Convert sound pressure level in dB to pressure, reverse pressure to dB, or solve the reference pressure. Supports air, underwater, and custom references with worked steps.
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dB To Pressure Formula
The following formula is used to calculate the pressure for a given sound pressure level and reference pressure.
Variables:
- P is the pressure in pascals
- P₀ is the reference pressure in pascals
- L is the sound pressure level in decibels (dB)
To calculate the pressure, multiply the reference pressure by 10 raised to the power of the sound pressure level divided by 20.
| Decibels (dB) | Pressure (Pa) |
|---|---|
| -20 | 0.000002 |
| -10 | 0.00000632 |
| 0 | 0.00002 |
| 10 | 0.0000632 |
| 20 | 0.0002 |
| 30 | 0.000632 |
| 40 | 0.002 |
| 50 | 0.00632 |
| 60 | 0.02 |
| 70 | 0.0632 |
| 80 | 0.2 |
| 85 | 0.356 |
| 90 | 0.632 |
| 94 | 1.002 |
| 100 | 2.000 |
| 110 | 6.325 |
| 120 | 20.00 |
| 130 | 63.246 |
| 140 | 200.0 |
| 150 | 632.456 |
| *Assumes air reference sound pressure p_ref = 20 µPa (2.0×10⁻⁵ Pa). Formula: p = p_ref × 10^(L/20). | |
What is Sound Pressure Level?
Sound pressure level (SPL) expresses RMS sound pressure relative to a reference: 20 micropascals in air or 1 micropascal underwater. It is distinct from sound intensity and does not by itself determine perceived loudness. Use L = 20 log10(P/P₀), with both pressures in the same unit. The calculator’s optional intensity result assumes a progressive plane wave and illustrative acoustic impedance; actual impedance depends on conditions.
How to Calculate Sound Pressure Level?
The following steps outline how to calculate the Sound Pressure Level.
- First, select Sound level from pressure and enter the RMS pressure with its unit.
- Next, determine the reference pressure (P₀) in pascals.
- Next, calculate the sound pressure level using the formula L = 20 * log10(P / P₀).
- Select Calculate to find the sound pressure level relative to the chosen air, underwater or custom reference.
- After inserting the values and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Pressure (P) = 2 pascals
Reference Pressure (P₀) = 20 micropascals; L = 20 log10(2/0.00002) = 100 dB re 20 µPa.
