How to Calculate Decibels (dB) | Formulas and Charts for Adding, Subtracting, Averaging and Distance Attenuation, from Why 60 dB + 60 dB Is 63 dB to Background Noise Correction and Noise Standards

The short answer: convert dB back to “sound energy”, do the arithmetic, then convert back to dB

A decibel (dB) value expresses the strength of a sound as the logarithm of “how many times the reference” it is. Because it is a logarithm, you can't simply add or average dB values. To calculate with them, you first convert each one back to 10^(L/10), a quantity proportional to sound energy, add or subtract those, and finally convert back to dB with 10 × log10. Almost every noise calculation is a repeat of this “convert back, calculate, convert to dB again” pattern.

Below, we first look at what kind of value dB is, then go through adding, averaging, subtracting and distance attenuation in turn, each with its formula, a chart and worked examples. The Decibel Calculator gives the same results for every calculation, so try your own numbers as you read.

What dB means: the logarithm of a ratio to the reference pressure of 20 µPa

Strictly speaking, the dB used for noise is the “sound pressure level”. A tiny sound pressure of 20 µPa (micropascals, 0.00002 Pa), roughly the quietest sound a person can hear, is taken as 0 dB, and the ratio of the measured pressure p to it is expressed as 20 × log10(p ÷ 20 µPa). Since sound energy (intensity) is proportional to the square of the pressure, writing it in terms of energy gives 10 × log10(energy ratio), which is the same value. That is why addition uses 10^(L/10).

Each tenfold increase in sound pressure adds 20 dB. The range of pressures from 0 dB to 120 dB spans a factor of a million, which is awkward to handle as plain numbers, so it is compressed with a logarithm. Because 1 Pa comes out at almost exactly 94 dB, sound level calibrators often produce a 94 dB tone.

How big a dB difference is depends on which ratio you look at: sound energy (intensity), sound pressure, or how loud it sounds to the human ear.

Adding dB (combining levels): 60 dB + 60 dB is 63 dB, not 120 dB

Adding dB means finding the level when two or more sounds play at once. Convert each to 10^(L/10), add them, and convert back to dB with 10 × log10. For 60 dB and 60 dB, 10^6 + 10^6 = 2 × 10^6, and 10 × log10(2 × 10^6) ≈ 63.0 dB. Doubling the energy only raises the level by 10 × log10(2) ≈ 3 dB — that is where “two sources add 3 dB” comes from.

1. 1

   Convert each level to 10^(L/10)

   60 dB → 10^6 = 1,000,000; 65 dB → 10^6.5 ≈ 3,162,278; 70 dB → 10^7 = 10,000,000.

2. 2

   Add them all

   1,000,000 + 3,162,278 + 10,000,000 = 14,162,278.

3. 3

   Convert back to dB with 10 × log10

   10 × log10(14,162,278) ≈ 71.5 dB — only 1.5 dB more than the loudest source, 70 dB.

When there are n sources of the same level, the result is simply L + 10 × log10(n). Each doubling of the number of sources adds 3 dB, and each tenfold increase adds 10 dB.

When you add two sounds of different levels, the difference between them alone decides “how many dB to add to the louder one”. The formula is 10 × log10(1 + 10^(−difference/10)), and putting it in a table gives the dB addition chart. With this chart you can add any number of sources without a calculator, two at a time.

Averaging dB: noise uses the energy average (which comes out higher than the arithmetic mean)

When you combine several noise readings, or values taken at different times, use the energy average (power average), not the arithmetic mean you get by adding and dividing. The formula is 10 × log10((10^(L1/10) + 10^(L2/10) + … + 10^(Ln/10)) ÷ n), which is the same as the combined level minus 10 × log10(n).

The arithmetic mean of 60, 70 and 80 dB is 70 dB, but the energy average is about 75.7 dB. An 80 dB sound has 100 times the energy of a 60 dB sound, so the loud values dominate the average. The more the values vary, the further the energy average sits above the arithmetic mean; if all the values are the same, the two agree.

The “equivalent continuous sound level (LAeq)” that appears in noise standards and measurements is exactly this: noise that changes over time, condensed into a single value with the energy average. If a loud sound lasts just 10 minutes in an hour, the arithmetic mean dilutes it, but the equivalent level reflects it properly. If you use the arithmetic mean when reporting an “average” for a noise complaint or report, you will underestimate the noise.

Subtracting dB: remove the background noise to find the level of the source alone

A sound level meter reading includes not only the sound you care about (an outdoor unit, a machine) but also the surrounding sound, called background noise. If you measure both with the source running and with it switched off, subtraction gives you the level of the source alone. The formula is 10 × log10(10^(total/10) − 10^(background/10)).

