Decibel Calculator
With output value 2, input (reference) value 1, decibel comes to 3.0103 dB — decibels. It is reached in 3 steps, the last of which is 10 * log10(2), and each one is printed on the page with its numbers filled in. The formula is the one published by BIPM, not an approximation fitted to it.
The decibel figure for a ratio of two powers or two amplitudes, and the ratio a decibel figure stands for, using 10·log₁₀ and 20·log₁₀.
Formula and sources checked · How we check
The two values are Powers (watts) — 10·log₁₀, Output value 2, Input (reference) value 1
3.0103 dB
Decibels for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- Ratio out ÷ in
2 / 12 ×- Decibels
10 * log10(2)3.01 dB- Equivalent power ratio
10 ^ (3.0103 / 10)2 ×
Worked example
Doubling the power is 3.0103 dB, not 3. The rounded figure is where the "3 dB point" of a filter comes from — the frequency at which half the power is left. Switch the same 2:1 ratio to amplitudes and it becomes 6.0206 dB, because power goes as the square of voltage.
How to work it out yourself
- 1.Decide first whether your two numbers are powers or amplitudes. Watts, and sound intensity, take 10·log₁₀; volts, amps and sound pressure take 20·log₁₀. Using the wrong one doubles or halves the answer.
- 2.A negative result is a loss, not an error. Half the power out is −3.0103 dB.
- 3.Decibels add along a chain. Three stages of +12, −4 and +6 dB give +14 dB overall, which is a power ratio of about 25.
The formula
- Ratio out ÷ in
2 / 1 - Decibels
10 * log10(2) - Equivalent power ratio
10 ^ (3.0103 / 10)
Source: BIPM — the SI Brochure, on logarithmic ratio quantities, NIST Special Publication 811 — guide for the use of the SI
Questions people actually ask
- Why do amplitudes use 20 rather than 10?
- Power is proportional to amplitude squared, and log(x²) is 2·log(x). Putting the 2 into the multiplier gives 20·log₁₀, which is what makes a doubled voltage and a quadrupled power both come out at 6.0206 dB — the same physical change described two ways.
- Is a decibel a unit?
- Not in the ordinary sense: it is a dimensionless ratio expressed on a logarithmic scale, and the SI Brochure treats it as such. That is why it needs a reference to become absolute — dBm against a milliwatt, dB SPL against 20 micropascals.
- What does 10 dB sound like?
- Ten times the sound intensity, and roughly twice as loud to a listener. Perceived loudness and measured intensity are not the same scale, which is why the decibel figures on a noise chart look compressed compared to how large the difference feels.
Related
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