Decibel Calculator — Ratios to dB & Combine Levels

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)).

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.