dB SPL to Pascal: Formula, Table and Microphone Sensitivity

A decibel value in dB SPL is only a compact way to write a sound pressure. Behind every level there is a pressure in pascals (Pa), and switching between the two is a one-line calculation. The logarithmic scale is convenient because human hearing spans a range of about one to ten million in pressure, from 20 µPa to about 200 Pa.

1. The Formulas

dB SPL to pascals:  p = p_ref × 10^(L / 20)
pascals to dB SPL:  L = 20 × log10(p / p_ref)

where:
  L      = sound pressure level in dB SPL
  p      = RMS sound pressure in pascals
  p_ref  = 20 µPa = 2 × 10⁻⁵ Pa

The factor is 20, not 10, because pressure is a field quantity: power is proportional to the square of the pressure, and 10 × log10(p²) = 20 × log10(p). A practical consequence: doubling the pressure adds 6 dB, and multiplying it by ten adds 20 dB.

Worked examples

• 94 dB SPL to Pa: 20 µPa × 10^(94/20) = 20 µPa × 50 119 ≈ 1.002 Pa.
• 1 Pa to dB SPL: 20 × log10(1 / 0.00002) = 20 × 4.699 ≈ 93.98 dB SPL, which everybody rounds to 94 dB.
• 0.05 Pa to dB SPL: 20 × log10(2 500) ≈ 68 dB SPL.

2. Reference Table

The pressures are rounded: 94 dB SPL is exactly 1.002 Pa and 114 dB SPL is 10.02 Pa. The typical sources come from the European Commission's SCENIHR opinion (2008), which places the threshold of pain between 120 and 140 dB SPL. Every 20 dB step multiplies the pressure by ten, which makes the table easy to extend by hand.

3. Why Calibrators Use 94 dB and 114 dB

Sound calibrators produce a 1 kHz tone at 94 dB SPL because it is 1 Pa: dividing the microphone's output voltage by one gives its sensitivity directly in volts per pascal. The 114 dB SPL setting is 10 Pa, 20 dB higher, and is used when the ambient noise would disturb a 94 dB measurement. Pistonphones, the reference sources used in calibration labs, often work at other levels and frequencies, for example 124 dB SPL at 250 Hz.

4. Microphone Sensitivity: mV/Pa and dBV/Pa

Analog microphone datasheets give the sensitivity either in millivolts per pascal or in decibels relative to 1 V per pascal. The conversion is:

sensitivity (dBV/Pa) = 20 × log10(S_mV / 1000)

50 mV/Pa  →  −26.0 dBV/Pa
10 mV/Pa  →  −40.0 dBV/Pa
 1 mV/Pa  →  −60.0 dBV/Pa

Digital MEMS microphones give their sensitivity in dBFS: the digital level they output for a 94 dB SPL tone. A MEMS microphone rated at −26 dBFS reads −26 dBFS at 1 Pa, so for that microphone dB SPL = dBFS + 94 + 26 = dBFS + 120. In the dBFS converter, that is a sensitivity correction of +26 dB.

5. From Pascals to dBFS

With the sensitivity known, the full chain from a pressure in the room to a digital level is three steps: pressure to dB SPL, dB SPL to dBFS through the calibration offset, then the gain of the recording chain.

import numpy as np

P_REF = 20e-6  # 20 µPa

def spl_to_pa(spl_db):
    return P_REF * 10 ** (np.asarray(spl_db) / 20)

def pa_to_spl(pressure_pa):
    return 20 * np.log10(np.asarray(pressure_pa) / P_REF)

print(spl_to_pa(94))   # 1.0024 Pa
print(pa_to_spl(1.0))  # 93.98 dB SPL

6. Two Common Mistakes

• Using peak instead of RMS pressure. dB SPL is defined on the RMS pressure. For a sine wave the peak pressure is √2 times higher, which would read 3 dB too high.
• Adding decibels directly. Two uncorrelated sources at 80 dB SPL do not make 160 dB SPL but about 83 dB SPL: their energies add, so the level rises by 10 × log10(2) ≈ 3 dB.