Decibel (dB) definition, how to convert, calculator and dB to ratio table.
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:
RatioB = log10(P1 / P0)
Decibel is one tenth of a bel, so 1 bel is equal to 10 decibel:
1B = 10dB
The power ratio in decibels (dB) is 10 times base 10 logarithm of the ratio of P1 and P0:
RatiodB = 10⋅log10(P1 / P0)
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:
RatiodB = 10⋅log10(V12 / V02) = 20⋅log10(V1 / V0)
Convert dB, dBm, dBW, dBV, dBmV, dBμV, dBu, dBμA, dBHz, dBSPL, dBA to watts, volts, ampers, hertz, sound pressure.
The gain GdB is equal to 10 times base 10 logarithm of the ratio of the power P2 and the reference power P1.
GdB = 10 log10(P2 / P1)
P2 is the power level.
P1 is the referenced power level.
GdB is the power ratio or gain in dB.
Find the gain in dB for a system with input power of 5W and output power of 10W.
GdB = 10 log10(Pout/Pin) = 10 log10(10W/5W) = 3.01dB
The power P2 is equal to the reference power P1 times 10 raised by the gain in GdB divided by 10.
P2 = P1 ⋅ 10(GdB / 10)
P2 is the power level.
P1 is the referenced power level.
GdB is the power ratio or gain in dB.
For amplitude of waves like voltage, current and sound pressure level:
GdB = 20 log10(A2 / A1)
A2 is the amplitude level.
A1 is the referenced amplitude level.
GdB is the amplitude ratio or gain in dB.
A2 = A1 ⋅ 10(GdB/ 20)
A2 is the amplitude level.
A1 is the referenced amplitude level.
GdB is the amplitude ratio or gain in dB.
Find the output voltage for a system with input voltage of 5V and voltage gain of 6dB.
Vout = Vin⋅ 10 (GdB / 20) = 5V ⋅ 10 (6dB / 20) = 9.976V ≈ 10V
The voltage gain (GdB) is 20 times the base 10 logarithm of the ratio of the output voltage (Vout) and the input voltage (Vin):
GdB = 20⋅log10(Vout / Vin)
The current gain (GdB) is 20 times the base 10 logarithm of the ratio of the output current (Iout) and the input current (Iin):
GdB = 20⋅log10(Iout / Iin)
The acoustic gain of a hearing aid (GdB) is 20 times the base 10 logarithm of the ratio of the output sound level (Lout) and the input sound level (Lin).
GdB = 20⋅log10(Lout / Lin)
The signal to noise ratio (SNRdB) is 10 times the base 10 logarithm of the signal amplitude (Asignal) and the noise amplitude (Anoise):
SNRdB = 10⋅log10(Asignal / Anoise)
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 |
| 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 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.
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 | 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 | 0.1 | 0.01 |
| -10 dB | 0.316 | 0.1 |
| -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 | 1 |
| 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 |
| 20 dB | 10 | 100 |
| 30 dB | 31.623 | 1000 |
| 40 dB | 100 | 10000 |
| 50 dB | 316.228 | 100000 |
| 100 dB | 105 | 1010 |
