How this conversion works
Sound pressure level is logarithmic. With the standard reference for sound in air, 20 µPa, the level in decibels is L = 20 × log₁₀(p ÷ 20 µPa).
To go from decibels to pressure, p = 20 µPa × 10^(L ÷ 20). Every 20 dB increase is ten times the pressure; every 6 dB is roughly double.
Formula: L (dB SPL) = 20 × log₁₀(p ÷ 0.00002 Pa); p = 0.00002 Pa × 10^(L ÷ 20)
Where this conversion is used
- Calibrating microphones and sound level meters (94 dB ≈ 1 Pa).
- Converting between decibel readings and acoustic pressure in calculations.
- Understanding how much louder a sound is in physical terms.
Worked example: 94 dB SPL in pascals
- p = 0.00002 × 10^(94 ÷ 20).
- 10^4.7 ≈ 50,118.7, so p ≈ 1.0024 Pa (calibrators use 94 dB ≈ 1 Pa).
Decibels SPL to pascals
| Decibel (sound pressure level) (dB SPL) | Pascal (Pa) |
|---|---|
| 0 | 0 |
| 20 | 0.0002 |
| 40 | 0.002 |
| 60 | 0.02 |
| 80 | 0.2 |
| 94 | 1.0024 |
| 100 | 2 |
| 120 | 20 |
Pascals to decibels SPL
| Pascal (Pa) | Decibel (sound pressure level) (dB SPL) |
|---|---|
| 0.00002 | 0 |
| 0.002 | 40 |
| 0.02 | 60 |
| 0.2 | 80 |
| 1 | 93.9794 |
| 2 | 100 |
| 20 | 120 |
Things to watch for
- Pressures are RMS values. Decibels can be negative (quieter than 20 µPa), but pressure must be greater than zero.
- This is dB SPL for airborne sound. Weighted readings (dBA, dBC), sound power and underwater decibels (re 1 µPa) are different and cannot be converted with this formula.
Precision and sources
Results are calculated from the definitions above and rounded to 12 significant digits; the converter shows up to eight decimal places and the tables four. Reference: ISO 1683:2015, Acoustics — Preferred reference values for acoustical and vibratory levels (20 µPa for sound in air).
Frequently asked questions
Why does 0 dB not mean silence?
0 dB SPL is the reference pressure of 20 µPa, roughly the threshold of hearing for a young adult at 1 kHz. Quieter sounds have negative levels.
Can I add decibel values?
Not directly. Two equal, uncorrelated sources add about 3 dB, not double the number.