Statistics

Benford's Law Calculator

Find the expected leading-digit frequency under Benford's law.

Calculated Output

Expected frequency (%) 30.103

Formula: P(d) = log₁₀(1 + 1/d)

Step-by-Step Breakdown

1. Values used:

2. Leading digit (1-9) = 1

4. Expected frequency = 30.103%

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The math behind it

P(first digit = d) = log₁₀(1 + 1/d). Digit 1 appears ~30% of the time; 9 only ~4.6%.

Digit 1 → 30.1%.

Where is it used?

Detecting fraud in accounting, elections and scientific data.