Day–Evening–Night Sound Level (Lden)

Also known as Lden · day evening night level · END noise indicator · European noise directive · 2002/49/EC · noise mapping indicator · Lden calculation · evening penalty 5 dB

Lden=10log10 ⁣(1210Ld/10+410(Le+5)/10+810(Ln+10)/1024)L_{den} = 10\log_{10}\!\left(\frac{12 \cdot 10^{L_d/10} + 4 \cdot 10^{(L_e + 5)/10} + 8 \cdot 10^{(L_n + 10)/10}}{24}\right)

Worked example: 60/55/50 dB day-evening-night → 60.0 dB Lden (all three neutral)press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!

Learning zone

Lden is the European Union's indicator under Directive 2002/49/EC, and it does the same job as Ldn with a third period inserted: twelve day hours from 07:00, four evening hours from 19:00 carrying a 5 dB penalty, and eight night hours from 23:00 carrying 10 dB. The neutral case is correspondingly a staircase — 60 dB by day, 55 in the evening and 50 at night gives Lden=60L_{den} = 60 dB exactly, each period's penalty cancelling its own quiet. Every noise map and action plan published in the EU is drawn in this indicator.

The trap is treating Lden and Ldn as the same number. They are built from different periods with different penalties, and for one identical site they generally differ by a decibel or two — small enough to look like rounding, large enough to decide a compliance case. The directive also permits member states to shift the period boundaries by an hour, so an Lden from one country is not automatically an Lden from another; check which clock the limit was written on before comparing anything. Note too that the directive requires Lnight to be reported separately and assessed in its own right, and that it cannot be derived from this figure: a quiet day can pay for a loud night inside Lden, and the night indicator does not allow that trade. The WHO environmental noise guidelines set recommendations against both for exactly that reason. And like Ldn, Lden is a long-term average over a representative year — a survey afternoon is an input to it and never a substitute, which is why most noise maps are modelled rather than measured.

Day–Evening–Night Sound Level (Lden)
Lden=10log10 ⁣(1210Ld/10+410(Le+5)/10+810(Ln+10)/1024)L_{den} = 10\log_{10}\!\left(\frac{12 \cdot 10^{L_d/10} + 4 \cdot 10^{(L_e + 5)/10} + 8 \cdot 10^{(L_n + 10)/10}}{24}\right)
Where
  • LdenL_{den}= Day–evening–night level (dB)
  • LdL_d= Daytime average level (dB)
  • LeL_e= Evening average level (dB)
  • LnL_n= Night-time average level (dB)
Missing one of these? Work it out first, then come back