Meanings
- A law concerning the frequency distribution of digits in much real-world data, where the number 1 occurs as the leading digit about 30% of the time, and the expected distribution for digits beyond the first approaches a uniform distribution.
1 more example
The following argument can give an intuitive feeling for Benford's law.¹¹ Consider a set of numbers x, which are randomly chosen in the interval between 1 and 10. All x between 1 and 1.999 have 1 as the first digit, all x between 2 and 2.999 have 2 as the first digit, and so on. The ratio of the largest and the smallest x is (almost) 2 in the first interval. In the next interval it is 3/2, followed by 4/3, and so on, up to 10/9. The widths of the intervals decrease as in a logarithmic scale. There is more “room” for a number between 1 and 2 than there is between 8 and 9. [In other words, the numbers between 1 and 2 are more dissimilar to one another, quantitatively (regarding how big a factor it takes to get from one to another), than the numbers between other consecutive-integer pairs.]
2010, Göran Grimvall, “Chapter 1: Numbers”, in Quantify! A Crash Course in Smart Thinking, Johns Hopkins University Press, →ISBN
Origin
Named after physicist Frank Benford, who stated it in 1938.
Full word history & related roots →Cite this entry
Benford's law. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Benford's%20law
“Benford's law.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Benford's%20law. Accessed November 5, 2026.
WatkinsX Dictionary, s.v. “Benford's law,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Benford's%20law.
Source: Benford's law on Wiktionary, CC BY-SA 4.0.