Sound / Np → µPa RMS
Convert Nepers of pressure ratio to Micropascals RMS
Convert RMS sound pressure and logarithmic pressure levels with an explicit reference. Convert Nepers of pressure ratio (Np) to Micropascals RMS (µPa RMS). Find the formula, worked examples, unit definitions, and practical guidance below.
Reverse: Micropascals RMS to Nepers of pressure ratio →
How to convert nepers of pressure ratio to micropascals rms
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 Np, b for the intermediate value in Pa RMS, and y for the result in µPa RMS.
b = p₀ × 10^(x ÷ 2.30258509299); y = b ÷ 0.000001
Here p₀ = 0.00002 Pa. Static examples and tables use that default reference. The calculator supports another positive reference pressure.
Worked examples
10 Np ≈ 440529.315896 µPa RMS
Step 1: p₀ × 10^(10 ÷ 2.30258509299) ≈ 0.440529315896 Pa RMS.
Step 2: 0.440529315896 ÷ 0.000001 ≈ 440529.315896 µPa RMS.20 Np ≈ 9703303908.2 µPa RMS
Step 1: p₀ × 10^(20 ÷ 2.30258509299) ≈ 9703.3039082 Pa RMS.
Step 2: 9703.3039082 ÷ 0.000001 ≈ 9703303908.2 µPa RMS.
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 Nepers of pressure ratio
Nepers of pressure ratio expresses a pressure ratio logarithmically: level = 2.30258509299 × 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.
About Micropascals RMS
Micropascals RMS (µPa RMS) measures sound under the conventions above. The base value in Pa RMS is (x × 0.000001), where x is the numerical value in µPa RMS. Factors shown here are rounded for display; calculations use the stored factor.
Definitions and sources
Carry the same physical assumptions into subsequent physics calculations.
Nepers of pressure ratio to micropascals rms reference table
| Nepers of pressure ratio (Np) | Micropascals RMS (µPa RMS) |
|---|---|
| 1 | 54.3656365692 |
| 2 | 147.781121979 |
| 5 | 2968.26318205 |
| 10 | 440529.315896 |
| 20 | 9703303908.2 |
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