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A decibel (dB) is one tenth of a bel, a logarithmic way to compare two quantities. Hearing, signal strength and gain all span huge ranges, and logarithms squeeze them into manageable numbers. A decibel is always a ratio: it needs a reference, written in the unit (dB SPL, dBm, dBV). Convert and add levels with the Decibel Calculator; the glossary entry is Decibel (dB).
- For power (or intensity):
dB = 10 × log10(P2 / P1).
- For amplitude (voltage, current, sound pressure):
dB = 20 × log10(A2 / A1).
- A 0 dB change means no change; negative values mean a drop.
Ratios worth remembering
| Change |
Power ratio |
Amplitude ratio |
| −20 dB |
0.010 |
0.100 |
| −10 dB |
0.100 |
0.316 |
| −6 dB |
0.251 |
0.501 |
| −3 dB |
0.501 |
0.708 |
| 0 dB |
1.00 |
1.00 |
| +3 dB |
2.00 |
1.41 |
| +6 dB |
3.98 |
2.00 |
| +10 dB |
10.00 |
3.16 |
| +20 dB |
100 |
10.00 |
| +30 dB |
1,000 |
31.62 |
| +40 dB |
10,000 |
100 |
- +3 dB doubles the power (×1.995); +6 dB doubles the amplitude (×1.995) and quadruples the power (×3.98).
- +10 dB is ten times the power and about 3.16 times the amplitude; +20 dB is 100 times the power and 10 times the amplitude.
- Decibels add where ratios multiply: +10 dB then +20 dB is +30 dB, a 1000-fold power increase.
Adding levels and moving away
- Two equal sources: 60 dB + 60 dB = 63.01 dB (+3 dB, not 120).
- Ten equal sources: 60 dB each give 70 dB.
- A source 10 dB louder than another dominates: 60 dB + 50 dB = 60.4 dB.
- In free space, level falls 6.02 dB per doubling of distance (inverse-square law): 80 dB at 1 m is 74.0 dB at 2 m and 60 dB at 10 m.
Common references
| Reference |
Meaning |
| dB SPL |
Sound pressure level, relative to 20 µPa (the threshold of hearing) |
| dBm |
Power relative to 1 milliwatt (0 dBm = 1 mW, 30 dBm = 1 W) |
| dBV |
Voltage relative to 1 volt |
| dBu |
Voltage relative to 0.7746 volt |
| dBFS |
Digital level relative to full scale (0 dBFS is the maximum) |