Benford's Law Calculator

Your details

Enter any list of real-world numbers (financial figures, census counts, population data, invoice totals). The tool extracts only the first significant digit from each number and checks whether the distribution follows Benford's Law.
The threshold p-value below which the test declares the dataset does NOT conform to Benford's Law. Standard auditing practice uses 5%.
Chi-square statisticLikely natural
0.547

Goodness-of-fit statistic with 8 degrees of freedom (9 digit categories minus 1)

Sample size41
P-value0.9998
Mean absolute deviation0.0091
Benford conformanceConforms (p = 0.9998)
Digit 1 observed %29.3
Digit 2 observed %19.5
Digit 3 observed %12.2
Digit 4 observed %9.8
Digit 5 observed %9.8
Digit 6 observed %4.9
Digit 7 observed %4.9
Digit 8 observed %4.9
Digit 9 observed %4.9
Digit 129.3
Digit 219.5
Digit 312.2
Digit 49.8
Digit 59.8
Digit 64.9
Digit 74.9
Digit 84.9
Digit 94.9

Dataset likely conforms to Benford's Law (chi-square = 0.55, p = 0.9998).

  • Your sample has only 41 values. With fewer than 100 data points, the chi-square test has low statistical power and results should be interpreted cautiously.
  • The leading-digit distribution is statistically consistent with naturally occurring data.
  • Mean absolute deviation (MAD) of 0.91% per digit shows minor variation, which is normal for smaller samples.

Next stepConformance is a reassuring signal, not a guarantee of authenticity. For forensic use, combine this test with second-digit analysis and domain expertise.

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