Adding decibels
Used on the ASP, CSP and CHST. The worked example below is computed by code and checked against the source.
Ltotal = 10 × log10(10^(L1/10) + 10^(L2/10) + … + 10^(Ln/10))
L = sound pressure level of each source (dB). Decibels are logarithmic, so they can't be added arithmetically.
Worked example
OSHA example: two sources side by side, each 90 dB.
10 × log10(10^9 + 10^9) = 93 dB
The source prints this result, and our code reproduces it.
OSHA's quick table: if two levels differ by 0-1 dB add 3 dB to the higher; 2-4 dB add 2; 5-9 dB add 1; 10 dB or more add 0.
Run your own numbers: decibel addition calculator.
Where it appears on the exam
ASP: ASP11 Domain 1, Mathematical Calculations
Blueprint: ASP11 Domain 1, task 5: noise hazards
CSP: CSP11 Domain 6, Occupational Health and Applied Science
Blueprint: CSP11 Domain 6, task 1: occupational exposures (noise)
Practice: Occupational Noise
CHST: CHST5 Domain 1, Hazard and Risk Identification and Control
Blueprint: CHST5 Domain 1, knowledge 18: noise exposure
Source
The formula comes from
OSHA Technical Manual, Section III, Chapter 5 (Noise), Appendix B.3(opens osha.gov in a new tab)“Decibels are measured using a logarithmic scale, which means decibels cannot be added arithmetically. For example, if two noise sources are each producing 90 dB right next to each other, the combined noise sound pressure level will be 93 dB, as opposed to 180 dB. The following equation should be used to calculate the sum of sound pressure levels, sound intensity levels, or sound power levels: Total L = 10 x log10(Σ1n 10Ln/10)”
Questions
- What is the formula for adding decibels?
- Ltotal = 10 × log10(10^(L1/10) + 10^(L2/10) + … + 10^(Ln/10)). L = sound pressure level of each source (dB). Decibels are logarithmic, so they can't be added arithmetically.
- Will this formula be given on the BCSP exam?
- BCSP says the formula is included in the question whenever one is needed, unless the question is testing whether you know the formula. You can't bring a formula sheet into the exam, so learn what each formula does and when to use it.
BCSP on formulas at the exam
BCSP, What to Expect When Sitting for a BCSP Exam (item 7)(opens bcsp.org in a new tab)“For any question requiring a mathematical formula, the formula will be included within the exam question (unless the question is specifically testing your knowledge of a formula). You will not be provided or permitted to bring a formula sheet.”
Related
- Noise dose
- Noise TWA from dose
- Reference duration for a sound level
- Sound level at a distance
- Hearing protector NRR (estimated exposure)
- ASP formula sheet
- CSP formula sheet
- CHST formula sheet
Checked 2026-10-16. Spot a problem? Email hello@passcited.com.