Definition of Benford's Law in English:

Benford's Law

Pronunciation /ˈbenfərdz ˌlô/ /ˈbɛnfərdz ˌlɔ/


  • The principle that in any large, randomly produced set of natural numbers, such as tables of logarithms or corporate sales statistics, around 30 percent will begin with the digit 1, 18 percent with 2, and so on, with the smallest percentage beginning with 9. The law is applied in analyzing the validity of statistics and financial records.

    ‘Do their initial digits conform to Benford's Law?’
    • ‘Statistical sleuths are using a software package based on Benford's Law - which predicts how many times a given digit appears at the beginning or end of numbers within a data set - to ferret out accounting inconsistencies.’
    • ‘This relationship shown in the graph is known as Benford's Law, and is becoming more and more useful as we understand it better.’
    • ‘It describes how to use Excel and Benford's Law to detect irregularities in large data sets, which can monitor business financial statements for suspected fraud.’
    • ‘It is very difficult for people to make up credible numbers, as invented numbers are unlikely to follow Benford's law.’


Named for US physicist Frank Benford, whose 1938 paper demonstrated the statistical validity of the phenomenon.