Sound / Pa RMS → B
Convert Pascals RMS to Bels relative to reference pressure
Convert RMS sound pressure and logarithmic pressure levels with an explicit reference. Convert Pascals RMS (Pa RMS) to Bels relative to reference pressure (B). Find the formula, worked examples, unit definitions, and practical guidance below.
Reverse: Bels relative to reference pressure to Pascals RMS →
How to convert pascals rms to bels relative to reference pressure
Default reference pressure is 20 µPa, the conventional air SPL reference. Values are unweighted RMS pressure levels, not dBA or sound intensity. Logarithmic levels may be negative; physical pressure must be positive. Changing the reference changes the reported level.
Use x for the value in Pa RMS, b for the intermediate value in Pa RMS, and y for the result in B.
b = (x × 1); y = 2 × log₁₀(b ÷ p₀)
Here p₀ = 0.00002 Pa. Static examples and tables use that default reference. The calculator supports another positive reference pressure.
Worked examples
10 Pa RMS ≈ 11.3979400087 B
Step 1: (10 × 1) ≈ 10 Pa RMS.
Step 2: 2 × log₁₀(10 ÷ p₀) ≈ 11.3979400087 B.20 Pa RMS ≈ 12 B
Step 1: (20 × 1) ≈ 20 Pa RMS.
Step 2: 2 × log₁₀(20 ÷ p₀) ≈ 12 B.
Results are rounded to 12 significant digits. Converting units does not increase the precision of the original measurement. Very large or small values outside JavaScript’s finite numeric range are rejected.
About Pascals RMS
Pascals RMS (Pa RMS) measures sound under the conventions above. The base value in Pa RMS is (x × 1), where x is the numerical value in Pa RMS. Factors shown here are rounded for display; calculations use the stored factor.
About Bels relative to reference pressure
Bels relative to reference pressure expresses a pressure ratio logarithmically: level = 2 × log₁₀(p/p₀). Here p is RMS pressure in pascals and p₀ is the selected reference pressure. Zero level means pressure equal to the reference, not silence.
Definitions and sources
Carry the same physical assumptions into subsequent physics calculations.
Pascals RMS to bels relative to reference pressure reference table
| Pascals RMS (Pa RMS) | Bels relative to reference pressure (B) |
|---|---|
| 1 | 9.39794000867 |
| 2 | 10 |
| 5 | 10.7958800173 |
| 10 | 11.3979400087 |
| 20 | 12 |
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