1. 1

   Measure with the source running

   For example, 65 dB with the outdoor unit on.

2. 2

   Measure with the source off (background noise)

   At the same spot and time of day, 60 dB with the outdoor unit off.

3. 3

   Convert to energy and subtract

   10^6.5 − 10^6 ≈ 3,162,278 − 1,000,000 = 2,162,278.

4. 4

   Convert back to dB

   10 × log10(2,162,278) ≈ 63.3 dB is the level of the outdoor unit alone.

The Japanese standard for measuring noise, JIS Z 8731, gives an alternative to this calculation: a correction value determined by the “difference in readings” with and without the source. If the difference is 10 dB or more, the background has almost no effect and no correction is made. If it is less than 3 dB, the background is too loud to find the source level reliably, and you need to measure again.

In the example above, 65 dB and 60 dB differ by 5 dB, so the JIS correction is −2 dB, giving 63 dB. For 70 dB and 62 dB the difference is 8 dB: the formula gives 69.3 dB and the JIS correction of −1 dB gives 69 dB. The corrections are rounded to whole numbers, so they can differ from the formula by up to about 0.5 dB, but because meter readings are usually taken to the nearest 1 dB, this table is widely used in practice.

Distance attenuation: −6 dB per doubling of distance for a point source, −3 dB for a line source

Sound gets quieter as you move away from the source. How much quieter depends on whether the source can be treated as a “point” or a “line”. Sound coming from one place, such as an outdoor unit, a machine, a speaker or construction equipment, is a point source; sound from something long, such as a busy road or a railway line, is treated as a line source.

Sound from a point source spreads out like a sphere, so when the distance doubles the same energy spreads over four times the area and the intensity falls to a quarter (about −6 dB). This is the inverse square law. Sound from a line source spreads out like a cylinder, so doubling the distance only doubles the area and halves the intensity (about −3 dB). That is why road noise is so slow to fade.

Solving the formula the other way gives the distance at which the noise falls to a target level: r2 = r1 × 10^((L1 − target) ÷ 20) (÷ 10 for a line source). A point source of 80 dB at 1 m falls to 45 dB about 56 m away, but a line source of the same 80 dB doesn't reach 45 dB until about 3,162 m away.

Worked examples: how loud outdoor units, roads and construction will be

Combining the formulas so far lets you estimate everyday noise. All of these figures assume no obstacles; real levels vary with the equipment and the surroundings.

1. 1

   Two air conditioner outdoor units side by side

   Two outdoor units of 50 dB at 1 m add up to 53 dB. Treated as a point source, at 5 m that becomes 53 − 20 × log10(5) ≈ 39 dB; a single unit would be 36 dB at 5 m. This gives a rough comparison with the 45 dB night-time standard for residential areas in Japan.

2. 2

   Moving away from a main road

   If a road measures 75 dB at 10 m, as a line source it is 69 dB at 40 m: quadrupling the distance only takes off 6 dB. Getting down to 60 dB would take about 316 m on paper, which shows why road noise measures focus on noise barriers and window performance rather than distance.

3. 3

   Construction equipment

   A machine at 85 dB at 10 m, treated as a point source, is 75.5 dB at 30 m and falls to 60 dB at about 178 m. If two machines run at once, add 3 dB at every distance.

When you combine “how many sources” with “how far away”, you get the same answer whether you first add the sources and then apply distance attenuation, or apply attenuation to each and then add. If the sources are at different distances, work out the level from each at your position first, then add them.

Typical noise levels and environmental standards: how many dB counts as loud?

Whether a calculated level is “loud” is easier to judge against familiar sounds. The table below lists commonly quoted examples; actual values change with distance and how they are measured.

In Japan, the target for the living environment is the Ministry of the Environment's “Environmental Quality Standards for Noise”. Daytime is 6:00 to 22:00 and night is 22:00 to 6:00; values are equivalent continuous sound levels (LAeq), and the standard is met at or below them. Prefectures and cities designate which category each area falls into.

Environmental standards are targets for government policy, not limits used to regulate individual factories or building sites directly. Noise from factories, businesses and construction is regulated by Japan's Noise Regulation Act and local ordinances; for example, noise from specified construction work must not exceed 85 dB at the site boundary. The exact values and hours differ by municipality, so check your local authority's guidance. Other countries have their own standards, so look up the rules where you live.

