Calculation
Lges = 10·log10(10^(L1/10) + 10^(L2/10))
Sound levels in decibels must not be added arithmetically; the underlying sound intensities add, while the levels themselves add only logarithmically.
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Addition of two sound levels
Sound levels in decibels must not be added arithmetically; the underlying sound intensities add, while the levels themselves add only logarithmically.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Total sound level Lges in dB — Resulting sound level of both sources acting simultaneously.
- Sound level source 1 L1 in dB — Sound pressure level of the first source alone, measured at the same location.
- Sound level source 2 L2 in dB — Sound pressure level of the second source alone, measured at the same location.
Example
70 dB and 73 dB together give Lges≈74.76 dB, not 143 dB.
Assumptions and limits
Incoherent (not phase-locked) sound sources at the same measurement location; interference, directivity and frequency weighting (e.g. dB(A)) are excluded.
Understand Addition of two sound levels
This calculator determines the resulting sound level of two simultaneously acting, incoherent sound sources, making the logarithmic nature of the decibel scale tangible.
What does this quantity describe?
Sound intensities add physically, but sound levels in decibels do not add arithmetically. Converting back to intensity ratios and re-applying the logarithm gives Ltotal=10·log10(10^(L1/10)+10^(L2/10)).
Formula and variables
Lges = 10·log10(10^(L1/10) + 10^(L2/10))
Ltotal = 10·log10(10^(L1/10) + 10^(L2/10))
| Symbol / input | Meaning |
|---|---|
| Total sound level Lges in dB | Resulting sound level of both sources acting simultaneously. |
| Sound level source 1 L1 in dB | Sound pressure level of the first source alone, measured at the same location. |
| Sound level source 2 L2 in dB | Sound pressure level of the second source alone, measured at the same location. |
Choose the inputs correctly
L1 and L2 are the individual sound levels of the two sources, measured or calculated at the same location.
How to use the calculator
Enter both levels from the same measurement location and with the same frequency weighting (e.g. both unweighted or both dB(A)).
Worked example
70 dB and 73 dB together give Ltotal≈74.76 dB, not 143 dB.
Understand the result and units
Two equally loud sources raise the level by about 3 dB; a second source 10 dB quieter barely changes the total level.
L1, L2 and Ltotal are sound levels in decibels.
Typical applications
Estimating total noise exposure from multiple machines or noise sources in a workplace, and teaching the logarithmic decibel scale.
Assumptions, limits and common mistakes
Incoherent sound sources with no fixed phase relationship at the same measurement location; interference effects of coherent sources, directivity and differing frequency weighting are excluded.
Common mistake: Do not add sound levels arithmetically (70 dB + 73 dB is not 143 dB); only the underlying intensities may be added directly.
Frequently asked questions
What is “Addition of two sound levels” used for?
Estimating total noise exposure from multiple machines or noise sources in a workplace, and teaching the logarithmic decibel scale.
Where do the input values come from?
L1 and L2 are the individual sound levels of the two sources, measured or calculated at the same location.
What does the result not cover?
Incoherent sound sources with no fixed phase relationship at the same measurement location; interference effects of coherent sources, directivity and differing frequency weighting are excluded.