Engineering
Decibel (dB) Power Gain, Voltage Gain & Logarithmic Sound Addition
Calculate 10*LOG10(P2/P1) power gain vs 20*LOG10(V2/V1) amplitude gain and add independent decibel sound levels accurately via 10*LOG10(10^(L1/10) + 10^(L2/10)).
Keep power, voltage and sound-level calculations separate
Power ratios use10*LOG10(Pout/Pin). Voltage amplitude ratios use20*LOG10(Vout/Vin); interpreting that as a power gain requires equal impedances and consistent amplitude measurements, such as RMS values. The worksheet now has separate voltage inputs rather than relabeling power values.
Two uncorrelated simultaneous sound levels can be combined by adding linear mean-square contributions, provided they use the same reference, frequency weighting, observation location and averaging interval. This does not apply to phase-coherent signals or to adding nonoverlapping exposure periods.
Equal independent levels add about3.01 dB. Coherent amplitudes can reinforce or cancel depending on phase, so this is not an unconditional rule for all sources. These calculations are not a hearing-safety assessment.
Positive finite powers and voltage magnitudes are required for finite gain results; zero output corresponds to a nonfinite logarithmic limit and is rejected here. Sound levels may be negative relative to their reference. The level-sum formula subtracts the larger level before exponentiation to avoid overflow at large levels.
| Decibel Calculation | Formula | 50 W / 0.5 W (100x Ratio) | Two 80 dB Fans | Half-Power Cutoff (0.25 W / 0.5 W) |
|---|---|---|---|
| Power Gain (10 * LOG10) | 10 * LOG10(B2 / B3) | +20.00 dB (100x power) | -3.01 dB (50% power cutoff!) |
| Amplitude / Voltage Gain (20 * LOG10) | 20*LOG10(B6/B7), separate voltage inputs | +40.00 dB (100x voltage = 10,000x P) | -6.02 dB (50% voltage) |
| Combined Sound Level (L1 (+) L2) | 10 * LOG10(10^(B4/10) + 10^(B5/10)) | 83.01 dB (+3.01 dB above 80 dB) | 83.01 dB |
Power Ratio Decibel Gain = 10 * LOG10(P2 / P1)
Positive dB indicates amplification; negative dB indicates attenuation/insertion loss (-3.01 dB = half power).
=IF(COUNT(B2:B3)<>2,"Invalid inputs",IF(OR(B2<=0,B3<=0),"Invalid inputs",ROUND(10*(LOG10(B2)-LOG10(B3)),2)))Logarithmic Addition of Two Independent Noise Levels (dB)
Shift both levels by their maximum before exponentiation. This calculates the same incoherent sum without exponentiating a very large positive level.
=IF(COUNT(B4:B5)<>2,"Invalid inputs",ROUND(MAX(B4,B5)+10*LOG10(10^((B4-MAX(B4,B5))/10)+10^((B5-MAX(B4,B5))/10)),2))Voltage amplitude gain
Use the separate RMS voltage inputs B6 and B7. Equal impedance is required when interpreting this as power gain.
=IF(COUNT(B6:B7)<>2,"Invalid inputs",IF(OR(B6<=0,B7<=0),"Invalid inputs",ROUND(20*(LOG10(B6)-LOG10(B7)),2)))Try the example
Use the original values or change them to test your understanding.