Histogram Calculator

Paste a list of numbers and get equal-width bins with their frequencies, a text histogram, and summary stats (min, max, range, and bin width).

Quick Facts

Method
Equal-width bins: bin width = (max − min) ÷ number of bins
Default bin count uses Sturges' rule: ceil(log₂ n + 1).

Your Results

Calculated
Number of bins
-
Equal-width intervals
Bin width
-
(max − min) ÷ bins
Data range
-
min to max
Count (n)
-
Values counted
Bins and frequencies
-

Ready

Paste your data and click Calculate to build the histogram.

What a histogram calculator does

A histogram summarizes a set of numeric measurements by dividing the range of the data into a series of adjacent, equal-width intervals called bins, and counting how many values fall into each bin. Plotting those counts as bars reveals the shape of the data: where values cluster, how spread out they are, whether the distribution is symmetric or skewed, and whether there are gaps or outliers. This calculator does the counting for you. You paste a list of numbers, choose how many bins you want (or let it pick a sensible default), and it returns the bin boundaries, the frequency in each bin, and a quick text bar chart.

The formula behind it

Two calculations define an equal-width histogram. First, the number of bins k. If you do not specify it, this tool applies Sturges' rule, one of the oldest and most widely cited defaults:

k = ⌈log₂(n) + 1⌉

where n is the number of data points and ⌈ ⌉ means round up. Second, the bin width, which spans the full data range evenly:

bin width = (maximum − minimum) ÷ k

The bins are then [min, min+w), [min+w, min+2w), and so on. Every bin is half-open (it includes its lower edge but not its upper edge) except the last bin, which is closed at the top so the maximum value is counted. A value x lands in bin index ⌊(x − min) ÷ w⌋.

Why bin count matters more than anything else

The single most important choice in a histogram is the number of bins. Too few bins over-smooth the data and hide real structure — two distinct clusters can merge into one flat block. Too many bins produce a spiky, noisy picture where random sampling wobble looks like signal. There is no universally correct answer, which is why several rules of thumb exist. Sturges' rule (used here by default) tends to under-bin large or skewed datasets, so it is common to also try the square-root rule, k = ⌈√n⌉, or Rice's rule, k = ⌈2·n^(1/3)⌉. The best practice is to try a few values and keep the one that shows the shape most honestly.

Common reference points

  • n = 30: Sturges gives ⌈log₂(30) + 1⌉ = ⌈4.907 + 1⌉ = 6 bins; the square-root rule gives ⌈√30⌉ = 6.
  • n = 100: Sturges gives ⌈6.644 + 1⌉ = 8 bins; the square-root rule gives 10; Rice's rule gives ⌈2·100^(1/3)⌉ = ⌈9.28⌉ = 10.
  • n = 1000: Sturges gives ⌈9.966 + 1⌉ = 11 bins; the square-root rule gives ⌈31.6⌉ = 32 — a big divergence that shows why Sturges under-bins large samples.

Frequently Asked Questions

How many bins should a histogram have?
There is no single correct number, but rules of thumb give a starting point. Sturges' rule (this calculator's default) uses k = ⌈log₂(n) + 1⌉; the square-root rule uses ⌈√n⌉; Rice's rule uses ⌈2·n^(1/3)⌉. For 100 points, Sturges gives 8 bins and the square-root rule gives 10. Try two or three values: too few bins hide structure, too many make random noise look like real features.
How is bin width calculated?
Bin width = (maximum − minimum) ÷ number of bins, using equal-width bins across the whole data range. For data from 10 to 90 split into 8 bins, the width is (90 − 10) / 8 = 10, giving bins [10, 20), [20, 30), … , with the final bin [80, 90] closed at the top so the maximum is counted.
Which bin does a value on a boundary fall into?
Bins here are half-open on the right: a value equal to a bin's upper edge goes into the next bin up, following the standard [lower, upper) convention. The one exception is the final bin, which is closed at both ends so the dataset's maximum value is always counted rather than dropped.
What is the difference between a histogram and a bar chart?
A bar chart compares separate categories and its bars have gaps between them. A histogram shows the distribution of one continuous numeric variable: the bars are adjacent with no gaps because the bins are contiguous intervals, and the horizontal axis is a number line, not a set of labels.

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