Decibels Explained

Why do two 80 dB speakers make only 83 dB, not 160 dB? The answer is that a decibel is not a simple amount of sound. It is a ratio, written on a logarithmic scale.

Once you see the ratio behind the number, decibel math stops feeling strange. This guide covers the formula, adding sources, distance loss, loudness, and the hearing limit that NIOSH recommends.

What a Decibel Really Measures

A decibel measures how many times bigger one power or intensity is than another. It is always a comparison. A sound level in dB compares a sound to a fixed reference, the standard threshold of hearing.

The formula for power and intensity is dB = 10 x log10(I / I0). Here I is the sound you measure and I0 is the reference. The log10 part simply counts the powers of ten in the ratio.

HyperPhysics gives a clean example. A sound 10,000 times the threshold intensity has a ratio of 10 to the 4th power. The power of ten is 4, so the sound is 40 dB.

Each 10 dB step multiplies intensity by 10. So 20 dB means 100 times the reference, and 30 dB means 1,000 times. The same source notes that the threshold of pain sits about ten trillion times above the threshold of hearing. That huge span shrinks to about 130 dB.

One note on pressure: sound pressure uses 20 x log10 instead, because intensity grows with pressure squared. Doubling the pressure adds about 6.02 dB. The same log idea measures pitch, which our guide to cents and musical intervals explains for tuning.

How Do Two Sound Sources Add Up?

Two equal, unrelated sources add about 3 dB, not double the number. Two 80 dB machines together make 83.01 dB. The power doubles, and 10 x log10(2) is 3.01 dB.

The logic is short. You cannot add decibels directly, because they are logs. You must turn each level back into a power, add the powers, and then turn the sum back into decibels.

1. Convert each level. Divide each dB value by 10 and raise 10 to that power. For 80 dB, that gives 10 to the 8th.
2. Add the powers. Two 80 dB sources give 2 x 10 to the 8th. Add as many sources as you have.
3. Take the log. Find log10 of the sum. For 2 x 10 to the 8th, the result is about 8.301.
4. Multiply by 10. Scale the log back to decibels. Here 10 x 8.301 gives 83.01 dB.
5. Sanity check. The total must sit at or above the loudest single source, and never near the plain sum.

Unequal sources barely move the total. A 90 dB saw beside an 80 dB fan makes only 90.41 dB. The quieter source adds less than half a decibel, because it carries a tenth of the power.

Why Does Sound Drop 6 dB When Distance Doubles?

Sound from a point source spreads over a growing sphere, so intensity falls with the square of distance. Doubling the distance cuts intensity to one quarter, which is about 6.02 dB.

HyperPhysics puts the rule plainly: doubling the distance drops the level by about 6 dB. Ten times the distance drops it by 20 dB. The math is 20 x log10 of the distance ratio.

Picture a speaker reading 94 dB at 1 meter. At 2 meters it reads about 88 dB, and at 4 meters about 82 dB. At 8 meters it reads about 76 dB, and at 10 meters it reads 74 dB.

Real rooms bend this rule. The same source calls the inverse square law an idealization, since walls and ceilings reflect sound back. Indoors, levels usually fall more slowly than 6 dB per doubling. Treat the rule as a first estimate for fairly open spaces.

Loudness, Noticeable Changes and Safe Listening Time

Your ear does not hear decibels the way a meter reads them. HyperPhysics notes that intensity must rise about ten times to sound twice as loud. So 70 dB sounds roughly twice as loud as 60 dB, not slightly louder.

Small changes are hard to hear. The same source puts the just noticeable difference at about 1 dB for the normal ear. For loud sounds, it can drop to between one third and one half of a decibel. A 3 dB boost doubles the power, yet it sounds like a modest step.

Pitch works on its own separate scale. Loudness depends on intensity, while pitch depends on frequency, as our guide to note frequencies and A440 shows.

Hearing safety uses the same 3 dB logic. The CDC’s NIOSH page sets a recommended exposure limit of 85 dBA averaged over an 8-hour workday. For each 3 dBA increase, NIOSH recommends cutting the exposure time in half. The “A” marks an A-weighted reading, a standard filter setting on sound level meters.

These are workplace recommendations from NIOSH, not a medical test. OSHA sets its own legal limits for workplaces, so check that agency directly for compliance work.

Decibel Arithmetic Traps and Better Habits

Most decibel errors come from treating a log value like a normal count. The table pairs each trap with a habit that keeps the math honest.

One habit covers most cases. Before you trust a total, ask whether it is at least as large as the loudest source. Also check that it stays well below the plain sum of the numbers.

Ten equal 60 dB sources show why. Their powers add to ten times one source, so the total is exactly 70.0 dB. Four equal sources give 6.02 dB more than one, since the power is four times larger.

Try it with your own numbers: the decibel level calculator combines any two levels in one step.

Decibels: Frequently Asked Questions

Sources and Further Reading

This article is general acoustics education, not medical or legal advice. Exposure figures follow NIOSH recommendations as published on the CDC site. Reviewed for accuracy by Prof. Dr. Khalil Mudassar, PhD. Last updated September 27, 2026.