dB Calculator - SPL, SIL, and inverse square law

The dB calculator converts sound pressure in pascals into sound pressure level (SPL) and sound intensity in W per square meter into sound intensity level (SIL), using the IEC 61672-1 reference pressure of 20 microPascals and the standard 1e-12 W per square meter reference intensity. It also applies the inverse square law so the same screen reports the SIL at any chosen distance from the source. Use this dB calculator for an acoustics homework problem, a noise exposure estimate, or a quick check against a sound level meter reading.

• • Acoustics homework and lab checks: Convert a measured pressure or intensity into decibels and confirm against a textbook table.
• • Noise exposure estimates: Quote the SPL of a machine or speaker against OSHA and NIOSH thresholds.
• • Audio engineering sanity checks: Translate a microphone sensitivity in mV/Pa into a dB SPL reading for a known source.
• • Outdoor sound propagation: Estimate the SIL at a receiver distance from a fan, generator, or traffic source.

The decibel is a logarithmic ratio. A ten-fold increase in sound pressure produces a 20 dB jump in SPL; a ten-fold increase in sound intensity produces a 10 dB jump in SIL.

When the SPL problem is really about how the medium changes the relationship between pressure and intensity, the Acoustic Impedance Calculator covers the Z = rho x c picture behind the same sound field.

The calculator divides the measured sound pressure in pascals by the 20 microPascal reference and multiplies the base-10 log by 20 to get SPL. It divides the sound intensity in W per square meter by 1e-12 and multiplies the base-10 log by 10 to get SIL. It then applies the inverse square law to source power and distance and converts the receiver intensity back into SIL in decibels.

• P (sound pressure): Sound wave pressure in pascals. The SPL formula divides this by Pref = 20 microPascals.
• I (sound intensity): Sound intensity in W per square meter. The SIL formula divides this by Iref = 1e-12.
• Psrc (source power): Acoustic source power in watts, used with distance in the inverse square law.
• r (distance): Distance from source to receiver in meters.
• SPL (sound pressure level): SPL in decibels: SPL = 20 x log10(P / Pref).
• SIL (sound intensity level): SIL in decibels: SIL = 10 x log10(I / Iref).

The 20 multiplier in SPL and the 10 in SIL come from intensity scaling as the square of pressure: a ten-fold pressure increase produces a hundred-fold intensity increase, and 20 x log10(10) = 10 x log10(100) = 20 dB.

According to Wikipedia: Sound pressure, sound pressure level is defined as SPL = 20 x log10(P / Pref) with Pref = 20 microPascals in air, and the same source lists the standard reference intensity of 1e-12 W per square meter used in the SIL formula.

Once the SPL is on screen, the Harmonic Wave Equation Calculator handles the related textbook problem of relating that pressure amplitude to the wave speed and density of the air it travels through.

Four ideas sit behind the formulas: a logarithmic ratio, separate reference values for pressure and intensity, a 20-versus-10 multiplier that follows from the square-law relationship between pressure and intensity, and the inverse square law that turns source power into SIL at the receiver.

These four ideas explain why two readings on the same screen can sit 30 dB apart, and why the inverse square law predicts a 6 dB drop per doubling of distance even when the SPL value barely changes.

When the 6 dB per doubling rule needs to be combined with material absorption or barrier loss, the Attenuation Calculator covers the decibel attenuation side of the same propagation problem.

Four numbers go in: sound pressure, intensity, source power, and distance. Three decibel readouts and one intensity-at-distance value come out, recalculated on every keystroke.

1. 1 Enter the sound pressure: Type the sound wave pressure in pascals. The default of 0.02 Pa reproduces the conversational-speech SPL of 60 dB.
2. 2 Enter the sound intensity: Type the sound intensity in W per square meter. The default of 1e-6 reproduces the conversational-speech SIL of 60 dB.
3. 3 Read the SPL row: The SPL row reports 20 x log10(P / 0.00002) in decibels, the IEC 61672-1 sound level meter value.
4. 4 Read the SIL row: The SIL row reports 10 x log10(I / 1e-12) in decibels, the standard textbook value.
5. 5 Enter source power and distance: Type the acoustic source power in watts and the receiver distance in meters.
6. 6 Read the intensity and SIL at distance: The intensity-at-distance row reports Psrc / (4 x pi x r squared), and the SIL-at-distance row converts that intensity into decibels.

For a portable speaker rated at 0.05 W near a listener at 0.5 m, intensity is 0.0159 W per square meter and the SIL is 102.02 dB. Double the distance to 1 m and the SIL drops by 6.02 dB to 96.00 dB.

When the SPL row is being read against an indoor room reading rather than an outdoor point source, the Reverberation Time Calculator covers the room acoustics side so the same speaker reading can be corrected for the room response.

The calculator is most useful when you need the IEC 61672-1 reference values built in, both decibel forms on the same screen, and the inverse square law without rebuilding the sphere-of-radiation equation.

• • IEC 61672-1 anchored: Uses Pref = 20 microPascals and Iref = 1e-12 W per square meter from the IEC 61672-1 standard.
• • SPL and SIL on one screen: Reports both decibel forms from the same inputs, so the pressure side and the intensity side are read together.
• • Inverse square law included: Reads the SIL at any distance from a power and a distance input, the propagation answer most field measurements need.
• • Bidirectional pressure ratio: Shows the linear pressure ratio P / Pref alongside the SPL row.
• • Input clamping for division-by-zero: Clamps zero or out-of-range distances to a small positive minimum so the inverse square law does not produce a NaN.

These benefits matter most in a noise survey, where one screen must show the source SPL, the receiver SIL, and the propagation loss for an OSHA or NIOSH check.

For a generic power or voltage ratio without the IEC 61672-1 acoustic references, the Decibel Calculator covers the broader decibel conversion that this acoustic calculator complements rather than duplicates.

Four input numbers drive the result, and three contextual factors determine whether the SIL is comfortable, hazardous, or out of range.

• • The inverse square law assumes a point source radiating uniformly into free space. A line source (such as a long pipe) drops by 3 dB per doubling of distance.
• • The 20 microPascal reference is for sound in air, not for hydrophone readings where the underwater reference is 1 microPascal.
• • The calculator does not apply A-weighting. Real-world noise exposure tables quote dBA, so a 110 dB reading here would be a lower dBA value on a sound level meter.

These caveats matter because the inverse square law is a free-field idealization. A speaker in a room corner reflects off three walls and adds 4 to 6 dB at the listener; outdoors with no reflections, the speaker matches the calculator reading almost exactly.

According to Wikipedia: Sound intensity, sound intensity falls off as the inverse square of the distance for a point source, so SIL drops by 6.02 dB every time the distance to the source is doubled, and the same article lists the 1e-12 W per square meter reference intensity used in the SIL formula.

When the SPL reading needs to be interpreted alongside a frequency difference between two tones, the Beat Frequency Calculator covers the beat-frequency side of the same acoustic problem.