Convert ratios to decibels and combine multiple sound levels.
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How do you calculate decibels?
For a power ratio, dB = 10·log₁₀(ratio); for an amplitude ratio, dB = 20·log₁₀(ratio). To combine levels, total = 10·log₁₀(Σ 10^(Lᵢ⁄10)). Because the scale is logarithmic, sound power adds: two equal 60 dB sources combine to about 63 dB, not 120 dB, and a 100× power ratio is 20 dB.
Understanding your result
The decibel is logarithmic, so ratios become additions. Because sound power adds, two equal sources are 3 dB louder, and ten equal sources are 10 dB louder — not double or ten times the number.
Formula and method
Power ratio: dB = 10·log₁₀(ratio). Amplitude ratio: dB = 20·log₁₀(ratio). Combine levels: total = 10·log₁₀(Σ 10^(Lᵢ⁄10)).
Assumptions and limitations
Combining levels assumes the sources are uncorrelated, so their powers add; correlated tones can interfere and add differently. It works with dB values sharing the same reference, and does not model distance, frequency weighting such as dBA, room acoustics or human loudness perception. Choose 10 log for power ratios and 20 log for amplitude ratios.
Worked example
Two 60 dB sources combine to about 63 dB, not 120 dB. A 100× power ratio is 20 dB.
How to use this tool
- Choose to combine levels or convert a ratio.
- Enter the dB values or the ratio.
- Read the result in decibels.
Common mistakes to avoid
- Adding decibel levels arithmetically instead of on a power basis.
- Using 10·log for amplitude ratios — they need 20·log.
About the Decibel Calculator
The Decibel Calculator converts a power or amplitude ratio into decibels, and combines several sound levels into a single total — added correctly on a power basis, not arithmetically.
Who should use this tool
Audio engineers, acousticians and electronics students.
Benefits
- Power and amplitude ratio conversions.
- Combine any number of dB levels.
- Shows the formula used.
- Instant and private.
Practical use cases
- Adding the noise from multiple machines.
- Converting a gain ratio to dB.
- Understanding amplifier or signal levels.
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Frequently asked questions
Why don’t two 60 dB sounds make 120 dB?
Because decibels are logarithmic. Two equal sources add about 3 dB, giving roughly 63 dB.
When do I use 10·log vs 20·log?
Use 10·log for power (or intensity) ratios and 20·log for amplitude ratios such as voltage or sound pressure.
Can I subtract one decibel level from a total to find a single source?
Yes, if you know the combined level and one component you can back out the other by subtracting on a power basis, converting each level to its power ratio, subtracting, then converting back. This tool focuses on combining levels, but the same logarithmic arithmetic applies in reverse.