Measuring tips: A-weighting, where to measure, and smartphone sound meter apps

• Noise is normally measured with A-weighting, which counts low and high frequencies as quieter to match how the human ear responds. That is what dB(A) or LA means, and environmental standards use A-weighted values too.
• Sound changes over time, so don't rely on a single reading: take several, or use the equivalent continuous level (LAeq) over a set period. When you combine several readings taken by hand, use the energy average, not the arithmetic mean.
• Always measure the background noise (with the source off) at the same spot and time of day as well. Correct if the difference is under 10 dB, and measure again if it is under 3 dB.
• Right next to a wall or fence, reflections can push readings up. Hold the meter about 1.2–1.5 m above the ground and away from your body for steadier readings.
• Smartphone sound meter apps can differ by several dB between models because of the built-in microphone and its calibration. They are handy for spotting trends, but use a calibrated sound level meter for values you will use in a complaint or official report.

Note that values such as “−20 dB” on a recording program or the level meter of a mic test are input levels (dBFS) where the digital maximum is 0 dB, which uses a different reference from noise dB based on 20 µPa. Even though both say “dB”, a meter showing negative values isn't directly telling you how loud the noise is. Both are logarithmic, though, so the ideas behind adding and subtracting are the same.

How to calculate with the Decibel Calculator

1. 1

   Add and average

   In “Add & average”, enter your measured dB values one per line (or separated by commas) to get the combined level, the energy average and how it differs from the arithmetic mean. For several identical sources, enter one level and the number of sources.

2. 2

   Remove background noise

   In “Subtract (background noise)”, enter the levels with the source on and off to get the level of the source alone by formula and the JIS Z 8731 correction. If the difference is under 3 dB, it tells you to measure again.

3. 3

   Check distance attenuation

   In “Distance attenuation”, choose a point or line source and enter the measured level and distance plus the distance or target level you want, to get the level at that distance, the distance to reach the target and a chart by distance.

4. 4

   Look up conversions and charts

   In “Conversions & charts”, convert between sound pressure in Pa and dB, see how many times stronger a dB difference is in energy, pressure and perceived loudness, and check the addition chart, typical noise levels and environmental standards.

All calculations run inside your browser, and the values you enter are not sent anywhere. Every figure in this guide was produced with the same calculations as the tool, so you can enter the examples to check them.

FAQ

What is 60 dB plus 60 dB?

63 dB (not 120 dB). Because dB is logarithmic, converting back to 10^(L/10) and adding doubles the energy, which raises the level by only 10 × log10(2) ≈ 3 dB. Four sources of the same level add 6 dB, and ten add 10 dB.

What happens when I add sounds of different levels?

The difference between the two decides how much to add to the louder one: +3.0 dB for a 0 dB difference, +1.2 dB for 5 dB and +0.4 dB for 10 dB. Combining 60, 65 and 70 dB gives about 71.5 dB, only 1.5 dB more than the loudest, 70 dB.

How do I average dB values?

Average noise with the energy average (power average), not the arithmetic mean you get by adding and dividing: 10 × log10((10^(L1/10) + 10^(L2/10) + …) ÷ n). For 60, 70 and 80 dB, the arithmetic mean is 70 dB but the energy average is about 75.7 dB.

How do I correct for background noise?

If the level is 65 dB with the source on and 60 dB with it off (background noise), the source alone is 10 × log10(10^6.5 − 10^6) ≈ 63.3 dB. With the JIS Z 8731 correction, the difference of 5 dB means −2 dB, giving 63 dB. No correction is made for a difference of 10 dB or more, and you should measure again if it is under 3 dB.

How many dB does the level drop when the distance doubles?

About 6 dB for a point source such as an outdoor unit or a machine, and about 3 dB for a line source such as a busy road. At ten times the distance, a point source drops 20 dB and a line source 10 dB. A point source of 80 dB at 1 m is 60 dB at 10 m and 40 dB at 100 m (with no obstacles).

How far away do I need to be for the noise to fall to 45 dB?

For a point source, use r2 = r1 × 10^((L1 − 45) ÷ 20). For a sound of 80 dB at 1 m that is about 56 m. For a line source, replace ÷ 20 with ÷ 10: the same 80 dB gives about 3,162 m. In practice walls and buildings usually lower the level a little more, so treat this as an estimate.

How big is a 10 dB difference?

Ten times the sound energy (intensity), about 3.16 times the sound pressure, and roughly twice as loud to the human ear. A 20 dB difference is 100 times the energy, 10 times the pressure and about four times as loud. A 3 dB difference doubles the energy but sounds only about 1.23 times as loud.

How many dB is a sound pressure of 1 Pa?

About 94 dB. Sound pressure level is 20 × log10(p ÷ 20 µPa): the reference 20 µPa (0.00002 Pa) is 0 dB, 0.02 Pa is 60 dB and 2 Pa is 100 dB. Each tenfold increase in sound pressure adds 20 dB.