Decibel converter
power: L = 10·log₁₀(P/P₀)
Five conversions around the decibel: ratio ↔ dB (choosing the nature of the quantity, power, factor 10, or amplitude, factor 20: the classic trap), dBm ↔ power (1 mW reference), dBµV ↔ voltage (1 µV reference), dB SPL ↔ sound pressure (20 µPa reference), and the addition of two incoherent source levels. Where 60 dB + 60 dB make 63 dB, not 120.
3.0103 dB
- Calculation
- L = 10·log₁₀(2) = 3.0103 dB
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulaspower: L = 10·log₁₀(P/P₀)
power: L = 10·log₁₀(P/P₀)
amplitude: L = 20·log₁₀(A/A₀)
dBm: P₀ = 1 mW (dBµV: U₀ = 1 µV) dB SPL: p₀ = 20 µPa
sum (incoherent sources): L = 10·log₁₀(10^(L₁/10) + 10^(L₂/10))
One definition behind both factors: the decibel compares powers. For an amplitude (voltage, current, sound pressure), power goes as the square, and 10·log(a²) = 20·log(a). Factor 20 is not another definition, it is the same one applied to the square. The references of the absolute scales (1 mW, 1 µV, 20 µPa) are exact conventions, not measurements.
- dB (relative) vs dBm, dBµV, dB SPL (absolute)
- · a plain dB level compares two quantities to each other (gain, attenuation); suffixed (dBm, dBµV, dB SPL) it compares to a fixed reference and becomes an absolute measurement.
- Factor 10 or factor 20
- · factor 10 for a quantity that IS a power (W, mW); factor 20 for one whose square is proportional to power (V, A, Pa). +3 dB = doubled power = amplitude ×1.41.
- Incoherent sources
- · two signals with no stable phase relation (two machines, two noises): their powers add. Correlated signals interfere, up to +6 dB in phase. Extinction in opposition.
Validity domainLevel addition holds for incoherent sources, the assumption is displayed in the tool.
Level addition holds for incoherent sources, the assumption is displayed in the tool. dB SPL uses the 20 µPa reference of airborne acoustics; underwater acoustics uses 1 µPa, outside this tool. No frequency weighting (dBA, dBC) is applied: these are physical levels, not perceived ones.
Common pitfall: adding decibelsTwo machines at 60 dB each do not make 120 dB: they make 63 dB: powers add (10⁶ + 10⁶ = 2·10⁶), not levels.
Two machines at 60 dB each do not make 120 dB: they make 63 dB: powers add (10⁶ + 10⁶ = 2·10⁶), not levels. And doubling the power adds 10·log₁₀(2) ≈ 3 dB. Useful corollary: a source 10 dB weaker than another changes the total by only 0.4 dB, the loudest dominates almost everything. And the factor trap: an amplifier that doubles the voltage gains 6 dB, not 3.