Decibel calculator
Add noise levels and convert a ratio of quantities into decibels.
Fill in the fields and the result will appear here automatically.
Add levels of independent incoherent sources with a common reference, or convert a positive power/amplitude ratio to dB. Coherent waves require phase-aware amplitude addition first; this form has no phase input. The result is not subjective loudness.
How it works
Formula and logic
LΣ=Lmax+10 log₁₀(Σ10^((Li −Lmax)/10)); shifting to the maximum avoids overflow of individual powers. Ratios use 10 log₁₀(P 2/P 1), or 20 log₁₀(A 2/A 1) only with the same P∝A² proportionality, e.g. unchanged impedance.
Example
80;80 dB gives≈83.010 dB, a≈3.010 dB increase, not 160. Power ratio 2/1 gives≈3.010 dB; amplitude ratio 2/1 at unchanged impedance gives≈6.021 dB and four times the power.
Fields and units
- What to find — list option
- Levels — dB
- Initial value — same chosen unit
- Final value — same chosen unit
- Quantity type — list option
How to use
- — Separate levels by spaces, semicolons or commas; commas delimit the list, so use a decimal point.
- — For ratios select power or amplitude and enter two positive values in the same units.
- — Only visible fields are used in each mode; negative dB levels are allowed.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: logarithmic levels and amplitude squared
- Limitation
- Common reference and compatible levels, not arbitrary dB scales mixed together. Ratios must be positive. Lists have up to 10000 levels; all displayed ratios and the illustrative arithmetic sum must fit the numeric range.0 dB means ratio 1;20 µPa is an air-SPL reference, not every dB reference.
FAQ
Why do two 80 dB sources give 83 and not 160?
80;80 dB gives≈83.010 dB, a≈3.010 dB increase, not 160. Power ratio 2/1 gives≈3.010 dB; amplitude ratio 2/1 at unchanged impedance gives≈6.021 dB and four times the power. Add levels of independent incoherent sources with a common reference, or convert a positive power/amplitude ratio to dB. Coherent waves require phase-aware amplitude addition first; this form has no phase input. The result is not subjective loudness.
Does doubling always add 3 dB?
Yes, and that is a property of the logarithm: the increment does not depend on the starting level. From 40 dB or from 100 dB, doubling the power adds the same 3.01 dB.
When is the multiplier 10 and when 20?
LΣ=Lmax+10 log₁₀(Σ10^((Li −Lmax)/10)); shifting to the maximum avoids overflow of individual powers. Ratios use 10 log₁₀(P 2/P 1), or 20 log₁₀(A 2/A 1) only with the same P∝A² proportionality, e.g. unchanged impedance.
Can loudness be added this way?
Add levels of independent incoherent sources with a common reference, or convert a positive power/amplitude ratio to dB. Coherent waves require phase-aware amplitude addition first; this form has no phase input. The result is not subjective loudness.