Day–Night Average Sound Level (Ldn)

Ldn — DNL in the American literature — is the twenty-four-hour energy average of a place's noise with ten decibels added to every night-time hour. Fifteen day hours from 07:00, nine night hours from 22:00, the energies added and the logarithm taken once at the end. The arithmetic is the ordinary decibel-averaging of combining sound levels; the only thing added is the penalty, and the penalty is policy, not physics. No meter measures a night decibel as ten times a day one. It is the 1974 US EPA judgement about sleep, carried since into HUD, FAA and FTA practice.

One case is worth memorising because it makes the whole metric intuitive: a night exactly 10 dB quieter than the day is precisely neutral. Sixty decibels by day and fifty by night gives $L_{dn} = 60$ dB exactly, because the penalty cancels the quiet. Leave the night at 60 as well and the Ldn climbs to 66.4 — six and a half decibels added by nine hours, purely for being night hours. That is why moving work out of the night is so often cheaper than any barrier or enclosure: the same equipment running the same hours at noon drops the Ldn by very nearly 10 dB. The thresholds it is judged against are 65 dB Ldn, the long-standing American mark for "incompatible with residential use", and 55 dB, the level the EPA identified as protective outdoors. Two cautions come with the number. In most regulatory use it is an annual average, so one loud night vanishes into it and a complaint about one loud night is not answered by it. And an average conceals its events — an Ldn that meets a limit can still contain individual pass-bys loud enough to wake every sleeper on the street, which is why event metrics such as SEL and maximum level exist beside it.