Decibel Converter
Our free signal & frequency converter handles decibel conversions. See tables, ratios, and examples for quick reference.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
dB(power) = 10 log10(P2/P1) | dB(voltage) = 20 log10(V2/V1) | 1 Np = 8.686 dB
Decibels express ratios logarithmically. Power ratios use the factor 10 and voltage ratios use 20, because power is proportional to voltage squared. Sound pressure level (SPL) uses 20 log10(p/p_ref) with a reference of 20 micropascals. Nepers are related by the factor 8.686 dB per neper.
Worked Examples
Example 1: Amplifier Gain
Problem:An amplifier has a gain of 20 dB. What are the power and voltage ratios?
Solution:Power ratio = 10^(20/10) = 10^2 = 100\nVoltage ratio = 10^(20/20) = 10^1 = 10\nSo 20 dB gain multiplies power by 100 and voltage by 10.
Result:20 dB = 100x power ratio = 10x voltage ratio
Example 2: Signal Loss in Cable
Problem:A cable has 3 dB loss. What fraction of the power reaches the other end?
Solution:Power ratio = 10^(-3/10) = 10^(-0.3) = 0.5012\nApproximately 50% of the power reaches the far end.\nVoltage ratio = 10^(-3/20) = 0.7079 (about 70.8%)
Result:-3 dB = 50.12% power = 70.79% voltage
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy