What does the chi-square statistic tell me about my data?

The chi-square statistic measures the gap between your observed leading-digit frequencies and Benford's predicted values; a higher value suggests greater deviation from the expected distribution, while a low value indicates good conformity.

Can I use this tool with very small datasets?

The tool works best with datasets containing at least 20 to 30 numbers; smaller samples may produce erratic leading-digit frequencies that are not statistically meaningful.

Do I need to format my data in a specific way before entering it?

Enter one number per line or separate them with commas or spaces; the calculator extracts the first digit of each value, so avoid including non-numeric characters or currency symbols in the list.

What if my data naturally follows a different distribution?

Benford's Law applies to datasets that span multiple orders of magnitude and are not artificially constrained; if your values are uniformly distributed or have a fixed range, the observed frequencies may deviate significantly from the expected Benford pattern.

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Benford's Law Calculator

Provided byTesting Benford's Lawtestingbenfordslaw.com

This tool visualizes leading-digit frequencies against Benford’s predicted distribution. You can inspect how closely ...

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About this tool

What Benford's Law Calculator does

The Benford's Law Calculator on Testing Benford's Law lets users upload or paste a numeric dataset to compare the frequency of leading digits against the expected Benford distribution. The tool produces a side-by-side table of observed and predicted counts, a bar chart visualization, and summary metrics such as the chi-square statistic and p-value to help assess conformity. Users can also select from several built-in sample datasets to see the interface in action before entering their own numbers. The site’s version stands out for its clean, minimal interface that places the data table and chart front-and-center without overwhelming options. Compared with other Benford calculators, it offers built-in sample datasets and clear, plain-English explanations of the summary metrics, making it accessible for users who want quick statistical interpretation guidance without needing to consult external references.

Step by step

How to use the Testing Benford's Law Benford's Law Calculator

1
Paste or type your list of numeric values into the input field
2
Click the Calculate button to generate the leading-digit frequency table
3
Review the bar chart and summary metrics showing observed vs. predicted counts
4
Optionally select a sample dataset from the dropdown to test the tool’s built-in examples
5
Interpret the chi-square statistic and p-value provided to assess conformity with Benford's Law

Is it right for you

Best for

Researchers, students, or data analysts who want a quick, free way to test whether their numeric data follows Benford's Law and need clear interpretation of the chi-square results.

Limitations

No unit conversion or data preprocessing options
Results are estimates based on first-digit analysis only
Large datasets may require manual formatting before pasting

Questions

Benford's Law Calculator FAQ

What does the chi-square statistic tell me about my data?: The chi-square statistic measures the gap between your observed leading-digit frequencies and Benford's predicted values; a higher value suggests greater deviation from the expected distribution, while a low value indicates good conformity.
Can I use this tool with very small datasets?: The tool works best with datasets containing at least 20 to 30 numbers; smaller samples may produce erratic leading-digit frequencies that are not statistically meaningful.
Do I need to format my data in a specific way before entering it?: Enter one number per line or separate them with commas or spaces; the calculator extracts the first digit of each value, so avoid including non-numeric characters or currency symbols in the list.
What if my data naturally follows a different distribution?: Benford's Law applies to datasets that span multiple orders of magnitude and are not artificially constrained; if your values are uniformly distributed or have a fixed range, the observed frequencies may deviate significantly from the expected Benford pattern.

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