Benford's Law Calculator
Test a data set against Benford's Law, the first-digit law used in accounting and election forensics. Paste your numbers to see the observed leading-digit frequencies against the expected curve, plus a chi-square goodness-of-fit test, the Nigrini MAD conformity score and a z-statistic for every digit.
How to run a Benford's Law test
- Paste your numbers, separated by commas, spaces or new lines.
- The tool extracts every value and counts its leading digit (1 to 9).
- Compare the observed bars to the expected Benford curve.
- Read the chi-square, MAD verdict and per-digit z-scores to judge conformity.
Frequently asked questions
What is Benford's Law?
Benford's Law, or the first-digit law, says that in many natural data sets the leading digit is 1 about 30 percent of the time and gets rarer up to 9 at about 4.6 percent. The expected share of digit d is log10(1 + 1/d).
How many numbers do I need?
Benford tests are unreliable on small samples. Aim for at least a few hundred values that span several orders of magnitude. With under 100 values the result is only a rough indication.
What do the chi-square and MAD results mean?
Chi-square measures total deviation from the expected curve; below the critical value of 15.507 (8 degrees of freedom, 0.05) the data is consistent with Benford. MAD is the average per-digit deviation, scored against Nigrini's conformity ranges.
Does failing the test prove fraud?
No. Many legitimate data sets do not follow Benford's Law, for example values with a fixed range, assigned numbers or strong rounding. Nonconformity is a flag for further review, not proof of manipulation.
Which numbers are excluded?
Zero and any non-finite values are skipped because they have no leading significant digit. Negative numbers are included using their absolute value.
Learn more
- What is Benford's Law?
A plain-language guide to Benford's Law, why leading digits follow a logarithmic curve and how auditors use it to spot anomalies.
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