Convert Pascals RMS to Nepers of pressure ratio

How to convert pascals rms to nepers of pressure ratio

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 Np.

b = (x × 1); y = 2.30258509299 × 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 ≈ 13.1223633774 Np

  Step 1: (10 × 1) ≈ 10 Pa RMS.
  Step 2: 2.30258509299 × log₁₀(10 ÷ p₀) ≈ 13.1223633774 Np.

• 20 Pa RMS ≈ 13.815510558 Np

  Step 1: (20 × 1) ≈ 20 Pa RMS.
  Step 2: 2.30258509299 × log₁₀(20 ÷ p₀) ≈ 13.815510558 Np.

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.