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Benford's law analyzer for auditors.

Do these amounts look like numbers people did not make up?

Paste or upload a column of amounts and compare its leading digits with Benford's law: chart, chi-square, MAD and Nigrini's conformity ranges. Your data stays in your browser.

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Your amounts

The example below is already analyzed. Paste a column of amounts (one per line), or a CSV / tab-separated export from the general ledger, and pick the amount column. In a multi-column CSV, amounts with thousands separators must be quoted (most exports do this). Nothing is uploaded: the file is read in your browser.

Test

Analysis complete: 500 amounts, MAD 0.0100, Acceptable conformity.

MAD
0.0100
Acceptable conformity
Chi-square
6.5
8 df · 5% critical value 15.507
Amounts tested
500
0 skipped (under 10 or not numeric)
OK
Acceptable conformity
The leading digits follow Benford's law within Nigrini's first-digit MAD range. Still look at the individual spikes flagged below.
Actual vs Benford
Actual shareBenford expected
0%8%17%25%33%1: actual 28.20%, Benford 30.10%, count 141, Z 0.8812: actual 16.80%, Benford 17.61%, count 84, Z 0.4223: actual 14.00%, Benford 12.49%, count 70, Z 0.9534: actual 10.40%, Benford 9.69%, count 52, Z 0.4645: actual 10.20%, Benford 7.92%, count 51, Z 1.8156: actual 5.80%, Benford 6.69%, count 29, Z 0.7167: actual 5.80%, Benford 5.80%, count 29, Z 0.0078: actual 5.00%, Benford 5.12%, count 25, Z 0.0289: actual 3.80%, Benford 4.58%, count 19, Z 0.729
How this was worked out
Work shownrecomputed as you type
Expected P(d) = log10(1 + 1/d)
MAD = Σ|actual − expected| ÷ 9 = 0.01000 → Acceptable conformity
χ² = Σ (observed − expected count)² ÷ expected count = 6.51 ≤ 15.507 (5%, 8 df)
Nigrini MAD conformity ranges (first digit)
Work shownrecomputed as you type
Close ≤ 0.006 · Acceptable ≤ 0.012 · Marginally acceptable ≤ 0.015 · Nonconformity > 0.015
DigitCountActualBenfordZ
114128.2%30.1%0.88
28416.8%17.61%0.42
37014%12.49%0.95
45210.4%9.69%0.46
55110.2%7.92%1.81
6295.8%6.69%0.71
7295.8%5.8%0.00
8255%5.12%0.02
9193.8%4.58%0.72

* Z above 1.96: the digit's share differs from Benford at the 5% level (Nigrini's Z with continuity correction). Amounts under 10 are skipped (they have no second digit; the same cutoff is used for both tests here); negatives are tested on their absolute value. With large populations chi-square rejects almost everything, which is why MAD is the headline measure.

Benford's law as an audit analytic

A Benford test is a data analytic that helps target procedures. Under AU-C 315 analytics help identify risks of material misstatement, and AU-C 240 has auditors test the appropriateness of journal entries, where unusual digit patterns are a common selection criterion.

The test counts the leading digit (or first two digits) of each amount of 10 or more, compares the shares with Benford's expected log10(1 + 1/d), and measures the fit two ways. Chi-square compares counts; with 8 degrees of freedom (first digit) the 5% critical value is 15.507, and with 89 (first two digits) it is 112.02. MAD averages the absolute differences in proportions and is judged against Mark Nigrini's ranges (Benford's Law, 2012): first digit 0.006 / 0.012 / 0.015; first two digits 0.0012 / 0.0018 / 0.0022.

The first-two-digits test is the sharper tool for finding specific spikes, such as many invoices starting with 49 just under a $5,000 approval threshold. Use the digit table's Z-statistics to pick which amounts to pull.

Common questions

What is Benford's law?

Benford's law says that in many naturally occurring sets of numbers the leading digit is small more often than large: 1 leads about 30.1% of the time, 2 about 17.6%, falling to 9 at about 4.6%. The expected share of digit d is log10(1 + 1/d).

How do auditors use Benford's law?

As an analytical procedure to spot unusual patterns in large populations such as journal entries, vendor invoices, expense claims or sales transactions. Spikes at particular digits, for example just below an approval limit, point to items worth testing. A departure from Benford is a lead, not evidence of fraud.

Which data should follow Benford's law?

Amounts that arise from combining numbers (price × quantity), span several orders of magnitude, and are not capped, assigned or rounded by policy. Populations with fixed fees, minimums, maximums, assigned numbers (check numbers, ZIP codes) or a narrow range should not be expected to conform.

What is MAD and why is it preferred over chi-square?

MAD is the mean absolute deviation between actual and expected digit proportions. Chi-square grows with sample size, so on large populations it flags trivial differences. Nigrini's MAD ranges do not depend on sample size: for the first digit, up to 0.006 is close conformity, 0.012 acceptable, 0.015 marginally acceptable, and above that nonconformity.

Is my data uploaded anywhere?

No. The file is read and analyzed by JavaScript in your browser. Nothing is sent to CORAA or stored.

Runs in your browser. The figures you type are not sent to CORAA or stored. Check the result against your firm's methodology before relying on it.

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