dB Calculator — Sound Pressure Level (SPL), Intensity Level (SIL) & Distance Attenuation

What is the Sound Pressure Level (SPL)?

When we hear a very loud noise, we experience unpleasant feelings. It is because of the pressure of a sound wave. The sound pressure level, or SPL, is simply the measure of sound pressure with reference to the human hearing threshold. Even though this pressure can be measured in Pascals, like air pressure, it is more practical to use decibels — a logarithmic unit.

How Do I Compute the Sound Pressure Level?

The formula for the sound pressure level is:

SPL = 20 × log₁₀(P / P_ref)

Where:

• SPL — Sound pressure level in dB
• P — Sound wave pressure in Pascals (Pa)
• P_ref — Reference value of sound pressure = 0.00002 Pa (2 × 10⁻⁵ Pa), which corresponds to the threshold of human hearing

As you probably noticed, the SPL increases logarithmically. Also, it is a relative measure, while the regular sound wave pressure is an absolute measure of loudness. This means that doubling the pressure adds approximately 6 dB, and a tenfold increase adds 20 dB.

How Do I Find the Sound Intensity Level?

Sound intensity level (SIL) is defined as the sound wave power per unit area. This quantity allows us to measure the energy of sound (or, to be more precise, the energy per second per one squared meter). The formula is:

SIL = 10 × log₁₀(I / I_ref)

Where:

• SIL — Sound intensity level in dB
• I — Sound intensity in watts per square meter (W/m²)
• I_ref — Reference value of sound intensity = 10⁻¹² W/m², which corresponds to the threshold of hearing

Sound Intensity at a Distance

Sound intensity changes with the distance from the sound source. It's just common sense — if a car passes you, you hear a loud noise that gets quieter as the car moves away.

From a physical point of view, it happens because the energy of sound is now distributed over a larger area. Imagine a sphere surrounding the sound source. Even though the energy emitted by the source is constant, the sphere can get larger — its surface will increase. The energy will be distributed over the area of the sphere. The formula is:

I = P_src / (4π × R²)

Where:

• I — Sound intensity (W/m²)
• P_src — Power of the sound source (W)
• R — Radius of the sphere, i.e., the distance from the sound source (m or ft)

The calculator supports both metric (meters) and imperial (feet) unit systems for distance. This inverse square law means that doubling the distance reduces the intensity by a factor of 4, which corresponds to a drop of approximately 6 dB.

Pascals to dB Conversion

Our decibel calculator can be used to find the equivalent of sound wave pressure in decibels. Simply type the pressure in Pascals into the dB calculator to find the sound pressure level. You can also use the "dB to Pascals" mode to work in reverse — enter an SPL in dB and find the corresponding pressure in Pascals using the formula:

P = P_ref × 10^{SPL / 20}

Reference Sound Levels

FAQs

What does 0 dB mean?

0 dB corresponds to the threshold of human hearing — the softest sound a healthy young person can detect under ideal conditions. It does not mean silence; it means the reference pressure of 0.00002 Pa.

Can sound pressure level be negative in dB?

Yes — a negative SPL simply means the sound pressure is below the reference threshold of 0.00002 Pa. This is inaudible to humans but physically possible (e.g., very faint measurements in a laboratory).

Why does doubling distance reduce SPL by ~6 dB?

Because intensity follows the inverse square law (I ∝ 1/R²). Doubling distance reduces intensity by 4×, and since SIL = 10 × log₁₀(I/I₀), a 4× drop equals −10 × log₁₀(4) ≈ −6 dB.

What is the difference between SPL and SIL?

SPL measures pressure variations (using the factor 20 in the formula) while SIL measures power per area (using the factor 10). For a plane wave in air they are numerically equal, but in other media they can differ. For practical acoustics, both are measured in dB relative to their respective reference values.