🔢 Benford’s Law Calculator
Enter a leading digit and your dataset size to see what Benford’s Law predicts the natural frequency of that digit should be.
What Benford’s Law says
Benford’s Law describes how the leading (first) digit is distributed in many naturally occurring sets of numbers, such as financial statements, population figures, or physical constants. Rather than each digit 1-9 appearing equally often (about 11% each), the digit 1 appears as the leading digit around 30% of the time, and the frequency decreases as the digit gets larger.
The formula
The expected probability that a number’s leading digit equals d is given by P(d) = log10(1 + 1/d). Multiplying this probability by your dataset size gives the expected count of records that should start with that digit if the data follows Benford’s Law.
- Auditors and analysts use large deviations from Benford’s Law as a screening signal for further review, not as proof of anything on its own.
- Benford’s Law applies best to data spanning several orders of magnitude and is not a universal rule for every dataset.
This calculator is for general educational and data-analysis planning purposes only.