Deutsche Version 
● Convert Decibels to Voltage Gain / Loss ●
● Convert Voltage Gain / Loss to Decibels ●
• Voltage and Gain •
Enter any two values  the third will be calculated. 
V_{0} = 1 Volt 
To use the calculator, simply enter a value. The calculator works in both directions of the ↔ sign. 
Gain and Loss Gain is: Gain:The measure of how much a circuit amplifies a signal. Gain may be stated as Conductive Hearing Loss: a loss of sensitivity to sound, resulting from an Gain or Loss: These are reciprocal numbers; they will be given in several ways. dB (decibel): A technique for expressing voltage,power, gain, loss, or frequency in Voltage Controlled Attenuator (VCA): 
Sound level, loudness, and sound pressure are not the same things. There are variations in individual perception of the strength of sound. The sound pressure measured twice as much gives 6 dB more level. The sound perceived twice as loud needs roughly an increase in sound level by 10 dB. 
Common Gains and Losses Expressed in Decibels
Notice: Power gain is not used in audio engineering.
Gain/loss as a ratio (out/in) 
Gain/loss as a factor 
Gain/loss in dB Field sizes (Voltage gain) 
Gain/loss in dB Energy sizes (Power gain) 
10,000:1  10,000  +80.00 dB  +40.00 dB 
10,00:1  10,00  +60.00 dB  +30.00 dB 
100:1  100  +40.00 dB  +20.00 dB 
10:1  10  +20.00 dB  +10.00 dB 
5:1  5  +13.98 dB  +6.99 dB 
4:1  4  +12.04 dB  +6.02 dB ● 
2:1  2  +6.02 dB ●  +3.01 dB 
1:1  1  0,00 dB  0.00 dB 
1:2  0.5  −6.02 dB ●  −3.01 dB 
1:4  0.25  −12.04 dB  −6.02 dB ● 
1:5  0.2  −13.98 dB  −6.99 dB 
1:10  0.1  −20.00 dB  −10.00 dB 
1:100  0.01  −40.00 dB  −20.00 dB 
1:1,000  0.001  −60.00 dB  −30.00 dB 
1:10,000  0.0001  −80.00 dB  −40.00 dB 
40 dB voltage gain (amplitude) is 100 times the voltage factor (amplitude).
40 dB power gain is 10,000 times the power factor.
Voltage Gain = Voltage Amplification and Power Gain = Power amplification
Voltage (amplitude) gain  Power (energy) gain  
Voltage ratio Factor V_{2}/V_{1} 
Voltage amplification G_{V} in dB 
Power ratio Factor P_{2}/P_{1} 
Power amplification G_{P} in dB 

10^{3}  +60  10^{6}  +60  
10^{2}  +40  10^{4}  +40  
10^{1}  +20  10^{2}  +20  
√10 = 3.16  +10  10  +10  
2  +6  4  +6  
√2 = 1.414  +3  2  +3  
1  ±0  1  ±0  
1/√2 = 0.7071  −3  1/2 = 0.5  −3  
1/2 = 0.5  −6  1/4 = 0.25  −6  
1/√10 = 0.316  −10  10^{−1} = 0.1  −10  
10^{−1} = 0.1  −20  10^{−2} = 0.01  −20  
10^{−2} = 0.01  −40  10^{−4} = 0.0001  −40  
10^{−3} = 0.001  −60  10^{−6} = 0.000001  −60  
V_{2}/V_{1} = 10^{(GV in dB/20)}  G_{V} = 20×log (V_{2}/V_{1})  P_{2}/P_{1} = 10^{(GP in dB/10)}  G_{P} = 10×log (P_{2}/P_{1}) 

Questions: For an amplifier with an amplification factor of 100, calculate the following: a) voltage gain in dB. b) voltage gain at the cutoff frequency (break frequency) in dB. c) amplification factor at the cutoff frequency (break frequency). Answers: a) amplification factor 100 = gain 40 dB b) gain at the cutoff frequency is 3 dB, so it is 37 dB. c) gain 37 dB = amplification factor 70.7 at the cutoff frequency. 
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