Benford’s Law Calculator
Find the theoretical frequency of a first significant digit under Benford’s law and its expected count in a sample.
Formula
P(d) = log₁₀(1 + 1/d); expected count = N × P(d).
Benford probability ≈ 100×log10(1+1÷(1)) · Expected count ≈ (1,000)×(30.10299957)÷100
How to use
- Choose the first nonzero digit, 1–9.
- Enter the number of observations.
- Read the model probability and expected count.
Examples
- For digit 1, P ≈ 30.103%; N = 1,000 gives ≈ 301.03.
Frequently asked questions
Does every dataset follow this law?
No. Assigned IDs, fixed ranges and other constraints may not fit Benford’s law.
Does a mismatch prove fraud?
No. The model alone cannot establish fraud or data quality.
Why is zero excluded?
The first significant digit of a nonzero value is never zero.
Sources
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