Convert Nepers of pressure ratio to Pascals RMS

How to convert nepers of pressure ratio to pascals 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 Pa RMS.

b = p₀ × 10^(x ÷ 2.30258509299); y = b ÷ 1

Here p₀ = 0.00002 Pa. Static examples and tables use that default reference. The calculator supports another positive reference pressure.

Worked examples

• 10 Np ≈ 0.440529315896 Pa RMS

  Step 1: p₀ × 10^(10 ÷ 2.30258509299) ≈ 0.440529315896 Pa RMS.
  Step 2: 0.440529315896 ÷ 1 ≈ 0.440529315896 Pa RMS.

• 20 Np ≈ 9703.3039082 Pa RMS

  Step 1: p₀ × 10^(20 ÷ 2.30258509299) ≈ 9703.3039082 Pa RMS.
  Step 2: 9703.3039082 ÷ 1 ≈ 9703.3039082 Pa 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.

Carry the same physical assumptions into subsequent physics calculations.