Check credit figures against Benford's law in a minute
Drop in a column of amounts or paste them. The calculator compares their leading digits with Benford's law and shows which stand out before you set a rule in your decision flow.
Your amounts
Your amounts are read in this browser and never uploaded, and only the digit counts go into the link and any email you request.
The demo has 2,000 generated amounts, with 300 invented between 4,000 and 9,999.
Mean absolute deviation
Across 2,000 values, the fit is nonconformity, and the leading digits 9, 8, 5, 6 occur more often than Benford's law expects.
Actual share by digit
Bars show the actual share of each leading digit, in red where it stands out, and the orange line shows what Benford's law expects.
Digit results
| Digit | Count | Actual share | Expected share | Difference | z | Stands out |
|---|---|---|---|---|---|---|
| 1 | 513 | 25.7% | 30.1% | −4.45 pp | 4.32 | Fewer than expected |
| 2 | 284 | 14.2% | 17.6% | −3.41 pp | 3.97 | Fewer than expected |
| 3 | 201 | 10.1% | 12.5% | −2.44 pp | 3.27 | Fewer than expected |
| 4 | 208 | 10.4% | 9.7% | +0.71 pp | 1.03 | |
| 5 | 190 | 9.5% | 7.9% | +1.58 pp | 2.58 | More than expected |
| 6 | 161 | 8.1% | 6.7% | +1.36 pp | 2.38 | More than expected |
| 7 | 136 | 6.8% | 5.8% | +1.00 pp | 1.87 | |
| 8 | 156 | 7.8% | 5.1% | +2.68 pp | 5.40 | More than expected |
| 9 | 151 | 7.5% | 4.6% | +2.97 pp | 6.31 | More than expected |
| Total | 2,000 | 100.0% | 100.0% |
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The next step is to test a rule in the decision flow on past applications, then use it to refer applications whose declared figures look invented. Start free
Show formulas
Expected share (d) = log10(1 + 1 ÷ d) z = (|Actual share − Expected share| − 1 ÷ 2n) ÷ √(Expected share × (1 − Expected share) ÷ n) (Stands out: z > 1.96) MAD = Σ |Actual share − Expected share| ÷ Number of digits First digit: 0.006 / 0.012 / 0.015 First two digits: 0.0012 / 0.0018 / 0.0022
A mismatch is a reason to look and does not prove fraud. Capped, assigned or narrow-range figures do not follow Benford's law, and the bands are a rule of thumb.
What Benford's law shows
Benford's law describes the expected share of each leading digit in a set of amounts. This calculator compares the observed shares with those expected shares and reports the mean absolute deviation.
A difference can help you spot figures for review, but it does not establish fraud. Check whether the figures suit the law, since capped, assigned or narrow-range data may not follow it.
Common questions
What is Benford's law?
Benford's law describes the expected distribution of leading digits in a set of figures. This calculator compares the share of each digit with the share the law expects.
How do I test data against Benford's law?
Enter a column of amounts from a CSV file or paste amounts one per line. Choose the first-digit or first-two-digits test to compare actual shares with expected shares.
How is Benford's law used to find fraud?
Benford's law can help screen figures for values that merit a closer look. A mismatch is a reason to look. It does not prove fraud.
Which data does not follow Benford's law?
Capped, assigned or narrow-range figures may not follow Benford's law. A mismatch in that data may mean nothing.
What does the first-two-digits test show?
It compares the shares of the first two significant digits with the shares Benford's law expects. It can catch amounts bunched just under a limit, and values below 10 are left out.