Decibel converter
dB, dBm, dBµV, dB SPL: ratios, powers, voltages and pressures converted both ways, plus adding two levels, with the factor 10 or 20 according to the quantity.
Result
63.0103 dB
- Calculation
- L = 10·log₁₀(10^(60/10) + 10^(60/10)) = 63.0103 dB
Note
Total 63.0103 dB, that is 3.0103 dB above the loudest source.
Calculation, assumptions and sources
OverviewFive conversions around the decibel: ratio ↔ dB (factor 10 for a power, 20 for an amplitude), dBm ↔ power (1 mW reference), dBµV ↔ voltage (1 µV reference), dB SPL ↔ sound pressure (20 µPa reference), and addition of two incoherent source levels.
Five conversions around the decibel: ratio ↔ dB (factor 10 for a power, 20 for an amplitude), dBm ↔ power (1 mW reference), dBµV ↔ voltage (1 µV reference), dB SPL ↔ sound pressure (20 µPa reference), and addition of two incoherent source levels.
Method & formulaspower: L = 10·log₁₀(P/P₀)
The decibel compares powers. For an amplitude (voltage, current, sound pressure), power goes as the square, and 10·log(a²) = 20·log(a). The references of the absolute scales (1 mW, 1 µV, 20 µPa) are exact conventions.
- dB (relative) vs dBm, dBµV, dB SPL (absolute)
- a plain dB compares two quantities (gain, attenuation); suffixed (dBm, dBµV, dB SPL), it refers to a fixed reference and becomes an absolute measurement.
- Factor 10 or factor 20
- 10 for a power (W, mW), 20 for a quantity 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), whose powers add. Correlated signals interfere: up to +6 dB in phase, extinction in opposition.
Validity domainLevel addition assumes incoherent sources. dB SPL uses the 20 µPa reference of airborne acoustics; underwater acoustics, at 1 µPa, is not covered.
Level addition assumes incoherent sources. dB SPL uses the 20 µPa reference of airborne acoustics; underwater acoustics, at 1 µPa, is not covered. No frequency weighting (dBA, dBC) is applied: levels are physical, not perceived.
Adding decibel levelsTwo machines at 60 dB each make 63 dB: powers add (10⁶ + 10⁶ = 2·10⁶), not levels.
Two machines at 60 dB each make 63 dB: powers add (10⁶ + 10⁶ = 2·10⁶), not levels. Doubling the power adds 10·log₁₀(2) ≈ 3 dB. A source 10 dB weaker than another raises the total by only 0.4 dB. An amplifier that doubles the voltage gains 6 dB.