Calculating the daily noise exposure level

What the value tells you

Under section 2 of the German Noise and Vibration Ordinance, the daily noise exposure level is the time-averaged noise exposure level referred to an eight-hour shift. It covers all sound events at the workplace. When it is compared with the action values, the effect of hearing protection is not counted (section 6). EU Directive 2003/10/EC uses the same quantity, LEX,8h, with the action values 80 and 85 dB(A) and the exposure limit value 87 dB(A).

The formula

TRLV Lärm part 2: LEX,8h = LpAeq,Te + 10 · lg (Te / T0) dB. LpAeq,Te is the A-weighted equivalent continuous sound pressure level of the representative working day, Te its effective duration and T0 the reference duration of 8 hours.

If the levels change during the day, the partial times are combined energetically: each level is converted back from decibels, weighted with its share of time, the contributions are added and the sum is converted back to decibels.

LEX,8h = 10 · lg [ Σ (Ti / T0) · 10^(Li / 10) ] dB, with Li the level in dB(A) and Ti the duration of the respective section.

Three worked examples

Example 1: two sections. Four hours at 85 dB(A) and four hours at 79 dB(A). Each section is half of the day: 0.5 · 10^8.5 + 0.5 · 10^7.9 ≈ 1.58 · 10^8 + 0.40 · 10^8 = 1.98 · 10^8. 10 · lg of this gives 83.0 dB(A). The result is above the arithmetic mean of 82 dB(A) because the loud portions count more.

Example 2: short and loud. One hour at 100 dB(A) and seven hours at 70 dB(A): (1/8) · 10^10 + (7/8) · 10^7 ≈ 1.25 · 10^9 + 0.009 · 10^9 = 1.26 · 10^9. 10 · lg gives 91.0 dB(A). The one loud hour almost alone determines the daily value and puts it well above the upper action value.

Example 3: one activity only. If a constant level of 88 dB(A) acts for Te = 4 hours, LEX,8h = 88 + 10 · lg (4/8) = 88 − 3.0 = 85.0 dB(A). Halving the exposure time lowers the daily value by 3 dB.

How exposure time shifts the daily value

Common mistakes

• Averaging levels arithmetically. Decibels are logarithmic; it is the sound energy that is averaged.
• Deducting the hearing protection. It is not counted when comparing with the action values (health checks for noise).
• Treating breaks with residual noise as noise-free. Under TRLV Lärm part 2, a break only counts as noise-free if there is certainly no exposure.
• Overlooking rare loud days. A day with particularly high exposure, on which the upper action value is exceeded and which occurs less than once a week, counts as a separate representative working day.
• Forgetting peak levels. The peak sound pressure level LpC,peak, the maximum value of the instantaneous sound pressure level, has its own action values.

Weekly noise exposure level

If exposure varies so much from day to day that no typical daily value can be given, a weekly noise exposure level can be formed, referred to a 40-hour week. Under TRLV Lärm part 2, the authority may only approve this if the value does not exceed 85 dB(A), a suitable measurement proves this and measures are taken to minimise the hazard.

Let a tool do the sums

The DGUV’s IFA provides a noise exposure calculator for partial times (converting back from decibels, adding, converting to decibels; time shares in minutes, hours or per cent). How much attenuation is needed at the ear is shown by the hearing protection finder. How this fits into the measures is explained in the noise risk assessment.