# Why does the formula to compute the Noise Reduction Rating (NRR) subtract 3dB?

Context: NRR (Noise Reduction Rating) is the noise reduction standard used in the United States, and SNR (Single Number Rating) is the European Union's standard for showing the attenuation of hearing protection.

NRR is [...] subtracting 3dB [unlike SNR]

Looking at the NRR and SNR formulas from Tom_C's reference document "Affaiblissement Acoustique In Situ Des Protecteurs Individuels Contre Le Bruit Étude Bibliographique (2018)" cited in their answer, the NRR does indeed subtract 3dB (unlike SNR):

I found this `- 3 dB` the end of the NRR formula to be quite intriguing, as this matches the typical gap between the SNR and the NRR, so it's likely to be responsible for a great part of it, if not most of it.

Why does the formula to compute the Noise Reduction Rating (NRR) subtract 3dB?

• Note that the remaining of the formula is also different, especially the base factor at the beginning. With the exponential function in this formula it is hard to know who is responsible for the gap. The protected portion of the population is not the same and linked to APV. As it is inside the exp, you also expect a huge difference there.
– Tom
Jul 4, 2020 at 8:21

TL;DR: Subtracting 3 dB is done to avoid the underprotection that could result from variations in compute the rest of the NRR formula. But some manufacturers incorrectly (intentionally?) do not subtract 3 dB.

The US Code of Federal Regulations - 40CFR PART 211-Product Noise Labeling (mirror) gives the following rationale:

(v) Spectral uncertainty. Possible variation in exposure to the noise spectra in the workplace. (To avoid the underprotection that would result from these variations relative to the assumed ‘‘Pink Noise’’ used to determine the NRR, an extra three decibel reduction is included when computing the NRR.)

This is echoed by the The Noise Manual edited by Elliott H. Berger page 429:

The NRR is calculated in a manner analogous to the OB approach, except that a pink noise spectrum (cqual energy in cach OB) is used instead of the actual noise spectrum (line | in Table 10.3), the estimated protected A-weighted levels are subtracted from the C-weighted pink noise and not the A-weighted environmental noise, and an additional spectral safety factor of 3 dB is subtracted. The spectral factor accounts for errors arising from use of pink noise instead of the actual noise spectrum to which the wearer is exposed. As in the OB method, the computation incorporates a 2-SD adjustment for percentage of population protected (i.e., theoretically a 98% protection factor, sometimes explicitly denoted as NRR4,). The NRR computed for the example in Table 10.3 is 20.7 dB. For the full computational details of the NRR see EPA (1979) or Berger (1988).

Note that according to https://cleararmor.biz/pages/faq (mirror), some manufacturers "forget" to subtract 3dB:

"We have noticed some companies do not properly follow the ANSI standard and actually list a false NRR value. This happens when companies do not fully understand the standard and fail to deduct 3dB from their test results, which the ANSI standard specifies in section 40CFR PART 211-Product Noise Labeling.