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，远高于预期的 11.1%（即九个数字中的一个）。例如，通过检查对数表并注意到首页比后面的页更破旧和污损（Newcomb 1881），可以观察到本福特定律。虽然本福特定律无疑适用于现实世界中的许多情况，但最近才通过 Hill (1998) 的工作给出了令人满意的解释。
，那么它在尺度变换下必须是不变的，因此
，则 
，归一化意味着 
。对 
求导并设置 
得到
。虽然这不是一个合适的概率分布（因为它发散），但物理定律和人类惯例都施加了截止值。例如，随机选择的街道地址遵循接近本福特定律的规律。
的概率由对数分布给出
, ..., 9，如上所示并在下表中列出。
, 
, 
." 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