Calculate sound pressure level from pressure, convert dB back to pressure, and combine multiple dB levels using air or water reference levels.

Use RMS acoustic pressure, not static pressure. Combined levels must be uncorrelated and use the same reference, frequency weighting, bandwidth and time basis. This is not a hearing-risk assessment.

Sound Pressure Level Formula

The sound pressure level calculator uses the standard decibel relationship between RMS sound pressure and a reference pressure. The reference pressure depends on the medium.

SPL = 20 × log10(p / pᵣef)
p = pᵣef × 10⁽SPL / 20)
Lₜotal = 10 × log10(sum(10⁽Lᵢ / 10)))
  • SPL = sound pressure level in decibels, dB
  • p = RMS sound pressure in pascals, Pa
  • p_ref = reference sound pressure
  • L_total = combined sound pressure level in dB
  • L_i = each individual sound level being combined, in dB
  • log10 = base-10 logarithm

For air, the calculator uses a reference pressure of 20 µPa, which equals 0.00002 Pa. For water, it uses 1 µPa, which equals 0.000001 Pa.

The Pressure → dB mode converts a pressure value into SPL. The dB → Pressure mode reverses that calculation and returns pressure in Pa, mPa, and µPa. The Combine dB levels mode adds uncorrelated sources measured at the same receiving point, using the same pressure reference, frequency weighting, bandwidth and time basis. Coherent sources require phase information.

Reference Pressures and Common SPL Values

Medium Reference pressure Reference pressure in Pa
Air 20 µPa 0.00002 Pa
Water 1 µPa 0.000001 Pa
Approximate SPL in air Typical comparison Approximate pressure
20 dB Very quiet room or whisper 0.0002 Pa
60 dB Normal conversation 0.02 Pa
85 dB Loud traffic or noisy workplace 0.356 Pa
100 dB Very loud machinery or concert level 2 Pa
120 dB Near pain threshold 20 Pa

Example Problems

Example 1: Convert pressure to SPL

You have a sound pressure of 0.1 Pa in air. Use the air reference pressure of 0.00002 Pa.

SPL = 20 × log10(0.1 / 0.00002)
SPL = 73.98 dB

So, 0.1 Pa in air is about 74 dB SPL.

Example 2: Combine two equal dB levels

You have two uncorrelated sound sources, each measured at 80 dB at the same receiving point and on the same measurement basis.

Lₜotal = 10 × log10(10⁽80 / 10) + 10⁽80 / 10))
Lₜotal = 83.01 dB

Two equal, uncorrelated sound levels combine to about 3 dB above one source, so two 80 dB sources give about 83 dB.

FAQ

Why do you use 20 log for sound pressure level?

Sound intensity is proportional to pressure squared. Decibels are based on power or intensity ratios, which use 10 log. Because pressure is squared in the intensity relationship, the pressure formula becomes 20 log instead of 10 log.

Can you add dB values directly?

No. Decibels are logarithmic, so 80 dB plus 80 dB is not 160 dB. You first convert each level to a linear intensity ratio, add those ratios, then convert back to dB. Two equal, uncorrelated sound levels on the same measurement basis increase the total by about 3.01 dB.

Why are the reference pressures different for air and water?

The standard SPL reference in air is 20 µPa, which is near the threshold of human hearing at mid frequencies. Underwater acoustics commonly uses 1 µPa as the reference. Because the references are different, the same pressure value gives a different dB result in air than it does in water.