Decibel (dB)

Decibel (dB) definition, how to convert, calculator and dB to ratio table.

• Decibel (dB) definition
• Decibels to watts, volts, hertz, pascal calculator
• Power ratio to dB conversion
• dB to power ratio conversion
• Amplitude ratio to dB conversion
• dB to amplitude ratio conversion
• Absolute decibel units
• Relative decibel units
• Sound level meter
• dB-SPL table
• dB to ratio conversion table

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)

Decibels to watts, volts, hertz, pascal conversion calculator

Convert dB, dBm, dBW, dBV, dBmV, dBμV, dBu, dBμA, dBHz, dBSPL, dBA to watts, volts, ampers, hertz, sound pressure.

1. Set the quantity type and decibel unit.
2. Enter the values in one or two of the text boxes and press the corresponding Convert button:

Quantity type:

Power Voltage Current Frequency Sound pressure

Decibel unit:

dBm dBW dB

Reference level:

Level:

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Decibels:

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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:

Relative decibel units

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:

dB to ratio conversion table

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