Decibel Converter
Our free signal & frequency converter handles decibel conversions. See tables, ratios, and examples for quick reference.
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.
Why do power and voltage use different dB formulas?
Power uses 10 x log10 while voltage uses 20 x log10 because power is proportional to voltage squared (P = V^2/R). Since log10(V^2) = 2 x log10(V), the factor of 2 gets absorbed into the multiplier, changing it from 10 to 20. This ensures that a doubling of voltage (6.02 dB voltage) corresponds to a quadrupling of power (also 6.02 dB power). Both formulas give the same dB value when applied to their respective quantities for the same physical change. A 3 dB increase means double the power but only 1.414 times the voltage.
How does the dB scale relate to human hearing?
Human hearing spans an enormous range of sound pressures, from 20 micropascals (threshold of hearing, 0 dB SPL) to about 200 pascals (threshold of pain, 140 dB SPL), a ratio of 10 million to one. The dB SPL scale compresses this into 0-140 dB. Perceived loudness roughly doubles for every 10 dB increase. Prolonged exposure above 85 dB can cause hearing damage. The quietest sound most people can hear varies by frequency, with peak sensitivity around 1-4 kHz.
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.
What is the difference between dB, dBm, and dBW?
A plain decibel figure expresses a ratio and carries no absolute level. Suffixed units pin that ratio to a reference power: dBm is referenced to one milliwatt and dBW to one watt, so 0 dBm equals 1 mW and 0 dBW equals 1 W. Because a watt is 1,000 milliwatts, the same power expressed in dBW is always 30 dB lower than in dBm. Absolute units state a signal level, while plain dB describes gain or loss along a chain.
How do you add two sound levels expressed in decibels?
Decibels cannot be added arithmetically because the scale is logarithmic. Convert each level back to a power or intensity ratio, sum those ratios, then take ten times the base-ten logarithm of the total. Two uncorrelated sources of equal level sum to 3.01 dB above one alone, so two identical machines at 85 dB produce about 88 dB together. If one source is 10 dB louder than the other, the quieter one adds only around 0.4 dB.
What do A-weighting and C-weighting mean on a sound level meter?
Weighting filters shape the measured spectrum to reflect how the ear responds rather than reporting raw pressure. A-weighting strongly attenuates low frequencies and mildly attenuates the very high ones, approximating hearing sensitivity at moderate levels, with results reported in dB(A) for occupational and environmental noise. C-weighting is much flatter across the low end and is used for peak levels and bass-heavy sources. A large gap between the dB(C) and dB(A) readings signals dominant low-frequency content.
Why does underwater acoustics use a reference pressure of 1 micropascal?
Airborne sound pressure level uses 20 micropascals because that approximates the quietest tone a healthy ear detects near 1 kHz, a reference with no meaning underwater. Hydroacoustics standardised on 1 micropascal instead, so the same physical pressure produces a number twenty times log ten of twenty, about 26.0 dB, higher than the airborne figure. Underwater and airborne dB values are therefore never directly comparable, and any report should state its reference explicitly.
What is dBFS and why are digital audio levels always negative?
Decibels relative to full scale measure a digital signal against the largest sample value the word length can represent, so 0 dBFS is a ceiling rather than a physical loudness. Every level below clipping is a negative number, and pushing past 0 dBFS truncates the waveform into hard distortion. Engineers record with peaks well under the ceiling to leave headroom for later processing, and use separate loudness meters because peak dBFS says very little about perceived level.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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