Calculator Input
Paste numeric values separated by commas, spaces, semicolons, or line breaks.
Example Data Table
This sample dataset can be copied into the calculator to test different rules.
| Observation | Value | Observation | Value | Observation | Value |
|---|---|---|---|---|---|
| 1 | 12 | 7 | 24 | 13 | 31 |
| 2 | 15 | 8 | 25 | 14 | 34 |
| 3 | 16 | 9 | 27 | 15 | 36 |
| 4 | 18 | 10 | 28 | 16 | 39 |
| 5 | 20 | 11 | 29 | 17 | 42 |
| 6 | 22 | 12 | 30 | 18 | 45 |
Formula Used
The calculator compares several well-known histogram binning rules and returns the selected width plus a working frequency table.
1) Sturges Rule
k = ceil(log2(n) + 1)
bin width = range / k
2) Rice Rule
k = ceil(2 × n^(1/3))
bin width = range / k
3) Square-root Rule
k = ceil(sqrt(n))
bin width = range / k
4) Scott Rule
bin width = 3.5 × standard deviation / n^(1/3)
5) Freedman-Diaconis Rule
bin width = 2 × IQR / n^(1/3)
6) Doane Rule
k = 1 + log2(n) + log2(1 + |g1| / sigma_g1)
bin width = range / k
7) Relative Frequency
relative frequency = bin count / included values
Here, n is sample size, IQR is interquartile range, and g1 is sample skewness.
How to Use This Calculator
- Paste your numeric dataset into the dataset box.
- Choose a binning rule or select auto mode.
- Set decimal places for displayed results.
- Optionally define a custom histogram start and end range.
- Enter a custom width or custom bin count only when needed.
- Click Calculate Bin Width to generate results.
- Review the recommended width, method table, and frequency table.
- Use the CSV or PDF buttons to export the output.
Frequently Asked Questions
1. What is histogram bin width?
Histogram bin width is the size of each interval used to group values on a histogram. Smaller widths show more detail, while larger widths smooth the distribution and reduce visual noise.
2. Which rule should I choose first?
Start with auto or Freedman-Diaconis for most real datasets. It handles skew and outliers better than simple count-based rules, while still giving practical widths for visualization and reporting.
3. Why do Scott and Freedman-Diaconis give different widths?
Scott uses standard deviation, so extreme values can affect it strongly. Freedman-Diaconis uses the interquartile range, making it more stable when the sample contains outliers or long tails.
4. Why do small samples often produce fewer bins?
Small samples contain less information about the underlying distribution. Fewer bins reduce random visual noise and make the chart easier to interpret without overreacting to tiny count changes.
5. Can I force my own bin width?
Yes. Custom width is useful when you need consistent reporting periods, fixed measurement classes, or standardized dashboards. It also helps when multiple histograms must share the same scale.
6. What happens if my custom range excludes some values?
The calculator counts excluded values separately and builds the histogram only from values inside the selected range. This is useful for focused analysis or trimmed presentation windows.
7. Is one universal bin width always best?
No. The best width depends on sample size, spread, skewness, and analysis goals. Exploratory charts, publication figures, and operational dashboards may all need different settings.
8. Can this calculator be used for times, percentages, or scores?
Yes. Any quantitative numeric data can be analyzed, including times, rates, percentages, costs, test scores, and measurements, as long as the values are entered in numeric form.