Convert between decibels and voltage/power ratios. Calculate amplifier gain, signal attenuation, dBm, dBV and more.
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dB
Ω
dB Reference Table
Common dB values and their equivalent power and voltage ratios:
dB
Power ratio
Voltage ratio
Note
−20 dB
×0.01
×0.1
−20 dB attenuation
−10 dB
×0.1
×0.316
10× power reduction
−6 dB
×0.25
×0.5
Half voltage
−3 dB
×0.5
×0.707
Half power (filter cutoff)
0 dB
×1
×1
No change
+3 dB
×2
×1.414
Double power
+6 dB
×4
×2
Double voltage
+10 dB
×10
×3.162
10× power increase
+20 dB
×100
×10
Decade gain
+40 dB
×10 000
×100
Typical op-amp open-loop gain
dB Formulas
Key Formulas
Power ratio → dB
dB = 10 × log₁₀(P₂/P₁)
Voltage ratio → dB
dB = 20 × log₁₀(V₂/V₁)
dB → power ratio
ratio = 10^(dB/10)
dB → voltage ratio
ratio = 10^(dB/20)
dBm
dBm = 10 × log₁₀(P/1mW)
dBV
dBV = 20 × log₁₀(V/1V)
Frequently Asked Questions
What is a decibel (dB)? ▾
A decibel is a logarithmic unit for expressing ratios. For power: dB = 10×log₁₀(P₂/P₁). For voltage: dB = 20×log₁₀(V₂/V₁). The factor 20 vs 10 exists because power is proportional to voltage squared.
Why is −3 dB the filter cutoff frequency? ▾
−3 dB corresponds to half the input power (voltage ratio 0.707). Filter cutoff is defined where the output power drops to half, which equals −3 dB. This is where the frequency response transitions from passband to stopband.
What is dBm and how is it used? ▾
dBm is power relative to 1 milliwatt: dBm = 10×log₁₀(P/1mW). It is standard in RF engineering, Wi-Fi signal strength (typically −30 to −90 dBm) and audio equipment.
How many dB is doubling the power? ▾
Doubling power = +3 dB. Doubling voltage = +6 dB. Multiplying power by 10 = +10 dB. These three reference points cover most practical calculations.
What is the difference between dBV and dBu? ▾
dBV is voltage relative to 1 V RMS. dBu (formerly dBm in unloaded conditions) is relative to 0.7746 V RMS (the voltage that delivers 1 mW into 600 Ω). Professional audio uses dBu; consumer audio uses dBV.