Histogram Bins Calculator

Find the optimal number of histogram bins and bin width by three rules — Sturges, Scott, and Freedman-Diaconis — from your data.

Result

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How to use this calculator

Paste your dataset, separated by commas, spaces, or new lines.
Read the suggested bin counts from Sturges, Scott, and Freedman-Diaconis.
Use Freedman-Diaconis for skewed data or when outliers are present.
Adjust the chosen bin count visually until the histogram shape is clear.

About this calculator

Choosing the number of bins for a histogram is a balance: too few bins hide the shape of the distribution, too many make it noisy. Several rules formalize the choice. Sturges' rule, k = ⌈log₂n + 1⌉, is simple and works for small, roughly bell-shaped datasets but tends to use too few bins for large samples. Scott's rule sets the bin width from the standard deviation and sample size, assuming the data is approximately normal. The Freedman-Diaconis rule uses the interquartile range instead of the standard deviation, which makes it robust to outliers and skew. This calculator computes all three from your pasted data, reporting both the bin count and bin width for each, so you can pick the one that best matches your data and visualize accordingly.

How it works — the formula

Sturges:            k = ⌈log₂ n + 1⌉
Scott:              h = 3.49 · s · n^(−1/3),  k = ⌈range / h⌉
Freedman-Diaconis:  h = 2 · IQR · n^(−1/3), k = ⌈range / h⌉

Sturges counts bins directly from sample size; Scott and Freedman-Diaconis derive a bin width from spread and sample size, then divide the range by it.

Source: Wikipedia — Histogram: number of bins and width

Worked examples

Example 1

n = 12 dataset

Inputs:: data=4,8,15,16,23,42,11,19,27,33,5,9
Output:: Sturges ⌈log₂12+1⌉ = 5 bins

Example 2

n = 100 (Sturges)

Inputs:: 100 values
Output:: Sturges = ⌈6.64+1⌉ = 8 bins

Example 3

n = 1000 (Sturges)

Inputs:: 1000 values
Output:: Sturges = ⌈9.97+1⌉ = 11 bins

Limitations

Sturges under-bins large datasets; Scott assumes normality.
Freedman-Diaconis can give very many bins for tight IQR with wide range.
All are guidelines — final bin count is a visualization judgment.

Bin-count rules are heuristics; always sanity-check the resulting histogram.

Frequently asked

How many bins should a histogram have?+

There is no single right answer — it depends on the data. Common rules give a starting point: Sturges for small normal-ish data, Scott for larger normal data, and Freedman-Diaconis for skewed data or data with outliers. Then refine visually.

What is Sturges' rule?+

Sturges' rule sets the number of bins to k = ⌈log₂n + 1⌉, where n is the number of data points. It is simple but assumes roughly normal data and tends to under-bin large datasets.

How does Scott's rule differ from Freedman-Diaconis?+

Scott's rule bases the bin width on the standard deviation (3.49·s·n^(−1/3)), so outliers inflate it. Freedman-Diaconis uses the interquartile range (2·IQR·n^(−1/3)) instead, making it resistant to outliers and better for skewed data.

Why does bin width scale with n^(−1/3)?+

Both Scott and Freedman-Diaconis derive from minimizing the difference between the histogram and the true density. The optimal width shrinks as the cube root of the sample size grows, so more data supports narrower bins and finer detail.

Which rule should I use?+

For everyday, roughly symmetric data, any of them works. For large datasets or skewed/heavy-tailed data, prefer Freedman-Diaconis. When in doubt, compute all three and compare the resulting histograms.

Do I round bins up or down?+

Bin counts are rounded up (ceiling) so the bins cover the full data range. The resulting width is the range divided by that bin count; nudge either to land on round numbers for axis labels.