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Benford's Law Checker

In many real data sets, about thirty per cent of values begin with a 1 and only five per cent with a 9. That is Benford's law, and it holds for figures spanning several orders of magnitude. This counts the leading digits of your numbers, compares them against the law with a chi-square test, and is direct about the limit: a poor fit is not evidence of anything on its own, because plenty of honest data does not follow Benford at all.

What this generator does

Counts the first significant digit of every positive value, compares the shares against Benford's expected distribution, and computes a chi-square statistic against the threshold for eight degrees of freedom at the five per cent level.

How to use this tool

  1. Paste at least thirty positive numbers.
  2. Read the observed share of each leading digit against the expected one.
  3. Read the chi-square statistic against its threshold.
  4. Note the caveat before drawing any conclusion.

Understanding the controls

Your numbers
At least thirty positive values, separated by spaces, commas or newlines. Data spanning several orders of magnitude fits the law; data with a narrow range does not.

Common use cases

  • Checking whether a data set follows Benford's law
  • Teaching the first-digit law with real numbers
  • Comparing observed leading digits against the expected distribution
  • Screening figures as one input among many during a review
  • Demonstrating why the law works on some data and not other

How this generator works

Benford's law says the chance of a leading digit d is the base-ten logarithm of one plus one over d, which is why 1 appears about thirty per cent of the time and 9 about five. The chi-square statistic sums the squared difference between observed and expected counts, divided by the expected count, across all nine digits. Before display the expected shares are confirmed to sum to one, every share is recomputed from the counts, and the statistic is re-derived.

Randomness and fairness

Nothing here is random. A set of numbers has exactly one leading-digit distribution.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

  • A poor fit is not evidence of manipulation. Benford's law applies to data generated by multiplicative processes across several orders of magnitude — heights, ages, prices with a fixed range and anything capped will fail it honestly.
  • Small samples fail the chi-square test easily; below a few hundred values the result says very little.
  • Assigned numbers such as invoice references, postcodes and phone numbers have no reason to follow the law.
  • This is one screening indicator among many, and never a conclusion on its own.

Privacy and your data

Your numbers stay in your browser. Nothing is uploaded, no value is stored, and nothing you paste is ever included in analytics — only how many values were checked.

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