Benford First Digit Calculator
Compare observed leading digits of nonzero numeric amounts with Benford expected proportions.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Take absolute values, extract the first significant base-ten digit and compare nine digit counts with the Benford model.
Expected digit probability=log10(1+1/d); χ²=Σ(observed−expected)²/expected
Worked example
Amounts 1 through 9 produce one observation per digit, while Benford expects about 30.103% ones and 4.57575% nines. The tiny example has low expected cell counts.
Assumptions and input details
Zeros are rejected; signs are ignored. Benford is appropriate only for suitable naturally varying data, not assigned IDs, fixed ranges or every dataset. Asymptotic chi-square df=8 is unreliable with low expected counts and does not prove fraud or correctness.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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