dB converter formula

Decibel (dB) definition

Decibel (Symbol: dB) is a logarithmic unit that indicates ratio or gain.
Decibel is used to indicate the level of acoustic waves and electronic signals.
The logarithmic scale can describe very big or very small numbers with shorter notation.
The dB level can be viewed as relative gain of one level vs. other level, or absolute logarithmic scale level for well known reference levels.
Decibel is a dimensionless unit.
The ratio in bels is the base 10 logarithm of the ratio of P₁ and P₀:

Ratio_B = log₁₀(P₁ / P₀)

Decibel is one tenth of a bel, so 1 bel is equal to 10 decibel:

1B = 10dB

Power ratio

The power ratio in decibels (dB) is 10 times base 10 logarithm of the ratio of P₁ and P₀:

Ratio_dB = 10·log₁₀(P₁ / P₀)

Amplitude ratio

The ratio of quantities like voltage, current and sound pressure level are calculated as ratio of squares.
The amplitude ratio in decibels (dB) is 20 times base 10 logarithm of the ratio of V₁ and V₀:

Ratio_dB = 10·log₁₀(V₁² / V₀²) = 20·log₁₀(V₁ / V₀)

Power ratio to dB conversion

The gain G_dB is equal to 10 times base 10 logarithm of the ratio of the power P₂ and the reference power P₁.

G_dB = 10 log₁₀(P₂ / P₁)

P₂ is the power level.
P₁ is the referenced power level.
G_dB is the power ratio or gain in dB.

 

Example

Find the gain in dB for a system with input power of 5W and output power of 10W.

G_dB = 10 log₁₀(P_out/P_in) = 10 log₁₀(10W/5W) = 3.01dB

dB to power ratio conversion

The power P₂ is equal to the reference power P₁ times 10 raised by the gain in G_dB divided by 10.

P₂ = P₁  · 10^(GdB ^{/ 10)}

P₂ is the power level.
P₁ is the referenced power level.
G_dB is the power ratio or gain in dB.

Amplitude ratio to dB conversion

For amplitude of waves like voltage, current and sound pressure level:

G_dB = 20 log₁₀(A₂ / A₁)

A₂ is the amplitude level.
A₁ is the referenced amplitude level.
G_dB is the amplitude ratio or gain in dB.

dB to amplitude ratio conversion

A₂ = A₁  · 10^(GdB^{/ 20)}

A₂ is the amplitude level.
A₁ is the referenced amplitude level.
G_dB is the amplitude ratio or gain in dB.

 

Example

Find the output voltage for a system with input voltage of 5V and voltage gain of 6dB.

V_out = V_in· 10 ^(GdB ^{/ 20)} = 5V · 10 ^{(6dB / 20)} = 9.976V ≈ 10V

Voltage gain

The voltage gain (G_dB) is 20 times the base 10 logarithm of the ratio of the output voltage (V_out) and the input voltage (V_in):

G_dB = 20·log₁₀(V_out / V_in)

Current gain

The current gain (G_dB) is 20 times the base 10 logarithm of the ratio of the output current (I_out) and the input current (I_in):

G_dB = 20·log₁₀(I_out / I_in)

Acoustic gain

The acoustic gain of a hearing aid (G_dB) is 20 times the base 10 logarithm of the ratio of the output sound level (L_out) and the input sound level (L_in).

G_dB = 20·log₁₀(L_out / L_in)

Signal to Noise Ratio (SNR)

The signal to noise ratio (SNR_dB) is 20 times the base 10 logarithm of the signal amplitude (A_signal) and the noise amplitude (A_noise):

SNR_dB = 20·log₁₀(A_signal / A_noise)

Absolute decibel units

Absolute decibel units are referenced to specific magnitude of measurement unit:

Unit	Name	Reference	Quantity	Ratio
dBm	decibel milliwatt	1mW	electric power	power ratio
dBW	decibel watt	1W	electric power	power ratio
dBrn	decibel reference noise	1pW	electric power	power ratio
dBμV	decibel microvolt	1μVRMS	voltage	amplitude ratio
dBmV	decibel millivolt	1mVRMS	voltage	amplitude ratio
dBV	decibel volt	1VRMS	voltage	amplitude ratio
dBu	decibel unloaded	0.775VRMS	voltage	amplitude ratio
dBZ	decibel Z	1μm3	reflectivity	amplitude ratio
dBμA	decibel microampere	1μA	current	amplitude ratio
dBohm	decibel ohms	1Ω	resistance	amplitude ratio
dBHz	decibel hertz	1Hz	frequency	power ratio
dBSPL	decibel sound pressure level	20μPa	sound pressure	amplitude ratio
dBA	decibel A-weighted	20μPa	sound pressure	amplitude ratio

Relative decibel units

Unit	Name	Reference	Quantity	Ratio
dB	decibel	-	-	power/field
dBc	decibel carrier	carrier power	electric power	power ratio
dBi	decibel isotropic	isotropic antenna power density	power density	power ratio
dBFS	decibel full scale	full digital scale	voltage	amplitude ratio
dBrn	decibel reference noise

Sound level meter

Sound level meter or SPL meter is a device that measures the sound pressure level (SPL) of sound waves in decibels (dB-SPL) units.
SPL meter is used to test and measure the loudness of the sound waves and for noise pollution monitoring.
The unit for measuring of sound pressure level is pascal (Pa) and in logarithmic scale the dB-SPL is used.

dB-SPL table

Table of common sound pressure levels in dBSPL:

Sound type	Sound level (dB-SPL)
Hearing threshold	0 dBSPL
Whisper	30 dBSPL
Air conditioner	50-70 dBSPL
Conversation	50-70 dBSPL
Traffic	60-85 dBSPL
Loud music	90-110 dBSPL
Airplane	120-140 dBSPL

dB to ratio conversion table

dB	Amplitude ratio	Power ratio
-100 dB	10-5	10-10
-50 dB	0.00316	0.00001
-40 dB	0.010	0.0001
-30 dB	0.032	0.001
-20 dB	0.100	0.010
-10 dB	0.316	0.100
-6 dB	0.501	0.251
-3 dB	0.708	0.501
-2 dB	0.794	0.631
-1 dB	0.891	0.794
0 dB	1.000	1.000
1 dB	1.122	1.259
2 dB	1.259	1.585
3 dB	1.413	2 ≈ 1.995
6 dB	2 ≈ 1.995	3.981
10 dB	3.162	10.000
20 dB	10.000	100.000
30 dB	31.623	1000.000
40 dB	100.000	10000.000
50 dB	316.228	100000.000
100 dB	105	1010

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