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，遠高於預期的 11.1%（即九個數字中的一個）。例如，透過檢查對數表並注意到首頁比後面的頁更破舊和汙損（Newcomb 1881），可以觀察到本福特定律。雖然本福特定律無疑適用於現實世界中的許多情況，但最近才透過 Hill (1998) 的工作給出了令人滿意的解釋。
，那麼它在尺度變換下必須是不變的，因此
，則 
，歸一化意味著 
。對 
求導並設定 
得到
。雖然這不是一個合適的機率分佈（因為它發散），但物理定律和人類慣例都施加了截止值。例如，隨機選擇的街道地址遵循接近本福特定律的規律。
的機率由對數分佈給出
, ..., 9，如上所示並在下表中列出。
, 
, 
." Amer. Math. Monthly 73, 1056-1061, 1966.Franel, J. Naturforschende Gesellschaft, Vierteljahrsschrift (Zürich) 62, 286-295, 1917.Havil, J. "Benford's Law." §14.2 in