Histogram Bin Width Calculation

Histogram Bin Width Calculator Form

Enter raw data for full statistics. If raw data is empty, use the manual summary fields. The raw dataset takes priority.

Raw dataset

Separate values with commas, spaces, semicolons, or new lines.

Bin width rule

Choose the rule you want to highlight in the result area.

Custom width

Used only when the custom rule is selected.

Manual sample size

Manual minimum

Manual maximum

Manual standard deviation

Manual IQR

Decimal places

Chart x-axis label

Formula used

Freedman–Diaconis rule:

Bin width = 2 × IQR / n^1/3

Scott rule:

Bin width = 3.5 × s / n^1/3

Sturges rule:

Bin count = ceil(log₂(n) + 1), then width = range / bin count

Rice rule:

Bin count = ceil(2 × n^1/3), then width = range / bin count

Square-root rule:

Bin count = ceil(√n), then width = range / bin count

Here, n is sample size, s is standard deviation, IQR is the interquartile range, and range = maximum − minimum. Smaller widths reveal more detail, while larger widths smooth the histogram.

How to use this calculator

Paste your raw dataset into the raw data box for the most complete analysis.
Select the preferred rule, such as Freedman–Diaconis for robust spread handling.
Enter a custom width only when using the custom method.
Use manual sample size, range, standard deviation, and IQR if raw data is unavailable.
Choose the number of decimal places for clean reporting.
Click Calculate Bin Width to show results below the header and above the form.
Review the comparison table to see how different rules change the recommended width.
Download a CSV summary or PDF report when you need a shareable output.

Example data table

Example Dataset	n	Min	Max	Range	IQR	Std. Dev.	F–D Width	Scott Width	Sturges Width
2, 3, 4, 4, 5, 6, 7, 8, 9, 10	10	2	10	8	3.75	2.6583	3.4812	4.3186	1.6

Frequently asked questions

1. Why does histogram bin width matter?

Bin width controls how grouped your data appears. Very small bins can make noise look important. Very large bins can hide shape, clusters, and outliers. A reasonable width improves readability and preserves distribution meaning.

2. When should I use Freedman–Diaconis?

Use Freedman–Diaconis when your data may be skewed or contain outliers. It relies on the interquartile range, which is less sensitive to extreme values than standard deviation.

3. When is Scott’s rule a good choice?

Scott’s rule works well for smooth, roughly bell-shaped data. It uses standard deviation, so it is more influenced by extreme values than the Freedman–Diaconis rule.

4. What if I only know summary statistics?

You can still estimate bin width using manual sample size, minimum, maximum, standard deviation, and IQR inputs. The chart will compare candidate widths even when the raw observations are unavailable.

5. Why do different rules give different widths?

Each rule balances smoothness and detail differently. Some depend on spread measures like IQR or standard deviation. Others use only sample size, so their recommendations can vary noticeably.

6. Can I use a custom width instead?

Yes. A custom width is helpful when your field uses fixed class intervals, reporting standards, or teaching examples. This page still compares common statistical rules for reference.

7. What happens with constant data?

If all observations are the same, the range becomes zero. In that case, meaningful histogram spacing is limited because the dataset has no spread across the horizontal axis.

8. Does this calculator create the histogram too?

Yes. When raw data is available, the page draws a Plotly histogram using the chosen width. Without raw data, it shows a comparison chart of the available rule-based widths.