the bin width is rounded to 1, 2, 2.5 or 5 times a power of ten, and the first edge is placed on a multiple of that width. Edges such as 25, 30, 35 are easier to read and to quote than 25.76, 30.00, 34.24. The cost is that the number of bins may differ by one or two from the rule's suggestion. Tick "Exact bin count" to split the range from the minimum to the maximum into exactly the chosen number of equal bins instead.

Limits

A histogram's shape depends on the bin width and on where the first edge falls. With fewer than about 20 values, almost any shape can appear by chance; a plain list or a dot plot is more honest at that size. Dates and times of day are not supported as numbers. Convert them to minutes or days first. If you need the numbers behind the shape, the summary statistics calculator gives the mean, median, quartiles and outlier fences for the same column.

Common questions

How many bins should a histogram have?

There is no single correct number, which is why this page shows five rules. Sturges suits small, roughly bell-shaped data. Freedman–Diaconis is the safest general choice because it uses the interquartile range and is not thrown off by outliers. Try two or three settings: a real feature of the data survives a change of bin width, an artefact does not.

What is the difference between a histogram and a bar chart?

A bar chart compares separate categories, and the gaps between bars say the categories are distinct. A histogram shows how one continuous measurement is distributed, so its bars touch: each covers a range of values, and the ranges meet end to end. The bar heights here are counts of values in each range.

Which bin does a value on the boundary go into?

The upper one. Every bin includes its lower edge and excludes its upper edge, so with bins of width 5 a value of 30 is counted in 30–35, not 25–30. The only exception is the last bin, which also includes its upper edge so the maximum is never lost.

Why does the chart have a different number of bins from the rule?

Because the edges are rounded to readable numbers. A rule might ask for a width of 4.24, which would give edges like 25.76 and 30.00. The tool rounds the width to 1, 2, 2.5 or 5 times a power of ten and starts on a multiple of it, which can add or remove a bin. Tick "Exact bin count" to use the rule's number exactly.

My data has one huge outlier and everything is squashed into one bar. What do I do?

That is what a histogram should show: the outlier really is far from everything else. To see the shape of the bulk, remove the outlier from the pasted data and redraw, and say that you did. The summary statistics tool flags values outside the 1.5 × IQR fences, which is a reasonable place to start deciding.