# Histogram Bin Calculator
Work out how many bins a histogram needs. Compare Sturges, Scott, Freedman-Diaconis, Rice and square-root, then get the bin edges, counts and percentages.
## Run it
- **CLI:** `gizza tool histogram-bin-calculator "1
2
2
3
4
7
8
9
12
15
22
40"`
- **Web:** https://gizza.ai/tools/histogram-bin-calculator/
- **Agents:** machine-readable descriptor (parameters JSON Schema) at https://gizza.ai/tools/histogram-bin-calculator/tool.json
## Inputs
- `numbers` — Numbers _(field)_
- `rule` — Bin-count rule to apply _(field)_
- `bins` — Bin count (used when the rule is Manual) _(field)_
- `range_min` — Range start (blank = smallest value) _(field)_
- `range_max` — Range end (blank = largest value) _(field)_
- `nice_edges` — Round bin width and first edge to human-friendly steps _(field)_
- `right_closed` — Right-closed intervals (a, b] instead of [a, b) _(field)_
- `precision` — Decimal places _(field)_
- `output` — Output _(field)_
- `cumulative` — Add cumulative count and cumulative percent columns _(field)_
- `density` — Add a density column, count / (n × bin width) _(field)_
- `chart` — Draw an ASCII bar per bin (report output) _(field)_
## Output
- Result (text)
## Query parameters
Open the tool pre-filled and auto-run via URL:
- `numbers` — Numbers
- `rule` — Bin-count rule to apply
- `bins` — Bin count (used when the rule is Manual)
- `range_min` — Range start (blank = smallest value)
- `range_max` — Range end (blank = largest value)
- `nice_edges` — Round bin width and first edge to human-friendly steps
- `right_closed` — Right-closed intervals (a, b] instead of [a, b)
- `precision` — Decimal places
- `output` — Output
- `cumulative` — Add cumulative count and cumulative percent columns
- `density` — Add a density column, count / (n × bin width)
- `chart` — Draw an ASCII bar per bin (report output)
Example: `https://gizza.ai/tools/histogram-bin-calculator/?numbers=1%0A2%0A2%0A3%0A4%0A7%0A8%0A9%0A12%0A15%0A22%0A40&rule=auto&bins=10&range_min=0&range_max=40&nice_edges=true&right_closed=true&precision=4&output=report&cumulative=true&density=true&chart=true`
---
## About this tool
A histogram turns numeric data into ranges and counts, but the result changes a lot depending on the bin width. This calculator compares several common rules side by side — Sturges, Scott, Freedman-Diaconis, Rice, and square-root — then applies the rule you choose and prints the resulting bin edges, counts, percentages, and optional cumulative or density columns.
Use it when you have a pasted column from a spreadsheet, experiment, log, or small dataset and want a principled starting point before drawing a histogram. Sturges is simple and often smooth for small samples, Scott uses the sample standard deviation, and Freedman-Diaconis uses the IQR so it is less sensitive to outliers.
### Worked example
Paste this dataset:
```text
1,2,2,3,3,3,4,5,7,9,12
```
With the default `auto` rule, the output first shows the sample summary and every rule's recommended bin count and width. It then builds a histogram table for the selected rule, with interval labels, counts, percentages, and ASCII bars so you can see the distribution shape immediately.
### Input notes and limits
Numbers can be separated by newlines, commas, spaces, tabs, semicolons, or pipes. Use plain decimals or scientific notation such as `12`, `-3.5`, or `1.2e3`; strip currency symbols and thousands separators first. The tool accepts 2 to 100,000 finite values and caps manual/rule-generated bins at 1,000 rows.
## FAQ
Which bin rule should I use?
Start with `auto`, then compare the rule table. Sturges is often reasonable for small, roughly normal samples. Scott can work well for normal-ish data but is pulled by outliers. Freedman-Diaconis uses the IQR and is usually more robust for skewed data.
What does the auto rule do?
`auto` chooses the finer of Sturges and Freedman-Diaconis, similar to NumPy's default. It keeps Sturges from being too coarse while still falling back when the IQR rule is not informative.
Why do my bin edges look awkward?
Rule-derived widths are mathematical, so edges can land on values like `1.4286`. Turn on `nice_edges` to round the width up to a 1/2/2.5/5 × power-of-ten step and snap the first edge down when the range start is automatic.
What is density?
Density is `count / (n × bin_width)`, the bar height for a unit-area histogram. It is useful when comparing histograms with different bin widths or sample sizes.
How are edge values assigned?
By default bins are left-closed (`[a, b)`) and the final bin includes the maximum. Enable `right_closed` to use `(a, b]`, where values exactly on an edge fall into the lower bin.
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