Formula
Daily exposure normalised to 8 h (ISO 9612)
\[ L_{EX,8h} = 10 \log_{10}\!\left( \frac{1}{T_0}\sum_i T_{e,i}\, 10^{L_{Aeq,i}/10} \right) \]
What the symbols mean
- L_EX,8h — daily noise exposure level, normalised to 8 h (dB(A))
- L_Aeq,i — A-weighted equivalent continuous level of task i (dB(A))
- T_e,i — exposure duration of task i (min or h)
- T₀ — reference duration = 8 h
- D — noise dose (% ; 100 % = permissible exposure reached)
- q — exchange rate (3 dB ISO/EU or 5 dB OSHA)
- L_pC — C-weighted peak sound pressure level (dB(C))
Inputs
Add one row per task (or work phase). LEX,8h combines their energies and normalises the total to an 8-hour day.
| Task | LAeq dB(A) | Duration (min) | Remove task |
|---|
Result
LEX,8h on the regulatory scale
Breakdown by task
Understand the theory — from LAeq to the regulatory Lex,8hinteractive
Workplace noise does not damage hearing according to the instantaneous level alone, but according to the dose received over the day: a high level for a short time can equal a moderate level for hours. To compare very different situations, everything is reduced to a single indicator: the daily noise exposure level \(L_{EX,8h}\) — the continuous level that, sustained for 8 hours, would deliver the same sound energy as the real day. Drag the sliders below: raise the level by 3 dB and watch the allowed time halve.
From equivalent level to dose
The starting point is the equivalent continuous level \(L_{Aeq,T}\): the level of a steady noise that would contain, over duration \(T\), the same energy as the real fluctuating noise, A-weighted to follow the ear's sensitivity. For a day made of several tasks \(i\), each with level \(L_{Aeq,i}\) and duration \(T_{e,i}\), the energies are summed then normalised to the reference duration \(T_0 = 8\) h:
This is an energetic summation, never an arithmetic mean of the decibels. A short but intense task weighs heavily; a long but quiet one weighs little. The term \(10\log_{10}(T_e/T_0)\) "rewards" exposures shorter than 8 h and "penalises" longer ones.
Partial exposure and the dominant task
Each task can be assigned its partial exposure \(L_{EX,8h,i} = L_{Aeq,i} + 10\log_{10}(T_{e,i}/T_0)\). The overall Lex,8h is the energetic combination of these partial exposures. This is very useful for prevention: it reveals the dominant task, the one to act on first. Often a single noisy phase of a few tens of minutes dominates the whole day.
Dose, exchange rate and TWA
Another way to express exposure is the dose \(D\), as a percentage of the daily permissible dose. It depends on an exchange rate \(q\) (in dB) and a criterion level \(L_c\) (the level that equals 100 % over 8 h):
With \(q = 3\) dB (ISO/EU) the dose is strictly energetic and the time-weighted average (TWA) coincides with \(L_{EX,8h}\). With \(q = 5\) dB (OSHA), it takes +5 dB to double the dose: the same noise gives a smaller dose, hence less protective results. The dose-to-level conversion is \(\text{TWA} = L_c + q\,\log_2 D\).
Not every country "counts" time the same way. Europe and the ISO use a 3 dB exchange rate (the equal-energy principle). In the US, OSHA has historically used 5 dB, more permissive: it takes +5 dB to halve the allowed duration. Set the level and compare the allowed time under each rule.
The peak level LpC
Beyond the average dose, impacts (shocks, gunfire, hammering) can injure the ear instantly. Regulation therefore sets a separate limit on the peak sound pressure level \(L_{pC,peak}\), measured with C-weighting. The action values are 135 and 137 dB(C), the limit value 140 dB(C). A noise can comply on Lex,8h yet exceed the peak: both criteria must be checked.
The thresholds of directive 2003/10/EC
The European "noise" directive sets three reference points on \(L_{EX,8h}\) (and their weekly equivalent \(L_{EX,8h,w}\)):
- 80 dB(A) — lower action value — The employer makes hearing protectors available and informs/trains the workers.
- 85 dB(A) — upper action value — Wearing protectors becomes mandatory; a noise-reduction programme, audiometric surveillance and area signage are required.
- 87 dB(A) — exposure limit value — Never to be exceeded at the ear, including the protectors’ attenuation. Action values, by contrast, are assessed without protectors.
For the peak \(L_{pC,peak}\): 135 / 137 / 140 dB(C) respectively.
Weekly exposure
When exposure varies strongly from day to day, one can reason on the week: \(L_{EX,8h,w} = 10\log_{10}\!\left(\frac{1}{5}\sum_{k=1}^{m} 10^{0.1\,L_{EX,8h,k}}\right)\), the energetic average of the daily exposures over the working days. The directive allows it under conditions (notably not exceeding 87 dB(A) on a weekly basis and reinforcing surveillance).
Measuring well (ISO 9612)
ISO 9612 describes three strategies: task-based (what this tool does — the day is split and each phase measured), job-based, or full-day (dosimetry). A few pitfalls: use a calibrated sound level meter / dosimeter (class 1 or 2), place the microphone near the most exposed ear, integrate long enough to capture variability, and estimate the uncertainty (often ±2 to 4 dB), as it can tip the result either side of a threshold.
Worked examples
| Situation | Result | Reading |
|---|---|---|
| 85 dB(A) for 8 h | Lex,8h = 85 dB(A) | right at the upper action value |
| 88 dB(A) 4 h + 80 dB(A) 3 h | Lex,8h ≈ 85.5 dB(A) | the 88 dB task dominates |
| 91 dB(A) for 2 h | Lex,8h = 85 dB(A) | +6 dB offset by ÷4 duration |
| 100 dB(A) for 15 min | Lex,8h ≈ 85 dB(A) | short but already at the threshold |
- Taking the arithmetic mean of the tasks’ dB instead of an energetic sum.
- Forgetting to normalise to 8 h: a LAeq measured over 1 h is not the Lex,8h.
- Mixing exchange rates: an OSHA result (5 dB) is not comparable to a European Lex,8h (3 dB).
- Comparing an action value (without protectors) to a limit value (at the ear, with protectors).
- Looking only at the average and neglecting the peak level of impact noises.
Related tools
Sources : Directive 2003/10/EC (physical agents — noise); ISO 9612 (determination of occupational noise exposure); ISO 1999 (estimation of noise-induced hearing loss); NIOSH Publication 98-126; OSHA 29 CFR 1910.95.