Calculate sound pressure level from pressure, convert dB back to pressure, and combine multiple dB levels using air or water reference levels.
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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/p_ref)
p = p_ref*10^(SPL/20)
L_total = 10*log10(sum(10^(L_i/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 Add dB levels mode combines two or more sound levels by adding their intensities, not by adding the dB numbers directly.
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 sound sources, each at 80 dB.
L_total = 10*log10(10^(80/10) + 10^(80/10))
L_total = 83.01 dB
Two equal 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 sound levels 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.