The decibel compresses a huge range into manageable numbers. The loudest sound you can stand is about ten trillion times more intense than the faintest you can hear, yet on the decibel scale that span is just 0 to 130 dB. The catch is that decibels do not add like ordinary numbers. This calculator does the logarithmic arithmetic for five common jobs: combining several sources, removing background noise from a reading, predicting the level at a new distance, converting between decibels and physical units, and converting power or voltage ratios.
How to use the decibel calculator
- Pick a task under What do you want to do?
- Add sound levels: type each source’s level on its own line. The result is the combined level, the loudest single source, the energy average and each source’s share of the total energy.
- Remove background noise: enter the level with the source running and the background level alone.
- Level at another distance: enter the level measured at the first distance, both distances and whether the source is a point (a machine, a speaker) or a line (a road, a conveyor).
- Convert: choose whether you know the level in dB, the intensity in W/m² or the RMS sound pressure in pascals.
- Ratio ↔ dB: choose power or voltage (amplitude) and the direction of the conversion.
Decibel formulas
with I0 = 10⁻¹² W/m² and p0 = 20 µPa. Adding incoherent sources sums their energies:
Distance falloff from r1 to r2 is L2 = L1 − 20 log10(r2/r1) for a point source and − 10 log10(r2/r1) for a line source. In air at 20 °C, intensity and pressure are linked by I = p2 ÷ ρc, with ρc ≈ 413 Pa·s/m.
Worked example
Three machines in a workshop
Two machines measure 85 dB each and a third measures 82 dB, each on its own.
Energy terms: 108.5 + 108.5 + 108.2 = 790,945,000
Ltotal = 10 × log10(790,945,000) = 88.98 dB
The quieter machine supplies 20% of the noise energy but adds just under 1 dB to the total. To make a real difference, quiet the loudest sources first.
Background correction. A pump reads 78 dB when running, and the room reads 72 dB with it off. The pump alone is 10 log₁₀(107.8 − 107.2) = 76.74 dB. If the two readings differ by less than 3 dB, the correction becomes unreliable.
Distance. A speaker produces 100 dB at 1 m. At 10 m in open air it drops to 80 dB; at 2 m it is already down to 94 dB.
Typical sound levels
| Source | Approximate level |
|---|---|
| Threshold of hearing | 0 dB |
| Quiet library | 30–40 dB |
| Normal conversation at 1 m | 60 dB |
| Busy traffic | 80–85 dB |
| Lawn mower, motorcycle | 90–95 dB |
| Rock concert | 105–115 dB |
| Threshold of pain | 120–130 dB |
Hearing safety
The National Institute for Occupational Safety and Health (NIOSH) recommends limiting exposure to 85 dB(A) to 8 hours a day and halving the allowed time for every 3 dB increase, so 94 dB is safe for only about one hour. Because 3 dB is a doubling of energy, small-looking decibel increases matter.
The decibel itself is built on base-10 logarithms; the logarithm calculator shows the math step by step. For how motion shifts a sound’s pitch, see the Doppler effect calculator, and for frequency-to-wavelength conversions, the wavelength calculator.
Frequently asked questions
What is 90 dB plus 90 dB?
93 dB, not 180 dB. Decibels are logarithmic, so two equal sound sources double the sound energy, and doubling energy adds 10 × log₁₀ 2 ≈ 3.01 dB. Ten equal sources add 10 dB.
How much does sound drop when I double the distance?
About 6 dB for a small, compact source in open air, because the energy spreads over four times the area. A long line source such as a busy highway drops only about 3 dB per doubling, since it spreads over a cylinder rather than a sphere.
Does 10 dB more sound twice as loud?
Roughly. Each 10 dB step is ten times the sound intensity, but listeners typically judge it as about twice as loud. A 3 dB change is clearly noticeable, while 1 dB is near the limit most people can detect.
What is the difference between 10 log and 20 log?
Use 10 log₁₀ for ratios of power or intensity and 20 log₁₀ for ratios of amplitude such as voltage, current or sound pressure. Power goes as amplitude squared, so the same physical change gives the same number of decibels either way.
What do dB SPL and dB(A) mean?
dB SPL is sound pressure level relative to 20 µPa, the nominal threshold of hearing. dB(A) applies an A-weighting filter that discounts low and very high frequencies the way the ear does; noise regulations from OSHA and similar agencies use it. This calculator works with unweighted values.