Decibel Calculator
Convert a power or amplitude ratio to decibels and back, or add several sound levels together.
A decibel measures a ratio on a logarithmic scale. For power, dB = 10·log₁₀(P₁ ÷ P₂); for amplitude, voltage, or pressure, dB = 20·log₁₀(V₁ ÷ V₂). Doubling power is 10·log₁₀(2) = +3.01 dB, while doubling amplitude is 20·log₁₀(2) = +6.02 dB.
What a decibel is
A decibel (dB) is not an absolute unit like a metre or a volt — it expresses how much bigger one quantity is than a reference, compressed onto a logarithmic scale so that huge ranges fit into small numbers. Because our ears and many instruments respond to ratios rather than absolute differences, the log scale matches how loudness and signal strength are actually perceived.
The catch is the factor out front. When you compare power quantities (watts, acoustic intensity) you multiply the log by 10. When you compare amplitude quantities (voltage, sound pressure, signal level) you multiply by 20, because power is proportional to amplitude squared and log(x²) = 2·log(x). That single factor is why doubling power adds 3 dB but doubling amplitude adds 6 dB.
dB SPL is a special case: sound pressure level measured against the threshold of hearing (20 µPa). Everyday values run from a 30 dB whisper to a 110 dB concert. Because dB SPL is a power-like measure of intensity, incoherent sources add by summing their power ratios, not their decibel numbers.
Use 10 for power ratios (watts, intensity); use 20 for amplitude ratios (voltage, pressure). To combine incoherent sound levels: total = 10·log₁₀( Σ 10^(Lᵢ ÷ 10) ).
Worked example
An amplifier doubles the acoustic power of a speaker. How many decibels louder is that in power terms?
- 1 Pick power or amplitude. Power ratios use the factor 10; amplitude, voltage, and pressure ratios use 20. Here we are doubling power, so the factor is 10.
- 2 Write the ratio. Double the power means P₁ ÷ P₂ = 2.
- 3 Take the base-10 logarithm. log₁₀(2) = 0.30103.
- 4 Multiply by the factor. 10 × 0.30103 = 3.01 dB, so doubling power is about +3 dB.
- 5 Compare with amplitude. Doubling amplitude instead would be 20 × 0.30103 = 6.02 dB.
Common decibel changes
How familiar ratios translate into decibels, using 10·log for power and 20·log for amplitude.
| Change | Decibels | Why |
|---|---|---|
| Double the power | +3.01 dB | 10·log₁₀(2) |
| Double the amplitude / voltage | +6.02 dB | 20·log₁₀(2) |
| Ten times the power | +10 dB | 10·log₁₀(10) — roughly 2× as loud |
| Ten times the amplitude | +20 dB | 20·log₁₀(10) |
| Halve the power | −3.01 dB | 10·log₁₀(0.5) |
Typical sound levels (dB SPL)
Approximate everyday sound pressure levels for reference.
| Source | Level |
|---|---|
| Whisper | 30 dB |
| Normal conversation | 60 dB |
| Busy traffic | 80 dB |
| Rock concert | 110 dB |
Adding decibels correctly
You cannot simply add two decibel numbers — 60 dB plus 60 dB is not 120 dB. Because decibels are logarithmic, you convert each level back to a linear power ratio, add those, then convert to decibels again. Two equal incoherent sources of 60 dB give 10·log₁₀(10⁶ + 10⁶) = 63.01 dB — a rise of just about 3 dB, the same +3 dB you get from doubling any power. Ten equal sources add 10 dB, not ten times the level. This only holds for incoherent sources; correlated signals can add in amplitude and climb faster.