Decibel Converter
Our free signal & frequency converter handles decibel conversions. See tables, ratios, and examples for quick reference.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Decibel Converter
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Formula: dB(power) = 10 log10(P2/P1) | dB(voltage) = 20 log10(V2/V1) | 1 Np = 8.686 dB
Worked example โ 20 dB = 100x power ratio = 10x voltage ratio
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 Voltage ratio = 10^(20/20) = 10^1 = 10 So 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 Approximately 50% of the power reaches the far end. Voltage ratio = 10^(-3/20) = 0.7079 (about 70.8%)
Result:-3 dB = 50.12% power = 70.79% voltage
Frequently Asked Questions
What is a decibel and how does it work?
A decibel (dB) is a logarithmic unit that expresses the ratio between two values. For power ratios, dB = 10 x log10(P2/P1). For voltage or amplitude ratios, dB = 20 x log10(V2/V1) because power is proportional to voltage squared. The key advantage of decibels is that they compress large ranges into manageable numbers. A power ratio of 1,000,000 is just 60 dB. Additionally, gains and losses in a signal chain can be added rather than multiplied when expressed in dB.
What are nepers and how do they relate to decibels?
Nepers (Np) are an alternative logarithmic unit using natural logarithm (ln) instead of log10. For voltage ratios, Np = ln(V2/V1), and for power ratios, Np = 0.5 x ln(P2/P1). The conversion factor is 1 Np = 8.685889638 dB (or equivalently, 1 dB = 0.115129255 Np). Nepers are used primarily in some European telecommunications standards and in theoretical physics. The name comes from John Napier, the inventor of logarithms.
What do common dB values mean in practice?
Zero dB means no change (ratio of 1:1). Plus 3 dB doubles the power, minus 3 dB halves it. Plus 6 dB doubles the voltage or quadruples the power. Plus 10 dB means 10 times the power and sounds roughly twice as loud. Plus 20 dB means 100 times the power. Minus 10 dB means one-tenth the power. In audio, a 1 dB change is about the smallest difference most people can perceive, while 3 dB is clearly noticeable. In fiber optics, typical losses are 0.2 dB per kilometer.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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