Short answer: Yes, decibels are logarithmic. A decibel value is 10 × log10 of an energy ratio, so equal steps in dB mean equal multiplications of energy: every +10 dB is 10 times the sound energy and sounds about twice as loud, and every +3 dB doubles the energy. Seen the other way round, sound energy grows exponentially as the decibels rise in a straight line.
That is why 100 dB isn’t “twice 50 dB”: it has 100,000 times the sound energy and sounds about 32 times as loud. Below you’ll find the reasons the scale is built this way, the formula in plain terms, a quick conversion table, and what it means for adding noise sources and for safe listening times.
Decibels, Energy and Loudness in One Table
| Level change | Sound energy (intensity) | Sound pressure | How loud it sounds |
|---|---|---|---|
| +1 dB | × 1.26 | × 1.12 | Barely noticeable |
| +3 dB | × 2 | × 1.41 | Just noticeable |
| +6 dB | × 4 | × 2 | Clearly louder |
| +10 dB | × 10 | × 3.16 | About twice as loud |
| +20 dB | × 100 | × 10 | About 4 times as loud |
| +30 dB | × 1,000 | × 31.6 | About 8 times as loud |
| +50 dB | × 100,000 | × 316 | About 32 times as loud |
| +120 dB | × 1,000,000,000,000 | × 1,000,000 | From the threshold of hearing to the threshold of pain |
Why Is the Decibel Scale Logarithmic?
- The range is enormous. The loudest sound you can bear carries about a trillion (10¹²) times the energy of the quietest sound you can hear. On a linear scale, a whisper and a jet engine would need numbers from 1 to 1,000,000,000,000. The logarithm squeezes this into 0 to about 130.
- Your ears work logarithmically. Perceived loudness follows ratios, not differences (the Weber–Fechner law and Stevens’ power law). Adding the same amount of energy to a quiet room is obvious, while adding it to a rock concert is unnoticeable. A 10 dB step sounds about twice as loud whether it is 30 → 40 dB or 90 → 100 dB. Pitch works the same way: each octave doubles the frequency (see dB vs Hz).
- Multiplication becomes addition. Engineers can add the gains and losses of amplifiers, cables and walls in dB instead of multiplying ratios. That is why the bel (and its tenth, the decibel) came out of Bell Telephone Laboratories in the 1920s, named after Alexander Graham Bell.
The same idea appears wherever values span many orders of magnitude: the Richter and moment-magnitude scales for earthquakes, pH for acidity, and star magnitudes in astronomy are all logarithmic.
The Formula in Plain Terms
- For energy or power (intensity): L = 10 × log10(I ÷ I₀), where I₀ = 10⁻¹² W/m².
- For sound pressure: L = 20 × log10(p ÷ p₀), where p₀ = 20 µPa. The factor is 20 because energy grows with the square of pressure.
- Going back: I = I₀ × 10^(L ÷ 10) and p = p₀ × 10^(L ÷ 20). This is the exponential part: the decibel value sits in the exponent.
Try it with the SPL converter: 60 dB is 0.02 Pa, 80 dB is 0.2 Pa and 100 dB is 2 Pa, so every 20 dB multiplies the pressure by 10. For the physics behind the reference values, see sound pressure level and what a decibel is.
Are Decibels Exponential or Logarithmic?
Both descriptions point to the same relationship from opposite ends. The decibel is a logarithm of the energy ratio, so the dB scale itself is logarithmic. The energy is an exponential function of the decibel value, so when decibels increase steadily, the energy increases exponentially, as the chart above shows. When people ask “do decibels increase exponentially?”, the precise answer is: the decibel numbers increase in equal steps, and the sound energy they represent increases exponentially.
Adding Decibels: Why 60 dB + 60 dB = 63 dB
Because decibels are logarithmic, you can’t add them like ordinary numbers. Two identical 60 dB sources produce twice the energy, which is +3 dB, so 63 dB. Ten of them produce 70 dB. When the levels differ, add the amount below to the louder one:
| Difference between the two levels (dB) | Add to the louder level |
|---|---|
| 0 (equal levels) | +3.0 |
| 1 | +2.5 |
| 2 | +2.1 |
| 3 | +1.8 |
| 4 | +1.5 |
| 5 | +1.2 |
| 6 | +1.0 |
| 8 | +0.6 |
| 10 | +0.4 |
| More than 10 | Less than +0.4: the quieter source hardly counts |
Example: 70 dB + 64 dB → the difference is 6 dB → 70 + 1.0 = 71 dB. The decibel calculator adds, subtracts and averages any number of levels, and the volume level comparator shows how much louder one level is than another.
The Log Scale and Safe Noise Limits (NIOSH 3 dB Rule)
Hearing-safety rules follow the same maths. NIOSH recommends a limit of 85 dB(A) (A-weighted) for 8 hours with a 3 dB exchange rate: because +3 dB doubles the sound energy, the safe time halves with every 3 dB. OSHA’s US legal limit uses a 5 dB exchange rate instead, which allows more time at high levels.
| Level dB(A) | NIOSH safe time per day | Energy compared with 85 dB |
|---|---|---|
| 85 | 8 hours | × 1 |
| 88 | 4 hours | × 2 |
| 91 | 2 hours | × 4 |
| 94 | 1 hour | × 8 |
| 97 | 30 minutes | × 16 |
| 100 | 15 minutes | × 32 |
| 103 | 7.5 minutes | × 64 |
So a level that looks only “a bit higher”, such as 100 dB instead of 85 dB, allows 32 times less listening. Work out your own day with the noise exposure calculator, or read the noise exposure time limits guide.
What 0 dB and Negative Decibels Mean
0 dB doesn’t mean silence. It means the sound equals the reference (20 µPa), roughly the threshold of hearing. Negative decibels are quieter than the reference: many young people can hear a few decibels below 0 dB SPL at 3,000–4,000 Hz, where the ear is most sensitive. In digital audio, levels are negative because the reference is the maximum (0 dBFS).
Why It Matters in Everyday Life
- Turning a TV down from 70 dB to 60 dB removes 90% of the sound energy but only makes it sound half as loud.
- Soundproofing that cuts 10 dB is a big improvement; one that cuts 3 dB halves the energy but is barely noticeable.
- Moving twice as far from a small source lowers the level by about 6 dB, a quarter of the energy.
- A 70 dB vacuum cleaner is not “a bit louder” than 60 dB conversation: it has 10 times the energy. The decibel chart puts everyday sounds on the scale.
Frequently Asked Questions
Is the decibel scale linear?
No. It is logarithmic: each step of 10 dB multiplies the energy by 10.
Is 20 dB twice as loud as 10 dB?
It sounds about twice as loud (a 10 dB step) and has 10 times the energy. Doubling the number of decibels doesn’t double anything.
How much louder is 100 dB than 50 dB?
100,000 times the sound energy, 316 times the sound pressure, and about 32 times as loud to the ear.
Why do some formulas use 10 log and others 20 log?
Use 10 × log10 for power, energy and intensity, and 20 × log10 for pressure, voltage and other amplitudes, because power is proportional to the amplitude squared. Both give the same dB for the same sound. The decibel units guide covers dBm, dBV and the other variants.
Can I measure this myself?
Yes. Measure a sound with the free meter on our homepage, move twice as far away and watch the reading fall by about 6 dB. Our guide on how to measure decibels shows how to get a steady reading.